Your Time and Money

Wouldn’t you rather be doing something else with your time right now, instead of reading an economics textbook? You could be surfing on the Internet, reading blogs, or updating your Facebook profile. You could be reading a novel or watching television. You could be out with friends. But you aren’t. You have made a choice—a decision—to spend time reading this chapter.

Your choice is an economic one. Economics studies how we cope with competing demands for our time, money, and other resources. You have only 24 hours each day, so your time is limited. Each day you have to divide up this time among the things you like or need to do: sleeping, eating, working, studying, reading, playing video games, hanging out in your local coffee shop, and so on. Every time you decide to do one thing instead of another, you have made an economic decision. As you study economics, you will learn about how you and other people make such choices, and you will also learn how to do a better job when making these decisions.

Money is also a limited resource. You undoubtedly have many things you would like to buy if money were no object. Instead you must choose among all the different things you like because your money—or, more precisely, your income—is a limited resource. Every time you buy something, be it a T-shirt, a breakfast bagel, or a new computer, you are choosing to forgo something else you could have bought instead. Again, these are economic decisions. Economics is about how you make choices. Whenever there is a limited resource—be it your time, the amount of oil reserves in the world, or tickets to the Super Bowl—and decisions to be made about how to use that resource, then economics is there to help. Indeed, the fundamental definition of economics is that it is the study of how we, as individuals and as a society, allocate our limited resources among possible alternative uses.

eBay and craigslist

Suppose you want to buy an MP3 player. There are many ways you can do this. You can go to a local store. You can look for stores on the Internet. You can also visit sites such as eBay (http://www.ebay.com) or craigslist (http://www.craigslist.org). eBay is an online auction site, meaning that you can look for an MP3 player and then bid against other potential buyers. The site craigslist is like an online version of the classified advertisements in a newspaper, so you can look to see if someone in your town or city is selling the player you want to buy. You can also use these sites if you want to sell something. Maybe you have some old baseball cards you want to sell. Perhaps you have a particular skill (for example, web design), and you want to sell your services. Then you can use sites such as eBay or craigslist as a seller instead of as a buyer.

We have said that economics is about deciding how to use your limited resources. It is also about how we interact with one another, and, more precisely, how we trade with one another. Adam Smith, the founder of modern economics, observed that humans are the only animal that makes bargains: “Nobody ever saw a dog make a fair and deliberate exchange of one bone for another with another dog.”Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations (New York: Modern Library, 1994 [1776]), 14. Barter or trade—the exchange of goods and services and money—is central to the world we live in today.

Economists often talk about trade taking place in markets. Some exchanges do literally take place in markets—such as a farmers’ market where local growers bring produce to sell. Economists use the term more generally, though: a market is any institution that allows us to exchange one thing for another. Sites such as eBay and craigslist create markets in which we can transact. Normally, we exchange goods or services for money. Sometimes we exchange one good or service for another. Sometimes we exchange one type of money for another.

Most of the time, nobody forces you to buy anything, so when you give up some money in return for an MP3 player, you are presumably happier after the transaction than before. (There are some exceptions, of course. Can you think of any cases where you are forced to engage in an economic transaction?) Most of the time, nobody forces you to sell anything, so when you give up your time in return for some money, you are presumably happier after the transaction than before. Leaving aside the occasional mistake or the occasional regret, nearly every voluntary transaction makes both participants better off. Markets matter because they are a means for people to become happier.

Breathing the Air

Welcome to Mexico City! It is a wonderful place in many respects. But not in every way: from the picture you can see that Mexico City has some of the most polluted skies in the world.“Researchers to Scrutinize Megacity Pollution during Mexico City Field Campaign,” University Corporation for Atmospheric Research, last modified March 2, 2006, accessed January 22, 2011, http://www.ucar.edu/news/releases/2006/mirage.shtml.

Figure 2.1 The Skies of Mexico City

Source: This photo comes from the Center on Atmospheric Research, http://www.ucar.edu.

Mexico City was not always so polluted. Sadly, economic growth and population growth, together with the peculiarities of geography and climate, have combined to make its air quality among the worst you will encounter anywhere. Other cities around the world, from Beijing to Los Angeles, also experience significant air pollution, reducing the quality of life and bringing with it health risks and other costs.

It is hard to understand economists talking about the beauty and power of markets when you cannot breathe the air. So what is going wrong in Mexico City? Is it not full of people carrying out trades that make them better off? The problem is that transactions sometimes affect other people besides the buyer and the seller. Mexico City is full of gas stations. The owners of the gas stations are happy to sell gasoline because every transaction makes them better off. The owners of cars are happy to buy gasoline because every transaction makes them better off. But a side effect of all these transactions is that the air becomes more and more polluted.

Economics studies these kinds of problems as well. Economists seek to understand where and when markets work and where and when they don’t work. In those situations where markets let us down, economists search for ways in which economic policies can help.

Changing the Rules

We have explained that microeconomics studies choices and the benefits and problems that arise from trade. Perhaps most fundamentally, microeconomics studies how people respond to incentives. To illustrate the importance of incentives, here is an example of what can happen when they go wrong.

In February 1994, an extraordinary scene took place during a soccer match in the Caribbean. Grenada was playing Barbados, and with five minutes remaining in the match, Barbados was leading by two goals to one. As the seconds ticked away, it seemed clear that Barbados was going to win the match. Then, three minutes from the end of the game, the Barbados team did a remarkable thing. It intentionally scored an own goal, tying the game at two goals apiece.

After Grenada kicked off again, pandemonium ensued. The Grenada team tried not only to score against Barbados but also to score an own goal. Barbados desperately defended both its own goal and its opponents’ goal. The spectacle on the field had very little to do with soccer as it is usually played.

To explain this remarkable sight, we must describe the tournament in which the two teams were playing. There were two groups of teams, with the winner of each group progressing to the final. The match between Barbados and Grenada was the last group game and would determine which two teams would be in the final. The results of the previous matches were such that Barbados needed to win by two goals to go to the final. If Barbados won by only one goal, then Grenada would qualify instead. But the tournament organizers had introduced an unusual rule. The organizers decided that if a game were tied, the game would go to “golden goal” overtime, meaning that the first team to score would win the game, and they had also decided that the winning team would then be awarded a two-goal victory.

As the game was drawing to a close, Barbados realized it was unlikely to get the two-goal win that it needed. The team reasoned that a tie was a better result than a one-goal victory because it gave them roughly a fifty-fifty chance of winning in extra time. So Barbados scored the deliberate own goal. Grenada, once it realized what had happened, would have been happy either winning or losing by one, so it tried to score in either goal. Barbados’ strategy paid off. The game finished in a tie; Barbados scored in overtime and went on win the final.

The organizers should have consulted an economist before instituting the rules of the tournament. Economics has many lessons to teach, and among the most important is this: people respond to incentives. The change in the rules changed the incentives that the two teams faced. Because the tournament organizers had not realized that their rules could lead to a situation in which a team preferred a tie to a win, they failed to foresee the bizarre scene on the field.“Football Follies,” Snopes.com, last modified July 6, 2008, accessed January 22, 2011, http://www.snopes.com/sports/soccer/barbados.asp.

Individual Choice

One element of the microeconomic approach is individual choice. Throughout this book, we explore how individuals make decisions. Economists typically suppose that individuals make choices to pursue their (broadly defined) self-interest given the incentives that they face.

We look at individuals in their roles both as members of households and as members of firms. Individuals in households buy goods and services from other households and—for the most part—firms. They also sell their labor time, mostly to firms. Managers of firms, meanwhile, make decisions in the effort to make their firms profitable. By the end of the book, we will have several frameworks for understanding the behavior of both households and firms.

Individuals look at the prices of different goods and services in the economy when deciding what to buy. They act in their own self-interest when they purchase goods and services: it would be foolish for them to buy things that they don’t want. As prices change, individuals respond by changing their decisions about which products to buy. If your local sandwich store has a special on a breakfast bagel today, you are more likely to buy that sandwich. If you are contemplating buying an Android tablet computer but think it is about to be reduced in price, you will wait until the price comes down.

Just as consumers look at the prices they face, so do the managers of firms. Managers look at the wages they must pay, the costs of the raw materials they must purchase, and so on. They also look at the willingness of consumers to buy the products that they are selling. Based on all this information, they decide how much to produce and what to buy. Your breakfast bagel may be on special because the owner of your local sandwich shop got a good deal on bagels from the supplier. So the owner thinks that breakfast bagels can be particularly profitable, and to sell a lot of them, she sets a lower price than normal.

The buying and selling of a bagel may seem trivial, but similar factors apply to much bigger decisions. Potential students think about the costs and benefits of attending college relative to getting a full-time job. For some people, the best thing to do is to work full time. For others, it is better to go to school full time. Yet others choose to go to school part time and work part time as well. Presumably your own decision—whichever of these it may be—is one you made in your own best interests given your own specific situation.

From this discussion, you may think that economics is all about money, but economists recognize that much more than money matters. We care about how we spend our time. We care about the quality of the air we breathe. We care about our friends and family. We care about what others think of us. We care about our own self-image: what sort of a person am I? Such factors are harder to measure and quantify, but they all play a role in the decisions we make.

Markets

A second element of microeconomics has to do with how individual choices are interconnected. Economics is partly about how we make decisions as individuals and partly about how we interact with one another. Most importantly—but not exclusively—economics looks at how people interact by purchasing and selling goods and services.

In a typical transaction, one person (the buyer) hands over money to another (the seller). In return, the seller delivers something (a good or a service) to the buyer. For example, if you buy a chocolate bar for a dollar, then a dollar bill goes from your hands to those of the seller, and a chocolate bar goes from the seller to you. At the level of an individual transaction, this sounds simple enough. But the devil is in the details. In any given (potential) transaction, we can ask the following questions:

• How many? Will you buy 1, 2, or 10 chocolate bars? Or will you buy 0—that is, will the transaction take place at all?
• How much? How much money does the buyer give to the seller? In other words, what is the price?

You will see in different chapters of this book that the answers to these questions depend on exactly how buyers and sellers interact. We get a different answer depending on whether there are many sellers or only a few. We get a different answer if the good is sold at a retail store or at an auction. We get a different answer if buyers and sellers can or cannot negotiate. The exact way in which people exchange goods and services matters a great deal for the how many? and how much? questions and thus for the gains from trade in the economy.

The Role of Government

We have pointed out that individuals acting in their own self-interest benefit from voluntary trade. If you are not forced to buy or sell, then there is a presumption that every transaction makes the participants happier. What is more, markets are often a very effective institution for allowing people to meet and trade with one another. In fact, there is a remarkable result in economics that—under some circumstances—individuals acting in their own self-interest and trading in markets can manage to obtain all the possible benefits that can come from trading. Every transaction carried out is for the good, and every good transaction is carried out. From this comes a powerful recommendation: do whatever is possible to encourage trade. The phrase under some circumstances is not a minor footnote. In the real world, transactions often affect people other than the buyer and the seller, as we saw in our example of gas stations in Mexico City. In other cases, there can be problems with the way that markets operate. If there is only a small number of firms in a market, then managers may be able to set high prices, even if it means that people miss out on some of the benefits of trade. Later in this book, we study exactly how managers make these decisions. The microeconomic arguments for government intervention in the economy stem from these kinds of problems with markets. In many chapters, we discuss how governments intervene in an attempt to improve the outcome that markets give us. Yet it is often unclear whether and how governments should be involved. Pollution in Mexico City illustrates how complex these problems can be. First, who is responsible for the pollution? Some of it comes from people and firms outside the city and perhaps even outside the country. If pollution in Mexico City is in part caused by factories in Texas, who should deal with the problem: the Mexico City government, the Mexican government, the US government, or the Texas state legislature? Second, how much pollution should we tolerate? We could shut down all factories and ban all cars, but few people would think this is a sensible policy. Third, what measures can we use to combat air pollution? Should we simply place limits on production by firms and the amount of driving? Should we use some kind of tax? Is there a way in which we can take advantage of our belief that people, including the managers of firms, respond to incentives?

There are two traps that we must avoid. The first is to believe that markets are the solution to everything. There is no imaginable market in which the residents of Mexico City can trade with the buyers and sellers of gasoline to purchase the right amount of clean air. The second trap is to believe that the government can fix every market failure. Governments are collections of individuals who respond to their own incentives. They can sometimes make things better, but they can sometimes make things worse as well.

There is room for lots of disagreement in the middle. Some economists think that problems with markets are pervasive and that government can do a great deal to fix these problems. Others think that such problems are rare and that governmental intervention often does more harm than good. These disagreements result partly from different interpretations of the evidence and partly from differences in politics. Economists are as prone as everyone else to view the world through their own ideological lens. As we proceed, we do our best to present the arguments on controversial issues and help you understand why even economists sometimes come to differing conclusions about economic policy.

Incentives

Perhaps our story of the Barbados-Grenada soccer game did not seem related to economics. Economists believe, though, that the decisions we make reflect the incentives we face. Behavior that seems strange—such as deliberately scoring an own goal in a soccer game—can make perfect sense once you understand the underlying incentives. In the economic world, it is often governments that make the rules of the game; like the organizers of soccer tournaments, governments need to be careful about how the rules they set can change people’s behavior.

Here is an example. In some European countries, laws are in place that give a lot of protection to workers and keep them from being unfairly fired by their employers. The intentions of these laws are good; some of their consequences are not so beneficial. The laws also make firms more reluctant to hire workers because they are worried about being stuck with an unsuitable employee. Thus these laws probably contribute to higher unemployment.

Incentives affect all transactions. When you buy a breakfast bagel on sale, both you and the owner of the sandwich shop are responding to the incentives that you face. The owner responds to the lower price of bagels. You respond to the lower price of the sandwich. Economists think that we can understand a great deal about people’s behavior if we have a good understanding of the incentives that they face.

Notice that not everyone makes the same choices. There are two main reasons for this:

• People have different desires or tastes. Some people like bagels; others hate them. Some people like being students; others would prefer to work rather than study.
• People have different incentives. Some people face very different job prospects and thus make different decisions about schooling. If you have this great idea for a new web product (for example, the next Google or Facebook), then you might be wise to spend your time on this project instead of studying.

The Big Questions of Economics

To conclude our introduction to microeconomics, let us look at the big picture of what happens in an economy. An economy possesses some resources. These include the time and abilities of the people who live in the economy, as well as natural resources such as land, mineral deposits, and so on. An economy also possesses some technologies. A technology is a means of changing, or transforming, one set of things into other things. For example, we have a technology for making tea. This technology takes cold water, energy, and dried leaves and transforms them into a hot beverage. Finally, an economy, of course, contains its people, and these people like to consume things. Economics studies all aspects of this process. It considers the following:

• What goods and services are produced in an economy?
• How are these goods and services produced?
• Who gets to consume these goods and services?

These questions concern the allocation of resources.

The what in the first question reflects the choice among the multitude of goods and services an economy could produce. Think for a moment about the clothes you are wearing right now, the food you have eaten today, and the activities you undertake during a typical day. Someone made those clothes; someone prepared that food. Somehow, society must decide how much of each type of good and service to produce.

The how in the second question reflects competing ways to produce goods and services. Take a basic commodity such as rice. A large amount of rice is produced in the United States on large-scale, mechanized farms. A large amount of rice is also produced in Vietnam, but the production methods are very different. In Vietnam, people do much more work manually rather than by machine. A big part of the how question is deciding what mix of resources and what technologies should be used to produce goods and services. The answer in a rich country such as the United States is frequently different from the answer in a poor country such as Vietnam. Indeed, the answer may be different in different states in the United States or in the same place at different times.

The who in the third question concerns the distribution of goods and services in the economy. Suppose you were responsible for the distribution of all goods and services to your family. If there are 4 people in your family and each consumed 50 products in a typical day, you would have to make about 200 allocation decisions each day. It would be a very hard task. Yet somehow the economies of the world allocate billions of products to billions of people.

These three questions are answered in the world partly through individual decisions. The way in which you allocate your time each day is part of the allocation of resources in the economy. If each of us lived alone, engaging in subsistence farming and not interacting with others, then we would each determine our own allocation of resources. Because we interact with others, however, these questions are also answered in part by the way in which society is organized. Most of us produce only a few goods but consume many. We specialize in production and generalize in consumption. To do so, we must exchange what we produce with others. Most of these exchanges take place as a result of individual decisions in different kinds of markets. It is the operation of these countless markets that determines the allocation of goods and services in the economy. Remarkably, these markets somehow coordinate the decisions of the billions of people in the world economy.

Some of these exchanges are controlled by the government. In some economies, the government plays a very active role; in others, it intervenes less. When a government makes decisions about the allocation of resources, this is another mechanism in the production of goods and the distribution to individuals.

The State of the Economy

The top two panels in Figure 3.1 provide information on some key indicators of the state of the economy. The announcement from the Bureau of Economic Analysis (BEA) concerns one of the most closely watched indicators of the macroeconomy: real gross domestic product (real GDP). This is a measure of the goods and services produced by an economy in a year. We discuss real GDP in every macroeconomic application in this book.

Figure 3.3 Real GDP per Person in the United States, 1960–2009

Source: Alan Heston, Robert Summers, and Bettina Aten, Penn World Table Version 7.0, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, May 2011.

Figure 3.3 "Real GDP per Person in the United States, 1960–2009" shows real GDP per person (often called real GDP per capita) from 1960 to 2009. Pictures like this one show up all the time in newspapers, in magazines, on television, or on the Internet. One of the things you will learn in your study of macroeconomics is how to interpret such economic data. We devote an entire chapter to understanding exactly how real GDP is measured. For now, we draw your attention to some details to help you appreciate what the graph means.

The horizontal axis indicates the year. Real GDP per person is shown on the vertical axis. To read this graph, you would look at a particular year on the horizontal axis, such as 2000, and then use the curve to see that the real GDP per person in 1965 was about $39,000.

If you look at this picture, the single most notable thing is that real GDP per person has been increasing. It was about 2.6 times larger in 2009 than in 1960. This tells us that, on average, the typical individual in the United States was 2.6 times richer in 2000 compared to 1960. The increase in GDP is not caused by the fact that there are more people in the economy because the figure shows GDP per person. The increase in GDP is not because prices are going up: the word real in this discussion means that it has been corrected for inflation.In the bottom right of the picture, you can see the phrase Data in 1996 dollars. This means that the numbers in the table are based on how much a dollar would have bought in 1996. Do not worry if you do not understand exactly what this phrase means right now. Chapter 18 "The State of the Economy" will provide much more detail.

Another thing you can see from the picture is that the growth of the economy has not been smooth. Sometimes the economy grows fast; sometimes it grows more slowly. Sometimes there are even periods in which the economy shrinks rather than grows. From this figure, you can see that real GDP per person decreased in the mid-1970s, the mid-1980s, and most notably in 2008 and 2009. During these times, people were becoming poorer on average, not richer.

We keep using the phrase on average. This reminds us that, even though the economy as a whole has been getting richer, the picture doesn’t tell us anything about how those gains have been shared across the economy. In fact, some people became a lot richer over this period, while many others saw only small gains, and some became poorer.

We see this uneven distribution very clearly when the economy shrinks. When that happens, one of the things we also observe is that more people in the economy are unemployed—that is, they are looking for a job but unable to find one. The burden of an economic downturn is borne disproportionately by those who lose their jobs.

Although this figure displays the history of the US economy over these 50 years, similar figures can be constructed for other countries around the world. They do not all look identical, but the pattern of uneven growth that we observe for the United States is one that we also see for most other countries. However, it is not true everywhere. We will also see examples of countries that have become poorer rather than richer in recent decades.

Real GDP is the most frequently watched indicator of economic performance. A second key indicator is the one in the top right screen of Figure 3.1: the inflation rate. The Bureau of Labor Statistics (BLS) collects information on prices on an ongoing basis; each month it releases information on how fast prices are changing. The rate at which prices are changing is the inflation rate. Other countries similarly have government agencies entrusted with gathering information about the inflation rate and other economic indicators.

It may seem that the job of the BLS is pretty easy: get information on prices and report it. Their task is, in fact, rather complex. In part, it is difficult because there are so many goods and services in the economy. So when we say that prices are increasing, we must decide which goods and services we are talking about. In addition, new goods appear, and obsolete goods disappear; the BLS must take this into account. And the quality of goods changes as well. If the price of a computer increases, is this an example of inflation or does it reflect an increase in the quality of the computer?

What are the implications of an inflation announcement? All else being the same, higher prices mean that we are unable to afford goods and services we were able to buy when prices were lower. But “all else” is not the same. Generally when prices increase, wages also increase. This means that the overall effects of inflation on our ability to buy goods and services are not self-evident.

Another implication of inflation is the policy response it elicits. The monetary authorities in the United States and many other countries are focused on ensuring that inflation does not get out of control. A report of inflation might therefore lead to a response by a monetary authority. Inflation affects us directly through the prices we pay and the wages we receive and indirectly through the policy response it induces.

Though not included in our screens, another significant variable also indicates the state of the macroeconomy: the rate of unemployment. The BLS (http://www.bls.gov/news.release/empsit.toc.htm) reports the unemployment rateThe number of unemployed individuals divided by the sum of the number employed and the number unemployed. on a monthly basis. It measures the fraction of people in the labor force who do not have a job. When real GDP is relatively high, then the unemployment rate tends to be lower than average, but when real GDP decreases, more people find themselves out of a job.

The Making of Fiscal and Monetary Policy

The top screens in Figure 3.1 provide information that flows to the policymakers in an economy. These policymakers carefully watch the state of the economy and then, if appropriate, take actions. The bottom screens in Figure 3.1 show policy in action.

Fiscal Policy

For individuals and firms paying taxes in the United States, April 15 is an important day because tax forms are due for the previous calendar year. Each year US citizens fill out their tax forms and either make tax payments or receive reimbursements from the government.

The tax day differs across countries, but the experience is much the same everywhere: individuals and firms must pay taxes to the government. This is one of the key ways in which citizens interact with their governments.

A more complete version of the 1040EZ form for 2010 is shown in Figure 3.4 "Form 1040EZ".

Figure 3.4 Form 1040EZ

From the perspective of an individual filling out this form, the task is to get the data correct and determine exactly what figures go where on the form. This is no small challenge. From the perspective of economists working for the government, the tax form is an instrument of fiscal policy. Embedded in the tax form are various tax rates that must be paid on the different types of income you earn.

Where do these tax revenues go? The government collects taxes to finance its purchases of goods and services in the economy—such as roads, schools, and national defense—and also to make transfers to households, such as unemployment insurance.

The tax forms we fill out change each year, sometimes quite significantly. The tax rates households and firms confront are changed by governmental decisions. The government alters tax rates to affect the level of economic activity in the economy. It uses these tools when, in its judgment, the level of economic activity (as measured by real GDP, the unemployment rate, and other variables we will learn about) is insufficient. This is a delicate assessment that requires an understanding of the meaning and measurement of satisfactory economic performance and a deep understanding of how the economy works.

For example, consider the winter of 2008. Policymakers working in the White House and on Capitol Hill kept careful track of the state of the economy, looking as we just did at announcements from the BEA and the BLS on output and inflation. Eventually, they concluded that economic activity was not at a high enough level. They took actions to increase output by reducing taxes through the American Recovery and Reinvestment Act of 2009 (http://www.irs.gov/newsroom/article/0,,id=204335,00.html). The idea is as follows: when people pay less in taxes, they have more income available to spend, so they will purchase more goods and services. The link between the legislation and you as an individual is through tax forms like the one shown in Figure 3.4 "Form 1040EZ".

The Budget Set

We describe your personal decision making on a month-by-month basis (although we could equally well look at daily, weekly, or even annual decisions because the same basic ideas would apply). Suppose you receive a certain amount of income each month—perhaps from a job or a student grant. The government takes away some of this income in the form of taxes, and the remainder is available for you to spend. We call the income that remains after taxes your disposable incomeIncome after taxes are paid to the government..

You may want to put aside some of this income for the future; this is your savings. The remainder is your consumption, which is your spending on all the goods and services you buy this month: rent, food, meals out, movies, cups of coffee, CDs, music downloads, DVD rentals, chocolate bars, books, bus rides, haircuts, and so on. Figure 4.1 "What You Do with Your Income" shows this process.

Figure 4.1 What You Do with Your Income

Here is a schematic view of what happens to your income.

This view of your paycheck involves several economic decisions. Some of these are decisions made by the government. Through its tax policies, the government decides how much of your income it takes from you and how much is left as disposable income. You make other decisions when you allocate your disposable income among goods and services today and in the future. You choose how to divide your disposable income between consumption this month and saving for the future. You also decide exactly how much of each good and service you purchase this month. We summarize your ability to purchase goods and services by your budget setAll the possible combinations of goods and services that are affordable, given income and the prices of all goods and services..

Begin by supposing you neither save nor borrow. We can construct your budget set in three steps.

1. Look at spending on each good and service in turn. For example, your monthly spending on cups of coffee is as follows:

   spending on coffee = number of cups purchased × price per cup.

   A similar equation applies to every other good and service that you buy. Your spending on music downloads equals the number of downloads times the price per download, your spending on potato chips equals the number of bags you buy times the price per bag, and so on.

2. Now add together all your spending to obtain your total spending:

   total spending = spending on coffee + spending on downloads + … ,

   where … means including the spending on every different good and service that you buy.

3. Observe that your total spending cannot exceed your income after taxes:

   total spending ≤ disposable income.

   You are consuming within your budget set when this condition is satisfied.

In principle, your list of expenditures includes every good and service you could ever imagine purchasing, even though there are many goods and services you never actually buy. After all, your spending on Ferraris every month equals the number of Ferraris that you purchase times the price per Ferrari. If you buy 0 Ferraris, then your spending on Ferraris is also $0, so your total spending does include all the money you spend on Ferraris.

Imagine now that we take some bundle of products. Bundle here refers to any collection of goods and services—think of it as being like a grocery cart full of goods. The bundle might contain 20 cups of coffee, 5 music downloads, 3 bags of potato chips, 6 hours of parking, and so on. If you can afford to buy this bundle, given your income, then it is in the budget set. Otherwise, it is not.

The budget set, in other words, is a list of all the possible collections of goods and services that you can afford, taking as given both your income and the prices of the goods and services you might want to purchase. It would be very tedious to write out the complete list of such bundles, but fortunately this is unnecessary. We merely need to check whether any given bundle is affordable or not. We are using affordable not in the casual everyday sense of “cheap” but in a precise sense: a bundle is affordable if you have enough income to buy it.

It is easiest to understand the budget set by working though an example. To keep things really simple, suppose there are only two products: chocolate bars and music downloads. An example with two goods is easy to understand and draw, but everything we learn from this example can be extended to any number of goods and services.

Suppose your disposable income is $100. Imagine that the price of a music download is $1, while the price of a chocolate bar is $5. Table 4.1 "Spending on Music Downloads and Chocolate Bars" shows some different bundles that you might purchase. Bundle number 1, in the first row, consists of one download and one chocolate bar. This costs you $6—certainly affordable with your $100 income. Bundle number 2 contains 30 downloads and 10 chocolate bars. For this bundle, your total spending on downloads is $30 (= 30 × $1), and your total spending on chocolate bars is $50 (= 10 × $5), so your overall spending is $80. Again, this bundle is affordable. You can imagine many other combinations that would cost less than $100 in total.

Bundles 3, 4, 5, 6, and 7 are special because they are affordable if you spend all your income. For example, you could buy 50 downloads and 10 chocolate bars (bundle 3). You would spend $50 on music downloads and $50 on chocolate bars, so your total spending would be exactly $100. Bundle 4 consists of 20 downloads and 16 chocolate bars; bundle 5 is 65 downloads and 7 chocolate bars. Again, each bundle costs exactly $100. Bundle 6 shows that, if you chose to buy nothing but downloads, you could purchase 100 of them without exceeding your income, while bundle 7 shows that you could buy 20 chocolate bars if you chose to purchase no downloads. We could find many other combinations that—like those in bundles 3–7—cost exactly $100.

Bundles 8, 9, and 10 are not in the budget set. Bundle 8 is like bundle 3, except with an additional chocolate bar. Because bundle 3 cost $100, bundle 8 costs $105, but it is not affordable with your $100 income. Bundle 9 costs $150. Bundle 10 shows that you cannot afford to buy 5,000 downloads and 2,000 chocolate bars because this would cost $15,000. There is quite literally an infinite number of bundles that you cannot afford to buy.

Figure 4.2 Various Bundles of Chocolate Bars and Downloads

This figure shows the combinations of chocolate bars and music downloads from Table 4.1 "Spending on Music Downloads and Chocolate Bars".

Figure 4.2 "Various Bundles of Chocolate Bars and Downloads" illustrates the bundles from Table 4.1 "Spending on Music Downloads and Chocolate Bars". The vertical axis measures the number of music downloads, and the horizontal axis measures the number of chocolate bars. Any point on the graph therefore represents a consumption bundle—a combination of music downloads and chocolate bars. We show the first nine bundles from Table 4.1 "Spending on Music Downloads and Chocolate Bars" in this diagram. (Bundle 10 is several feet off the page.) If you inspect this figure carefully, you may be able to guess for yourself what the budget set looks like. Look in particular at bundles 3, 4, 5, 6, and 7. These are the bundles that are just affordable—that cost exactly $100. It appears as if these bundles all lie on a straight line, which is in fact the case. All the combinations of downloads and chocolate bars that are just affordable represent a straight line.

Meanwhile, the bundles that are affordable with income to spare—like bundles 1 and 2—are below the line, and the bundles you cannot afford—like bundles 8, 9, and 10—are above the line. Building on these discoveries, we find that the budget set is a triangle (Figure 4.3 "The Budget Set").

Figure 4.3 The Budget Set

The bundles that are affordable are in the budget set, shown here as a triangle.

Every point—that is, every combination of downloads and chocolate bars—that lies on or inside this triangle is affordable. Points outside the triangle are not affordable, so they are not in the budget set.

The Budget Line

Continuing with our two-goods example, we know that

and

When total spending is exactly equal to total disposable income, then

The difference between the definitions of the budget set and the budget lineAll the goods and services that are affordable, given prices and income, assuming you spend all your income. is that there is an inequality in the budget set and an equality in the budget line:

Figure 4.4 The Budget Line

The bundles that are exactly affordable are on the budget line.

In the two-goods example, the budget line is the outside edge of the budget set triangle, as shown in Figure 4.4 "The Budget Line". What information do we need to draw the budget line? If we know both prices and the total amount of income, then this is certainly enough. In fact, we need only two pieces of information (not three) because basic mathematics tells us that it is enough to know two points on a line: once we have two points, we can draw a line. In practice, the easiest way to draw a budget line is to find the intercepts—the points on each axis. These correspond to how much you can obtain of each product if you consume 0 of the other. If you don’t buy any chocolate bars, you have enough income to buy 100 downloads. If the number of chocolate bars is 0, then the budget line becomes

so

Similarly, if the number of downloads is 0,

So we have two points on the budget line: (1) 0 chocolate bars and 100 downloads and (2) 0 downloads and 20 chocolate bars.

Another way to describe the budget line is to write the equation of the line in terms of its intercept (on the vertical axis) and its slope:To derive this equation, go back to the budget line and divide both sides by the price of a download:$$\begin{array}{l}\text{number of chocolate bars}\times \frac{\text{price of a chocolate bar}}{\text{price of a download}}\\ +\text{number of downloads}=\frac{\text{disposable income}}{\text{price of a download}}\text{.}\end{array}$$Rearranging, we get the equation in the text.

The intercept is $\frac{\text{disposable income}}{\text{price of downloads}}\text{,}$ which answers the following question: “How many downloads can you obtain if you buy no chocolate?” As we have already seen, this is 100 in our example.

The slope is

which answers the following question: “What is the rate at which you can trade off downloads for chocolate bars?” In our example, this is −5. If you give up 1 chocolate bar, you will have an extra $5 (the price of a chocolate bar), which allows you to buy 5 more downloads.

The negative slope of the budget line says that to get more downloads, you must give up some chocolate bars. The cost of getting more downloads is that you no longer have the opportunity to buy as many chocolate bars. More generally, economists say that the opportunity costWhat you must give up to carry out an action. of an action is what you must give up to carry out that action. Likewise, to get more chocolate bars, you must give up some downloads. The opportunity cost of buying a chocolate bar is that you do not have that the money available to purchase downloads. The idea of opportunity cost pervades economics.

You may well have heard the following quotation that originated in economics: “There is no such thing as a free lunch.” This statement captures the insight that everything has an opportunity cost, even if it is not always obvious who pays. Economists’ habit of pointing out this unpleasant truth is one reason that economics is labeled “the dismal science.”Although economists may dislike this characterization of their profession, they can take pride in its origin. The term was coined by Thomas Carlyle about 150 years ago, in the context of a debate about race and slavery. Carlyle criticized famous economists of the time, such as John Stuart Mill and Adam Smith, who argued that some nations were richer than others not because of innate differences across races but because of economic and historical factors. These economists argued for the equality of people and supported the freedom of slaves.

We said that a goal of this chapter is to help you make good decisions. One ingredient of good decision making is to understand the trade-offs that you face. Are you thinking of buying a new $200 mobile phone? The cost of that phone is best thought of, not as a sum of money, but as the other goods or services that you could have bought with that $200. Would you rather have 200 new songs for your existing phone instead? Or would you prefer 20 trips to the movies, 40 ice cream cones, or $200 worth of gas for your car? Framing decisions in this way can help you make better choices.

Your Preferences

Your choices reflect two factors. One is what you can afford. The budget set and the budget line are a way of describing the combinations of goods and services you can afford. The second factor is what you like, or—to use the usual economic term—your preferences.

Economists don’t pretend to know what makes everyone happy. In our role as economists, we pass no judgment on individual tastes. Your music downloads might be Gustav Mahler, Arctic Monkeys, Eminem, or Barry Manilow. But we think it is reasonable to assume three things about the preferences that underlie your choices: (1) more is better, (2) you can choose, and (3) your choices are consistent.

Your Choice

We have now looked at your opportunities, as summarized by the budget set, and also your preferences. By combining opportunities and preferences, we obtain the economic approach to individual decision making. Economists make a straightforward assumption: they suppose you look at the bundles of goods and services you can afford and choose the one that makes you happiest. If the claims we made about your preferences are true, then you will be able to find a “best” bundle of goods and services, and this bundle will lie on the budget line. We know this because (1) you can compare any two points and (2) your preferences will not lead you to go around in circles.

Figure 4.5 Choosing a Preferred Point on the Budget Line

An individual’s preferred point reflects opportunities, as given by the budget line, and preferences. The preferred point will lie on the budget line, not inside, because of the assumption that more is better.

In Figure 4.5 "Choosing a Preferred Point on the Budget Line", we indicate an example of an individual’s preferred point. The preferred point is on the budget line and—by definition—is the best combination for the individual that can be found in the budget set. At the preferred point, the individual cannot be better off by consuming any other affordable bundle of goods and services.

There is one technical detail that we should add. It is possible that an individual might have more than one preferred point. There could be two or more combinations on the budget line that make an individual equally happy. To keep life simple, economists usually suppose that there is only a single preferred point, but nothing important hinges on this.

Rationality

Economists typically assume rationalityThe ability of individuals to (1) evaluate the opportunities that they face and (2) choose among them in a way that serves their own best interests. of decision makers, which means that people can do the following:

• evaluate the opportunities that they face
• choose among those opportunities in a way that serves their own best interests

Is this a good assumption? Are people really as rational as economists like to think they are? We would like to know if people’s preferences do satisfy the assumptions that we have made and if people behave in a consistent way. If we could hook someone up to a machine and measure his or her preferences, then we could evaluate our assumptions directly. Despite advances in neurobiology, our scientific understanding has not reached that point. We see what people do, not the preferences that lie behind these choices. Therefore, one way to evaluate the economic approach is to look at the choices people make and see if they are consistent with our assumptions.

Imagine you have an individual’s data on download and chocolate bar consumption over many months. Also, suppose you know the prices of downloads and chocolate bars each month and the individual’s monthly income. This would give you enough information to construct the individual’s budget sets each month and look for behavior that is inconsistent with our assumptions. Such inconsistency could take different forms.

• She might buy a bundle of goods inside the budget line and throw away the remaining income.
• In one month, she might have chosen a bundle of goods—call it bundle A—in preference to another affordable bundle—call it bundle B. Yet, in another month, that same individual might have chosen bundle B when she could also have afforded bundle A.

The first option is inconsistent with our idea that “more is better.” As for the second option, it is generally inconsistent to prefer bundle A over bundle B at one time yet prefer bundle B over bundle A at a different time. (It is not necessarily inconsistent, however. The individual might be indifferent between bundles A and B, so she doesn’t care which bundle she consumes. Or her preferences might change from one month to the next.)

Individual Demand for a Good

As you visit stores at different times, you undoubtedly notice that the prices of goods and services change. At the same time, your income may also change from one month to the next. So if we were to look at your budget set monthly, we would typically find it changing from one month to the next. We would then expect that you would choose different combinations of goods and services from one month to the next.

To keep things simple, suppose we are still in a world of two goods—downloads and chocolate bars—and that you do no saving. We will describe your demand for chocolate bars. (If you like, you can think of downloads as representing all the other goods and services you consume.) Given prices and your income, you pick the best point on the budget line. Look again at the “preferred” point in Figure 4.5 "Choosing a Preferred Point on the Budget Line". One way to interpret this point is that it tells us how many chocolate bars you will buy, given your income and given the price of a chocolate bar and other goods. Using this as a reference point, we now ask how your choice will change as income changes and then as the price of a chocolate bar changes.

Changes in Income

Imagine that your income increases. Figure 4.6 "An Increase in Income" shows what happens to the budget line. Higher income means that you can afford to buy more chocolate bars and more downloads, so the budget line shifts outward. The slope of the budget line is unchanged because there is no change in the price of a chocolate bar relative to downloads.

Figure 4.6 An Increase in Income

An increase in income shifts the budget line outward.

What happens to your consumption of chocolate bars? There are two possibilities (Figure 4.7 "The Consequences of an Increase in Income"): the increase in income leads you to consume either more chocolate bars or fewer chocolate bars. Both are plausible, and either is possible. (Of course, you might also choose exactly the same amount as before.) We might think that the more normal case is that higher income would lead to higher chocolate bar consumption. If a good has a property that you will consume more of it when you have higher income, we call it a normal goodA good that is consumed more when income increases..

Figure 4.7 The Consequences of an Increase in Income

In response to an increase in income, two things are possible: the consumption of chocolate bars may increase (a) or decrease (b).

Under some circumstances, higher income leads to lower consumption. For example, suppose you are surviving in college on a diet consisting of mostly instant noodles. When you graduate college and have higher income, you can afford better things to eat, so you will probably consume a smaller quantity of instant noodles. Economists call such products inferior goodsA good that is consumed less when income increases.. If a particular product exists in several qualities (cheap versus expensive cuts of meat, for example), we often find that the low-quality version is an inferior good. A good might be normal for one consumer and inferior for another. More precisely, therefore, we say that a good is inferior if, on average, higher income leads to lower consumption.

Economists make a further distinction among different kinds of normal goods. If you spend a larger fraction of your income on a particular good as your income increases, then we say that the good is a luxury goodA normal good with the additional feature that consumption increases by a greater percentage than income.. Another way of saying this is that for a luxury good, the percentage increase in consumption is bigger than the percentage increase in income.

We can also define these ideas in terms of the income elasticity of demandA measure of how responsive the quantity demanded is to changes in income., which is a measure of how sensitive demand is to changes in income. For an inferior good, the income elasticity of demand is negative: higher income leads to lower consumption. For a normal good, the income elasticity of demand is positive. And for a luxury good, the income elasticity of demand is greater than one.

The distinctions among these different kinds of goods are crucial for managers of firms. To predict sales, managers need to know whether the products they are selling are normal, inferior, or luxury goods. Firms that sell inferior goods tend to do well when the economy as a whole is doing poorly and vice versa. By contrast, firms selling luxury goods will do particularly poorly when the economy as a whole is performing poorly.

Changes in Price

Now we look at what happens if there is a change in the price of a chocolate bar. Suppose the price decreases. First, let us analyze what this means in terms of our picture. Remember that the intercepts of the budget line tell you how much you can have of one good if you consume none of the other. If you consume no chocolate bars, then a decrease in the price of a chocolate bar has no effect on your consumption. You can consume exactly the same number of downloads as before. The intercept on the vertical axis therefore does not move. However, a decrease in the price of a chocolate bar means that, if you consume only chocolate bars, then you can have more than before. The intercept on the horizontal axis moves outward. One way to see this is to remember that this intercept is given by

Figure 4.8 "A Decrease in the Price of a Chocolate Bar" illustrates a decrease in the price of a chocolate bar. The new budget line lies outside the old budget line. Any bundle you could have bought at the old prices is still affordable now, and you can also get more. A decrease in the price of a chocolate bar, in other words, makes you better off. In addition, the slope of the budget line changes: it is flatter than before. The slope of the budget line reflects the way in which the market allows you to trade chocolate bars for other products. If you choose to consume fewer downloads, the reduction in the price of a chocolate bar means that you get relatively more chocolate bars in exchange.

Figure 4.8 A Decrease in the Price of a Chocolate Bar

A decrease in the price of a chocolate bar causes the budget line to rotate. The result is an increase in the quantity of chocolate bars consumed.

Figure 4.8 "A Decrease in the Price of a Chocolate Bar" also shows a new consumption point. In response to the decrease in the price of a chocolate bar, we see an increase in the consumption of chocolate bars. The idea that people almost always consume more of a good when its price decreases is one of the fundamental ideas of economics. Indeed, it is sometimes called the law of demandWhen the price of a good decreases, the quantity demanded increases.. It is certainly intuitive that lower prices lead people to consume more. There are two reasons why we expect to see this result.

First, if a good (for example, chocolate bars) decreases in price, it becomes cheaper relative to other goods. Its opportunity cost—that is, the amount of other goods you must give up to get a chocolate bar—has decreased. The lower opportunity cost means that there is a substitution effectIf one good becomes cheaper relative to other goods, this leads away from other goods and toward that particular good. away from other goods and toward chocolate bars. Second, a decrease in the price of a chocolate bar also means that you can afford more of everything, including chocolate bars. Provided chocolate bars are a normal good, this income effectWhen a good decreases in price, the buyer can afford more of everything, including that good. will also lead you to want to consume more chocolate bars. If chocolate bars are inferior goods, the income effect leads you to want to consume fewer chocolate bars.

In Figure 4.8 "A Decrease in the Price of a Chocolate Bar", the substitution effect is reflected by the fact that the budget line changes slope. The flatter budget line tells us that the opportunity cost of chocolate bars in terms of downloads has decreased. The income effect shows up in the fact that the new budget set includes the old budget set. You can consume your previous bundle of goods and still have some income left over to buy more.

Based on the idea of the law of demand, we can construct your individual demand curveThe quantity of a good that an individual demands at each price, all else being the same. for chocolate bars. We do so by drawing the budget set for each different price of a chocolate bar, seeing how much you buy, and then plotting this data. For example, we might find that your purchases of chocolate bars look like those in Table 4.2 "Demand for Chocolate Bars". If we plot these points on a graph and then “fill in the gaps,” we get a diagram like Figure 4.9 "The Demand Curve". This is your demand curve for chocolate bars. It tells how many chocolate bars you would purchase at any given price. The law of demand means that we expect this curve to slope downward. If the price increases, you consume less. If the price decreases, you consume more.

Figure 4.9 The Demand Curve

Table 4.2 "Demand for Chocolate Bars" contains an example of some observations on demand. At different prices from $1 to $6, we see the number of chocolate bars purchased. If we fill in the gaps, we obtain a demand curve.

We must be careful to distinguish between movements along the demand curve and shifts in the demand curve. Suppose there is a change in the price of a chocolate bar. Then, as we explained earlier, the budget line shifts, and the quantity demanded of both chocolate bars and downloads will change. This appears in Figure 4.9 "The Demand Curve" as a movement along the demand curve. For example, if the price of a chocolate bar decreases from $4 to $3, then, as in Table 4.2 "Demand for Chocolate Bars", the quantity demanded increases from three bars to four bars. The demand curve does not change; we simply move from one point on the line to another.

If a change in anything other than the price of a chocolate bar causes you to change your consumption of chocolate bars, then there is a shift in the demand curve. For example, suppose you get a pay raise at your job, so you have more income. As long as chocolate bars are a normal good, this increase in income will cause your demand curve for chocolate bars to shift outward. This means that, at any given price, you will buy more of the good when income increases. In the case of an inferior good, an increase in income will cause the demand curve to shift inward. You will buy less of the good when income increases. We illustrate these two cases in Figure 4.10 "Shifts in the Demand Curve: Normal and Inferior Goods".

Figure 4.10 Shifts in the Demand Curve: Normal and Inferior Goods

(a) If income increases and chocolate bars are a normal good, then the individual demand curve will shift to the right. At every price, a greater quantity of chocolate bars is demanded. (b) If income increases and chocolate bars are inferior goods, then the individual demand curve will shift to the left. In the event of a decrease in income, the two cases are reversed.

Changes in Other Prices

So far, we have said that the number of chocolate bars you want to buy is affected by income and the price of a chocolate bar. Changes in the prices of other goods also have an impact. In general, an increase in a price of another good could cause the demand for chocolate bars to increase or decrease.

Goods are substitutesAn increase in the price of one good leads to increased consumption of the other good. if an increase in the price of one good leads to increased consumption of the other good. CDs and music downloads are one example: if the price of CDs increases, you will obtain more music through downloads.

Goods are complementsAn increase in the price of one good leads to decreased consumption of the other good. if an increase in the price of one good leads to decreased consumption of the other good. For example, DVDs and DVD players are complements. If the price of DVD players decreases, more people will buy DVD players. As a result, more people will want to buy DVDs.

The Valuation Approach to Demand

There is another way of thinking about demand. Instead of focusing attention on the budget set and the budget line, we can think more directly about your preferences. Imagine you are asked the following question in an interview:

In answering this question, you should not worry about what would be a reasonable or fair price for a chocolate bar or even about the price at which this chocolate bar might actually be available. You should simply decide how much you want chocolate bars. For example, you might think that you would really like to have at least one chocolate bar, so you would be willing to pay up to $12 for one bar—that is, you would be happier with one more chocolate bar and up to $12 less in income. This is your valuationThe maximum amount an individual would be willing to pay to obtain that quantity. of one chocolate bar.

Now we ask you some more questions.

Perhaps you decide you would be willing to pay $18 for two bars, $22 for three bars, and so on. If we kept asking such questions, we might get the first two columns of Table 4.3 "Valuation and Marginal Valuation". We can also plot this valuation (part [a] of Figure 4.11 "Valuation of a Good"). Your valuation is increasing; you always like having more chocolate bars because “more is better.”

Figure 4.11 Valuation of a Good

Your valuation of a good is the maximum amount that you would be willing to pay, purely on the basis of your desire for the good.

Because you are willing to pay $12 for one bar and $18 for two bars, we know you would be willing to pay an additional $6 for the second chocolate bar. Similarly, if you have two chocolate bars, you would be willing to pay an additional $4 for a third bar. We call the change in your valuation your marginal valuationThe maximum amount an individual would be willing to pay to obtain one extra unit of that good. (see the third column of Table 4.3 "Valuation and Marginal Valuation", which is graphed in part [b] of Figure 4.11 "Valuation of a Good"). Notice that marginal valuation decreases as the quantity of chocolate bars increases. The change in your valuation gets smaller as you obtain more chocolate bars. We can see the same thing in part (a) of Figure 4.11 "Valuation of a Good" from the fact that the valuation curve gets flatter as the quantity of chocolate bars increases.

It usually seems reasonable to think that marginal valuations will indeed decrease in this way. If you don’t have any chocolate bars, then the first bar is worth a lot to you—$12 in our example. But if you already have five chocolate bars, then the sixth bar is worth only $2 to you. As you obtain more and more of any given product, each additional unit is less and less valuable. For most people, we expect that most products will exhibit such diminishing marginal valuation.

Part (b) of Figure 4.11 "Valuation of a Good" may seem familiar. It is the demand curve for chocolate bars you saw previously in Figure 4.9 "The Demand Curve". This is not an accident or a coincidence. There is a simple decision rule to tell you how much you should buy: when your marginal valuation is greater than the price, you should buy more of the good, stopping only when the marginal valuation of the good has dropped to the level of the price. For example, suppose that chocolate bars are selling for $3.99. You should definitely buy the first chocolate bar, because it is worth $10 to you and will cost you only $3.99. You should buy the second bar as well because it is worth an additional $8 to you; likewise you should buy the third and fourth bars. You don’t buy the fifth bar because it is worth only $3 to you, which is less than what it costs. Thus your decision rule is as follows:

• Buy until the marginal valuation of a good equals the price of the good.

Because the demand curve, by definition, tells you how much you buy at a given price, it is the same as the marginal valuation curve.

Unit Demand

So far we have considered situations where you might buy multiple units of a good—for example, 20 music downloads or 5 chocolate bars. To keep things simple, we also supposed that you could buy fractional amounts, such as 20.7 downloads, or 3.25 chocolate bars. This assumption gives a decision rule for purchase: buy until marginal valuation equals price.

Some purchase decisions are better thought of as “buy or don’t buy.” Large, infrequent purchases fall into this category. Think, for example, about the decision to buy a new car, a new microwave, or an expensive vacation. You won’t buy five microwaves because they are cheap. The decision rule for purchase is even easier in this case: buy if your valuation of the good exceeds the price of the good. In fact, this is really no different from our earlier decision rule. Because you are only ever thinking about buying one unit, your valuation and your marginal valuation are the same thing (look back at the first two rows of Table 4.3 "Valuation and Marginal Valuation"). And because in this case it does not make sense to suppose you can buy fractional amounts of the good, you cannot keep buying until your marginal valuation decreases all the way to the price.

If a buyer is interested in purchasing one and only one unit of a good, the unit demand curveThe special case of the individual demand curve when a buyer might purchase either zero units or one unit of a good but no more than one unit. tells us the price at which he is willing to buy. Below his valuation, he buys the good. Above his valuation, he does not buy the good. A unit demand curve is shown in Figure 4.12 "Unit Demand". In this example, the buyer’s valuation is $3,000.

Figure 4.12 Unit Demand

The buyer follows this decision rule: “Buy if the price is less than valuation.” If the price is greater than $3,000, the buyer will not purchase. The quantity demanded is zero. If the price is less than $3,000, the buyer will purchase one unit. No matter how low the price decreases, the buyer will not want more than a single unit. This is an example of unit demand.

To see where such a valuation could come from, look at Figure 4.13 "The Valuation of a Car". Suppose you are thinking about buying a car. The figure shows our standard downloads-and-chocolate-bar diagram, except that there are two budget lines. The outer budget line applies in the case where you do not buy the car. You have a preferred point in terms of downloads and chocolate bars (A). If you buy the car, you have less income to spend on everything else. The effect is to shift your budget line inward, in which case you have a new preferred point (B). The thought experiment here is to decrease your income and shift your budget line inward until you are equally happy with the two bundles. The change in your income—the amount by which the budget line must shift—is your valuation of the car. Your valuation, in other words, is the opportunity cost of the car: if you buy the car, you can only consume bundle B rather than bundle A.

Figure 4.13 The Valuation of a Car

If you don’t buy a car, your preferred mix of chocolate bars and downloads is at point A. If you buy a car, then you no longer have that income available to spend on chocolate bars and downloads. Your budget line shifts inward, and you consume at your preferred point B. Now imagine that you are equally happy at point A and point B. Then the difference in income is equal to your valuation of the car. Thus the valuation of a car is its opportunity cost in terms of other goods.

Budget Studies

Economists’ theories are all well and good. But we do not actually get to see people’s preferences or marginal valuations. We observe what people actually do. To see our theory in action, we can look at household budget studies. These are surveys where government statisticians interview households and ask them how they spend their income. For example, Table 4.4 "Budget Shares in the United States" contains data on US consumer expenditures for the years 2005, 2007, and 2009.

You can see that, on average, households spend a little more than 45 percent of their income on food and housing. Insurance is also a large category, with about 11 percent of income being spent on it.Chapter 5 "Life Decisions" discusses why we buy insurance. Interestingly, the budget shares do not change much over the three years despite the differences in income and spending. From this we see that, although individual goods may be inferior or luxury goods, such differences are largely offset when we look at broad categories of goods or services.

The table also contains data for households under age 25.This is based on the age of the reference person in the household, who is the individual who owns or rents the property. We can compare the spending patterns of this group against all households. Not surprisingly, the younger group earns less than the average household. Also, this younger group often spends more than it earns, indicating that younger people are borrowing, on average. The younger group spends more on alcohol, transportation, and education and much less on health care and insurance than the average household. This makes sense given the health status of young individuals as well as their demand for education.

Table 4.5 "United Kingdom Budget Study" is a UK budget study for households headed by young people (under the age of 30) in 2009. It shows how these households allocated their expenditures over a week.The British source is as follows: Office for National Statistics, Family Spending, 2010, table A.11, accessed January 24, 2011, http://www.statistics.gov.uk/downloads/theme_social/family-spending-2009/familyspending2010.pdf. We can compare these figures against those for young people in the United States. (We need to be careful in making comparisons because the categories for spending are not exactly the same across surveys. Still, it is useful to explore these differences.) In the United Kingdom, spending on food and housing is much lower for these younger households than in the United States. Health also has a much lower expenditure share.

Choosing among Different Uses of Your Time

We begin with the most fundamental time allocation problem for all students: choosing between studying and sleeping. As before, we keep things simple by thinking about only two possible uses of your time. You are given 24 hours in the day to study and sleep. How should you allocate your time?

As with the allocation of your income, there are two aspects of this problem. First, there is a budget constraint—only now it is your time that is scarce, not money. Second, you have your own preferences about sleep and study time. Your ability to meet your desires is constrained by the scarcity of your time: you must trade off one activity for another.

The time budget constraintThe restriction that the sum of the time you spend on all your different activities must be exactly 24 hours each day. is the restriction that there are only 24 hours in the day. It is shown in Figure 4.14 "The Time Budget Constraint" and is the counterpart to the budget line in our earlier discussion. Any point in this figure represents a combination of sleep and study time. The sum of sleep and study time must equal 24 hours (remember we are supposing that these are the only ways you spend your time). Thus your allocation of your time must lie somewhere on this line.

Figure 4.14 The Time Budget Constraint

The time allocation line shows your options for dividing your time between study and sleep.

Figure 4.14 "The Time Budget Constraint" also shows one possible choice that you might make: allocating 8 hours to sleep and 16 hours to studying. The choice of this point reflects your desires for sleep and study. As with the spending decision, we pass no judgment, as economists, on the actual decision you make. We suppose you typically make the choice that makes you the happiest.

At your preferred point, your choice to sleep for 8 hours means that your study time must equal 16 hours; equivalently, your choice to study for 16 hours means that you must sleep for 8 hours. Any increase in one activity must be met by a reduction in time for the other. The opportunity cost of each hour of sleep is an hour of study time, and the opportunity cost of each hour of study time is an hour of sleep. If you choose this point, you reveal that you are willing to “pay” (that is, give up) 8 hours of study time to obtain 8 hours of sleep, and you are willing to pay 16 hours of sleep to obtain 16 hours of study time.

As with consumption choices, it is often enough to look at small changes to evaluate whether or not you are making a good decision. The opportunity cost of a little more sleep is a little less study time. If you are making a good decision about the allocation of your time, then the extra sleep is not worth the extra study time. Suppose you are contemplating a particular point on the time budget line, and you want to know if it is a good choice. If a very small movement away from your chosen point will not make you happier, then—in most circumstances—neither will a big movement. By a very small movement, we mean sleeping a little less and studying a little more or studying a little less and sleeping a little more. If you are making a good decision, then your willingness to substitute sleep for study time is exactly the same as that allowed by the time constraint.

Individual Labor Supply

Sleeping and studying are uses of your time that are directly for your own benefit. Most people—perhaps including yourself—also spend time working for money. So let us now look at the choice between spending time working and enjoying leisure. Our goal is to determine how much labor you will choose to supply to the market—which is equivalently a choice about how much leisure time to enjoy, because choosing the number of working hours is the same as choosing the number of leisure hours. Your choice between the two is based on the trade-off between enjoying leisure and working to earn money that allows the purchase of goods.

Once again—to make it easy to draw diagrams—we suppose that these are the only uses of your time. Part (a) of Figure 4.15 "Choosing between Work and Leisure" presents the allocation of time between work and leisure. As with the sleep-study choice, there is a time budget constraint, and you have preferences between these two ways to allocate time. Your best choice satisfies the same property as before: you allocate time such that no other division of your time makes you happier.

What makes this different from the sleep-study choice is the valuation of your time. We can think of sleep as a good thing in that you generally prefer more to less. Likewise, we can think of study as a good thing in that—even if you don’t always enjoy it—you perceive a gain to spending time studying. So Figure 4.14 "The Time Budget Constraint" is like our earlier diagrams with downloads and chocolate bars: it has a good thing on each axis. Now, people presumably prefer more leisure to less: leisure is a “good,” like chocolate bars, blue jeans, or cans of soda. But we have drawn part of (a) Figure 4.15 "Choosing between Work and Leisure" as if work is also a good thing. Most people, however, see work time as a “bad” rather than as a “good.” Even people who like their work would almost always prefer to work a little less and have a little more leisure time.

Figure 4.15 Choosing between Work and Leisure

(a) The time budget line shows your options for dividing your time between labor and leisure. However, we generally think of labor as a “bad” rather than as a “good.” (b) Now the choice is between consumption and leisure. For each hour of your time, you earn the nominal hourly wage. If you divide this by the price level, you get the real wage. The real wage tells you how many goods and services you can enjoy for one hour of work.

The gain from working, of course, is that you earn income, allowing you to purchase goods and services. Each extra hour of your work allows you to buy more goods and services. Conversely, if you want more leisure time, you must give up some goods and services. Thus the choice between labor and leisure is linked to the choice about how many chocolate bars and other goods you buy. The income we take as given in describing your budget set typically comes from your decision to supply labor time. (Of course, you may have other sources of income as well, such as loans or grants.)

Part (b) of Figure 4.15 "Choosing between Work and Leisure" takes the labor-leisure choice and converts it into a choice between leisure and consumption. Here, consumption refers to all the goods and services you consume. We lump together all the products you consume, just as we lump together all your different forms of leisure (sleep, study, watching television, and so on). As before, time is measured on the horizontal axis: there are 24 hours to the day, which must be split between leisure time and labor time. On the vertical axis, we measure consumption.

To get the budget constraint for this picture, we begin with the time budget constraint:

The value of an hour of time in dollars is given by the wages at which you can sell your time. Multiplying the time budget constraint by the wage gives us a budget constraint in dollars:

Wage income is equal to the number of hours worked times the hourly wage. Because wage income is used to buy goods, we can replace it by total spending on consumption, which is the price level times the quantity of consumption goods purchased:

This is the budget constraint faced by an individual choosing between leisure and consumption. Think of it as follows: The individual first sells all her labor at the going wage, yielding the income on the right-hand side. With this income, she then “buys” back leisure and also buys consumption goods. The price of an hour of leisure represents the wage rate, and the price of a unit of consumption goods represents the price level.

Dividing the time budget constraint by the price level, we get the budget in line in part (b) of Figure 4.15 "Choosing between Work and Leisure".

As you move along the budget line, you trade hours of leisure for consumption goods. The slope of the budget line is the negative of the real wageThe nominal wage (the wage in dollars) divided by the price level.. If you give up an hour of leisure, you obtain extra consumption equal to the real wage. Put differently, the opportunity cost of an hour of leisure is the amount of consumption you give up by not working. Once we have worked out how much leisure you consume, we have equivalently worked out how much labor you supply:

Part (a) of Figure 4.16 "The Effect of a Real Wage Increase on the Quantity of Labor Supplied" shows what happens when the real wage changes. When the real wage increases, the vertical intercept of the budget line is higher because the vertical intercept tells us how much consumption an individual could obtain if she worked for all 24 hours in the day. The horizontal intercept does not change as the real wage changes: if an individual does not work, then the level of consumption is zero regardless of wages. It follows that the budget line is steeper as the real wage increases. If an individual gives up an hour of leisure time, he or she gets more additional consumption when the real wage is higher. The opportunity cost of leisure in terms of forgone consumption is higher.

Figure 4.16 The Effect of a Real Wage Increase on the Quantity of Labor Supplied

(a) An increase in the real wage causes the budget line to rotate. Income and substitution effects are both at work: the income effect encourages more leisure (less work), while the substitution effect encourages more work. The substitution effect generally dominates, so higher real wages lead to more work. This means that the labor supply curve slopes upward, as shown in (b).

Part (b) of Figure 4.16 "The Effect of a Real Wage Increase on the Quantity of Labor Supplied" shows the individual labor supply curveA curve that indicates how many hours of labor an individual supplies at different values of the real wage. that emerges from the labor-leisure choice.

In fact, there are conflicting incentives at work here. As the real wage increases, the opportunity cost of leisure is higher, so you are tempted to work more. But at a higher real wage, you can enjoy the same amount of consumption with fewer hours of work, so this tempts you to work less. This is another example of substitution and income effects. The substitution effect says that when something gets more expensive, we buy less of it. When the real wage increases, leisure is more expensive. The income effect says that as the real wage increases, you can buy more of the things you like, including leisure. We know from our study of demand that, for normal goods, the income and substitution effects act in the same direction. In the case of supply, however, income and substitution effects point in different directions. Consistent with this, most economic studies find that, though the labor supply curve slopes upward, hours worked are not very responsive to changes in the real wage.

Some jobs do not give you any control over the number of hours that you must work. Labor supply then becomes a “unit supply” decision, analogous to the unit demand decisions we considered previously. Should you take a job at all and, if so, what job? To the extent that you can choose among different jobs that offer different hours of work, your decision about whether or not to work will still reflect a trade-off between leisure and consumption.

Individuals and Households

We have discussed almost everything in this chapter in terms of an individual’s decision making. However, economists often think in terms of households rather than individuals. In part this is because—as we saw with the budget studies—much more economic data are collected for households than for individuals. Also, many of the decisions we have discussed are really made by a household as a whole, rather than by the individual members of that household.

For example, many households have two working adults. Their decisions about how much to work will usually be made jointly on the basis of the real wages they both face. To see some implications of this, consider a two-person household in which both are working. Now suppose that the real wage increases for one person in the household. One person will probably respond by increasing the number of hours worked. However, the other person may choose to work less. Imagine, for example, that there are household chores that either could do. By working less, one person can do more of these chores and thus compensate the other person for the extra hours worked.This is an application of an important economic idea called comparative advantage, which we discuss in more detail in Chapter 6 "eBay and craigslist". Most of the time, though, we do not need to worry about the distinction between the individual and the household, and we often use the terms interchangeably.

Time Studies

Table 4.6 "Allocation of Hours in a Day" shows the allocation of time to certain activities for individuals in three countries: the United States, the United Kingdom, and Mexico. It shows the time allocated on average per day for each of four activities: work, study, personal care, and leisure.

For the United States and the United Kingdom, the average number of hours worked is between 2.65 and 3.00. This is an average: some people in this age group may work a full-time job, while others may be students who are not working for pay at all. The sample from Mexico differs from the US and UK samples. First, the group is slightly older. Second, Mexico is notably poorer than the United States and the United Kingdom. For these two reasons, individuals sampled in Mexico are more likely to be working and less likely to be studying and enjoying leisure—which is indeed what we see.

Combining Your Time and Spending Choices

So far we have looked at the allocation of your income separately from the allocation of your time. Yet these choices are linked. The allocation of your time influences the income you have to spend on goods and services. So a change in the wages you are paid will affect how you allocate your time and the goods and services you choose to buy.

In a similar fashion, the prices of goods and services you purchase will have an influence on your allocation of time. For example, if the price of a computer you want to buy decreases, you may respond by working a little more to earn extra income to purchase the computer. The reduction in the price of the computer raises your real wage, so you respond by working more.

The Budget Line with Two Periods

Now think about what the budget line looks like when we are choosing between now and the future. Just as we find it easier to think about the choice between two goods rather than among 2,000 goods, so too is it easier to think about the choice over only two periods of time. We call these two periods “this year” and “next year.” There is nothing special about the two-period example beyond the fact that it makes it easy to draw diagrams and see what is going on. The principles that we uncover for this case also apply to decisions made with more than two time periods in mind.

We also do not worry about all the different goods and services that are available, preferring instead to talk in general about consumption this year and consumption next year. We aggregate together all the different products that we consume. Thus “consumption” means the bundle of goods and services people consume. This consumption also has an associated price, which we call the price levelA measure of average prices in an economy.. Think of this as the average price of goods and services in the economy. If you find it easier, imagine there is a single good, like chocolate bars, that you consume, and think of the price level as simply being the price of a chocolate bar.

Saving and the Nominal Interest Rate

If you choose not to spend all your income on consumption this year, you are saving. When you save, you can put your money into a financial institution and earn interest on it. Suppose you have $100 this year that you save by putting it in a bank. You are then lending to the bank—saving and lending are really the same thing. The bank acts as an intermediary, taking your $100 and giving it to someone else who borrows from the bank.

The bank offers you interest on this loan—for example, it may pay a nominal interest rateThe rate at which individuals and firms in an economy can save or borrow. of 5 percent per year. After a year, your bank account will contain your original $100, plus an extra 5 percent. Because 5 percent of $100 is $5, you earn $5 worth of interest. We talk about interest rates in percentage terms, but you should remember that a percentage is simply a number. For example, 5 percent is 0.05, and 20 percent is 0.2. The nominal interest rate is the interest rate at which individuals and firms in the economy can save or borrow.There are actually many different interest rates in an economy. Chapter 10 "Making and Losing Money on Wall Street" looks at some of these. Here, we simplify the process by supposing there is only one interest rate. It is called a nominal interest rate because it is measured in monetary terms. Most interest rates are quoted on an annual basis, meaning that they specify the amount earned per year.

Of course, if you put a $100 in the bank for one year, then next year you will still have the original $100 as well as the interest you earned. At an interest rate of 5 percent, $100 this year is worth $105 next year. To calculate the total amount of money that you can earn, we simply add one to the nominal interest rate, giving us the nominal interest factorA factor, equal to 1 + the nominal interest rate, used to convert dollars today into dollars next year.:

nominal interest factor = 1 + nominal interest rate.

The nominal interest factor is used to convert dollars today into dollars next year.

Toolkit: Section 31.6 "The Credit Market"

The nominal interest rate is the rate at which individuals and firms in the economy can save or borrow. The nominal interest factor is 1 + the nominal interest rate.

In this chapter, we typically use the nominal interest factor rather than the nominal interest rate because it makes the equations easier to understand. Just keep in mind that it is easy to move back and forth between the interest rate and the interest factor by adding or subtracting one.

If you have $100 today, then tomorrow it will be worth $100 × the nominal interest factor. In general,

z this year will be worth z × the nominal interest factor next year.

Armed with this idea of the nominal interest factor, we can graph the budget line for a two-period consumption-saving problem. Figure 5.2 "The Budget Line with Two Periods" shows consumption this year on the horizontal axis and consumption next year on the vertical axis. To discover what the budget line looks like, we first determine its slope and then its position.

Figure 5.2 The Budget Line with Two Periods

This diagram shows the budget line for an individual choosing consumption over time. The slope of the budget line depends on the price level this year, the price level next year, and the nominal interest factor (= 1 + nominal interest rate). Suppose the price level this year is $9, the price level next year is $10, and the nominal interest rate is 20 percent. Then the slope of the budget line is −(9/10) × 1.2 = −1.08. This means that if you give up 1 unit of consumption this year, you can get 1.08 units next year.

The Position of the Budget Line

Whereas the slope of your budget line depends on the real interest rate, the position of your budget line depends on how much income you have. When you have more income, the budget line is further away from the origin. One way to determine the position of the budget line is by looking at its intercepts. The horizontal intercept is the amount you can consume this year if you spend all of this year’s income and borrow against your entire future income. The vertical intercept is the amount you can consume next year if you choose to consume nothing this year and save all of your current income.

It is easier and more instructive, however, to look at a different point on the budget line. Remember that the budget line is the bundles of consumption you can just afford. One bundle you can certainly afford is the bundle where you spend all of this year’s income on consumption this year and all of next year’s income on consumption next year. In other words, one available option is that you neither save nor borrow. In this case,

$$\text{consumption this year = real income this year =}\frac{\text{nominal income this year}}{\text{price level this year}}$$

and

$$\text{consumption next year = real income next year =}\frac{\text{nominal income next year}}{\text{price level next year}}\text{.}$$

On the right-hand side of these equations, we divided dollar income by the price level to give us real income (that is, income measured in terms of purchasing power). We must do this to find out how much you can consume in terms of goods and services.

For example, suppose your nominal income this year is $23,000, and your nominal income next year is $24,200. Suppose the price level this year is $10 and the price level next year is $11. This means that

$$\text{real income this year = }\frac{\text{\$23,000}}{\text{\$10}}$$

and

$$\text{real income next year = }\frac{\text{\$24,200}}{\text{\$11}}\text{.}$$

So one possible consumption choice, as shown in Figure 5.3 "Determining the Position of the Budget Line", is 2,300 units of consumption this year and 2,200 units of consumption next year. In this case, you are neither borrowing nor saving. Of course, you might choose some different point on the budget line. Figure 5.3 "Determining the Position of the Budget Line" shows that your real income this year and next year does indeed pick out a point on the budget line. And because we already know the slope of the budget line, we are done; we can now draw the budget line.

Figure 5.3 Determining the Position of the Budget Line

The position of the budget line depends on income this year and next year. We know that one possible choice of consumption is where the consumer neither saves nor borrows. This means that the budget line must pass through this point.

Adding Income and Consumption Spending over Two Periods

Your budget line describes the condition that total spending equals total income. This is true for the choice about the consumption of downloads and chocolate bars, and it is also true for the choice over time. But once we move to two periods, we must be careful about measuring both total income and total spending.

Income, Consumption, and Saving

Given your budget line, we suppose you choose a combination of consumption this year and next year that makes you as well off as possible. An example of such a preferred point is indicated in Figure 5.4 "The Preferred Point".

Figure 5.4 The Preferred Point

The consumer’s preferred point must lie somewhere on the budget line. In this example, the consumer is choosing to consume in excess of his income this year. The consumer must borrow against future income, which means that consumption next year will be below next year’s income.

The choice of a preferred point reflects two ideas. Whatever your tastes between consumption in the two years, we presume that you will not throw any income away. As a result, your choice will be on, not inside, the budget line. Further, if you choose well, according to your preferences, then you will pick the best combination of consumption; there is no other point on the budget line that you prefer.

Saving and Borrowing

Your preferred point implies a choice about how much saving or borrowing you do. Figure 5.5 "Consumption and Saving" shows two possible cases. In part (a) of Figure 5.5 "Consumption and Saving", you are a saver: you are consuming less than your income this year. The difference between your income and your consumption is the amount of your savings. Those savings, plus interest, are available to you next year, so next year you can consume in excess of your income. In part (b) of Figure 5.5 "Consumption and Saving", you are a borrower: you are consuming more than your income this year. When you borrow this year, you must repay the loan with interest next year, so your consumption next year is less than your income.

Figure 5.5 Consumption and Saving

(a) The individual is a saver this year. (b) The individual is a borrower this year.

The budget line tells you the rate at which the market allows you to substitute goods between this year and next year. This is distinct from your personal tastes about consuming this year or next year. The saver in part (a) of Figure 5.5 "Consumption and Saving" is a relatively patient person: she is willing to give up a lot of consumption this year to be able to consume more next year. The borrower in part (b) of Figure 5.5 "Consumption and Saving" is a relatively impatient person: he wants to consume a lot this year and is willing to sacrifice a great deal of future consumption.

You will sometimes hear discussions of how much individuals like to “discount the future.” This is a statement about their tastes. Someone who discounts the future a great deal is impatient. Such a person wants to consume right away, so he will give up a lot of future consumption to have more today. Someone who discounts the future only a little is patient. Such a person is willing to give up consumption today even if she gets only a little extra consumption in the future. Economists pass no judgment on whether it is better to be impatient or thrifty. These are matters of personal preference.

The Timing of Income

Interestingly, the timing of your income turns out not to matter for your choice of consumption, which is illustrated in Figure 5.6 "The Timing of Income".

Figure 5.6 The Timing of Income

The timing of income is irrelevant to the consumption choice. Here, one individual has low income this year and high income next year, while the opposite is true for the other individual. However, the discounted present value of income is the same in both cases. If they both have the same tastes, they will choose the same consumption point.

Suppose that the nominal interest rate is 10 percent and that the price level is $10 in both periods. This means that the inflation rate is zero, so—from the Fisher equation—the real interest rate is also 10 percent. Now imagine that there are two individuals who have identical tastes. One of them earns income of $40,000 this year and $22,000 next year, so real income (nominal income divided by the price level) is therefore 4,000 this year and 2,200 next year. The other person earns $20,000 this year and $44,000 next year, yielding a real income of 2,000 this year and 4,400 next year. Both of these individuals share the same budget line (see Figure 5.6 "The Timing of Income"). This is because the discounted present value of their nominal income is the same: $60,000. (Check to make sure you understand why this is true.) For example, suppose that the preferred point of both individuals is to consume the same amount in each year. Then they can both consume approximately 3,143 units of consumption in each period.

Let us see how this works. Because the price level is $10, this amount of consumption costs $31,430 in each period. The first individual takes her income of $40,000 and saves $8,570 by putting it in the bank. This saving earns 10 percent interest, so she gets an additional $857. She thus has income in the following year equal to $22,000 + $8,570 + $857 = $31,427. This allows her to buy 3,142.7 units of consumption goods. The second individual needs to borrow $11,430 to add to his income this year. Next year, he must repay this amount plus 10 percent interest (that is, another $1,143). So his income next year is $44,000 − $11,430 − $1,143 = $31,427. So one individual must save to reach her preferred consumption bundle, while the other must borrow to reach his. Yet because they have the same discounted present value of income and the same tastes, they will consume the same bundle of goods.

Keep in mind that our discussion so far ignores uncertainty. We assumed that both individuals know their current and future income with certainty. Just as importantly, we have supposed that a bank is confident that the borrower will have sufficient income next year to repay the loan. In a world of uncertainty, we do not know for sure how much money we will have next year, and lenders worry about the possibility that people might not make good on their loans. Later in the chapter, we explain more about decision making in an uncertain world.

Lifetime Budget Constraint

So far, we have worked everything out in terms of a two-period example. The two-period budget constraint tells us how income and consumption are linked over time. In reality, of course, you make these decisions with longer time horizons, and you can save or borrow for multiple years. But the same fundamental insight holds. If you save this year, then you will have extra resources to spend at some future date. If you borrow this year, then you will have to repay that loan sometime in the future, at which time you will have fewer resources to spend.

Again, it is important to be consistent in calculating the discounted present values in this expression. We have written the equation in terms of (real) consumption and (real) income, which means that the real interest factor must be used for discounting. An alternative is to measure both consumption and income in nominal terms and then use the nominal interest factor for discounting. There is a useful special case where real interest rates are zero, in which case it is legitimate simply to add income and consumption in different years. Thus the lifetime budget constraintThe discounted present value of lifetime consumption must equal the discounted present value of lifetime income. becomes

Although the principles of decision making are the same whether we are thinking about 2 months, 2 years, or an entire lifetime, it is obviously harder to make decisions over a 30-year horizon than over a 30-day horizon. One reason is that, over longer time horizons, we are more likely to face uncertainty. We don’t know what our income will be 30 years from now, and we don’t know our tastes. But even without that uncertainty, we may not always make good decisions.

In particular, economists and psychologists have discovered that we do not view choices involving the near future the same way as we view distant choices. For example, suppose an individual is given a choice between 1 cookie today or 2 cookies tomorrow. If he is impatient (or hungry), he is likely to choose the single cookie today. But if the same individual is given a choice between 1 cookie in 30 days or 2 cookies in 31 days, he or she may very well choose the 2-cookie option. Yet after 30 days have gone by, that person will be confronting the earlier decision, wishing that he or she could have the 2 cookies today.

Another way of saying this is that our decisions are not always consistent over time: our future selves may wish that our current selves had displayed more self-control. For example, we may choose to consume a lot today—instead of saving—and then regret that decision when we are older. Indeed, people often engage in tricks to get around their lack of self-control. For example, some people have a separate bank account for their savings, so they are less tempted to spend that money. Governments also take actions that compensate for our lack of self-control. Social security is in some ways a “forced saving” scheme: the government takes money from us when we are working but pays us money when we are retired.

There is a new and exciting field of economics called “neuroeconomics” that tries to understand the processes in the brain that underlie economic decision making. This field, while still very much in its infancy, promises to help us understand why the economic theory of how we make choices often works well, and why it sometimes does not. Some recent research suggests that different brain processes may deliver conflicting messages when making choices over time. Some processes are deliberative, in line with the economic model, while others are more impulsive. It is likely that the next two decades will bring a much deeper understanding of how the brain makes decisions, perhaps leading to a richer theory of economic decision making.

Changes in Interest Rates

Whenever the real interest rate changes, then the relative price of consumption this year and next year changes. As we already know, changes in the real interest rate can come from two different sources: changes in the nominal interest rate and changes in the inflation rate. (Look back at the Fisher equation for a reminder of this.) Figure 5.7 "An Increase in the Real Interest Rate" shows the effect of an increase in the real interest rate on your budget line. The budget line becomes steeper because the opportunity cost of consumption this year increases. Notice, though, that the point at which you just consume your income in each period is still on the budget line. This is the point at which you are neither saving nor borrowing. Thus no matter what the interest rate, this point is always available to you.

Figure 5.7 An Increase in the Real Interest Rate

A change in the real interest rate changes the slope of the budget line. At any real interest rate, however, it is possible to consume exactly one’s income. So the point corresponding to no saving or borrowing is always available, no matter what the real interest rate. An increase in the real interest rate therefore causes the budget line to become steeper and rotate through the income point.

Changes in relative prices lead to income and substitution effects. To understand the effect of an increase in the real interest rate, we must look at both effects.

• Substitution effect. An increase in the real interest rate makes consumption next year look more attractive relative to consumption this year. This encourages saving and discourages borrowing.
• Income effect. The income effect is somewhat more complicated. Look again at Figure 5.7 "An Increase in the Real Interest Rate". Savers are made better off by an increase in interest rates because, to the left of the income point, the new budget line lies outside the old budget set. This encourages savers to increase consumption this year and next year. Because income this year hasn’t changed, but there is an incentive to consume more this year, we can see that the income effect discourages saving. Borrowers, meanwhile, are worse off by the increase in interest rates. To the right of the income point, the new budget line lies inside the old budget set. This encourages borrowers to decrease consumption this year and next year. This incentive to consume less tells us that the income effect discourages borrowing. In sum, the income effect gives an incentive for savers to save less and for borrowers to borrow less.

Combining the income and substitution effects and following an increase in the interest rate, borrowers have an incentive to borrow less. The substitution effect encourages saving, while the income effect discourages saving. The overall effect is ambiguous.

The evidence suggests that most people are like the individual in Figure 5.8 "Individual Loan Supply". For this person, the substitution effect dominates: the amount of saving increases as the real interest rate increases. Because an individual’s savings represent funds that can be lent out to others in the economy, we call them the individual loan supplyThe amount of saving carried out by an individual at different values of the real interest rate..

Figure 5.8 Individual Loan Supply

For savers in the economy, the effects of an increase in the real interest rate are ambiguous. The substitution effect encourages saving, but the income effect discourages saving. The evidence suggests that, on balance, the substitution effect dominates, so that savings increase. (a) In this two-period diagram, an increase in interest rates causes consumption this year to decrease. Because income this year is unchanged, savings increases. (b) The same diagram is applied to an individual supply of loans.

As the real interest rate changes, the response of individual saving is a movement along the loan supply curve. What might cause the whole curve to shift? If an individual has a higher income in the current year, this will cause the budget line to shift outward, and the person will consume more goods in the current year and more goods in the future. To consume more in the future, the person will have to save more. In this case, the supply of savings shifts outward as current income increases. This is shown in Figure 5.9 "A Shift in an Individual’s Supply of Savings".

Figure 5.9 A Shift in an Individual’s Supply of Savings

An increase in this year’s income means that an individual will save more at any given interest rate. This means that the loan supply curve for the individual shifts outward.

Choosing a Career

A decision you typically make around the time that you graduate is your choice of a career. What makes the choice of a career so consequential is the fact that it can be very costly to switch from one career to another. For example, if you have trained as an engineer and then decide you want to be a lawyer, you will have to give up your engineering job (and give up your salary as well) and go to law school instead.

Suppose you are choosing among three careers: a lawyer, an insurance salesperson, or a barista. To make matters simple, we will work out an example with only two years. Table 5.2 "Which Career Should You Choose?" shows your earnings in each year at each occupation. In the first year in your career as a lawyer, we suppose that you work as a clerk, not earning very much. In the second year, you join a law firm and enjoy much higher pay. Selling insurance pays better than the legal career in the first year but worse in the second year. Working as a barista pays less than selling insurance in both years.

It is obvious that, if you care about the financial aspect of your career, you should not be a barista. (You would choose that career only if it had other benefits—such as flexible working hours and lack of stress—that outweighed the financial penalty.) It is less obvious whether it is better financially to work as a lawyer or as an insurance salesperson. Over the two years, you earn $65,000 as a lawyer and $63,000 as an insurance seller. But as we have already explained, simply adding your income for the two years is incorrect. The high salary you earn as a lawyer comes mostly in the second year and must be discounted back to the present.

To properly compare these careers, you should use the tool of discounted present value. With this tool, you can compare the income flows from the different occupations. Table 5.3 "Comparing Discounted Present Values of Different Income Streams" shows the discounted present value of the two-year flow of income for each career, assuming a 5 percent interest rate (that is, an interest factor equal to 1.05). Look, for example, at the lawyer’s income stream:

Similarly, the discounted present value of the income stream is $61,286 for the insurance salesperson and $37,048 for the barista. So if you are choosing your career on the basis of the discounted present value of your income stream, you should pick a career as a lawyer.

This conclusion, however, depends on the interest rate used for discounting. Table 5.4 "Discounted Present Values with Different Interest Rates" adds another column, showing the discounted present values when the interest rate is 10 percent. You can see two things from this table: (1) The higher interest rate reduces the discounted present value for all three professions. If the interest rate increases, then future income is less valuable in present value terms. (2) The higher interest rate reverses our conclusion about which career is better. Selling insurance now looks better than being a lawyer because most of the lawyer’s earnings come in the future, so the discounting has a bigger effect.

Of course, what you might really like to do is to sell insurance for the first year and work as a lawyer in the second year. This evidently would have higher income. Sadly, it is not possible: it is almost impossible to qualify for a high-paying lawyer’s job without investing a year as a law clerk first. Changing occupation can be very costly or even impossible if you don’t have the right skills. So choosing a career path means you must look ahead.

Going to College

If you are like most readers of this book, you have already made at least one very important decision in your life. You have chosen to go to college rather than taking a job immediately after graduating from high school. Ignoring the pleasures of going to college—and there are many—there are direct financial costs and benefits of a college education.

Think back to when you were deciding whether to go to college or to start work immediately. To keep our example from being too complicated, we again look at a two-year decision. What if you could obtain a college degree in one year, at a tuition cost of $13,000, and the interest rate is 5 percent annually? Your earnings are presented in Table 5.5 "Income from Going to College versus Taking a Job". In your year at college, you would earn no income, and you have to pay the tuition fee. In the following year, imagine that you can earn $62,143 working as a lawyer. Alternatively, you could bypass college and go to work as a barista, earning $10,000 in the first year and $37,048 in the second year. (We are assuming, as before, that you know these figures with certainty when you are making your decision.)

Going to college is an example of an investment decision. You incur a cost in the year when you go to college, and then you get a benefit in the future. There are two costs of going to college: (1) the $13,000 tuition you must pay (this is what you probably think of first when considering the cost of going to college) and (2) the opportunity cost of the income you could have earned while working. In our example, this is $10,000. The explicit cost and the opportunity cost together total $23,000, which is what it costs you to go to college instead of working in the first year.

By the way, we do not think about living expenses as a cost of going to college. You have to pay for food and accommodation whether you are at college or working. Of course, if these living expenses are different under the two scenarios, then you should take this into account. For example, if your prospective college is in New York City and has higher rental costs than in the city where you would work, then the difference in the rent should be counted as another cost of college.

The benefit of going to college is the higher future income that you enjoy. In our example, you will earn $62,143 in the following year if you go to college, and $37,048 if you do not. The difference between these is the benefit of going to college: $62,143 − $37,048 = $25,095. Even though this is greater than the $23,000 cost of going to college, we cannot yet conclude that going to college is a good idea. We have to calculate the discounted present value of this benefit. Suppose, as before, that the interest rate is 5 percent. Then

We can conclude that, with these numbers, going to college is a good investment. It is worth $900 more in discounted present value terms.

We could obtain this same conclusion another way. We could calculate the discounted value of the two-year income stream for the case of college versus barista, as in Table 5.6 "Income Streams from Going to College versus Taking a Job". We see that the discounted value of the income stream if you go to college is $46,184, compared to $45,284 if you work as a barista. The difference between these two is $900, just as before.

You might have noticed that the figures we chose as “income in the year after college” in Table 5.5 "Income from Going to College versus Taking a Job" are the same as the numbers that we calculated in Table 5.3 "Comparing Discounted Present Values of Different Income Streams". The numbers in Table 5.3 "Comparing Discounted Present Values of Different Income Streams" were themselves the result of a discounted present value calculation: they were the discounted present value of a two-year income stream. When we compare going to college with being a barista, we are therefore calculating a discounted present value of something that is already a discounted present value. What is going on?

To understand this, suppose you are deciding about whether to go to college in 2012. If you do go to college, then in 2013 you will decide whether to be a lawyer, an insurance salesman, or a barista. If you decide on the legal career, then you will be a law clerk in 2013, and you will earn the high legal salary in 2014. Our analysis in Table 5.3 "Comparing Discounted Present Values of Different Income Streams" is therefore about the choice you make in 2013, thinking about your income in 2013 and 2014. Table 5.3 "Comparing Discounted Present Values of Different Income Streams" gives us the discounted present value in 2013 for each choice. If we then take those discounted present values and use them as “income in the year after college,” as in Table 5.6 "Income Streams from Going to College versus Taking a Job", we are in fact calculating the discounted present value, in 2012, of the flow of income you receive in 2012, 2013, and 2014.

If you think carefully about this, you will realize that

This is the same answer that we got before. As this example suggests, you can calculate discounted present values of long streams of income, including income you will receive many years in the future.The toolkit gives a more general formula for calculating the discounted present value. (See the more formal presentation of discounted present value at the end of Chapter 5 "Life Decisions", Section 5.4 "Embracing Risk".)

Economists have worked hard to measure the return on investment from schooling: “Alan B. Krueger, an economics professor at Princeton, says the evidence suggests that, up to a point, an additional year of schooling is likely to raise an individual’s earnings about 10 percent. For someone earning the national median household income of $42,000, an extra year of training could provide an additional $4,200 a year. Over the span of a career, that could easily add up to $30,000 or $40,000 of present value. If the year’s education costs less than that, there is a net gain.”Anna Bernasek, “What’s the Return on Education?” Economic View, Business Section, New York Times, December 11, 2005, accessed February 24, 2011, http://www.nytimes.com/2005/12/11/business/yourmoney/11view.html. Notice several things from this passage. First, the gains from education appear as an increase in earnings each year. So even if a 10 percent increase in earnings does not seem like a lot, it can be substantial once these gains are added over one’s lifetime. Second, Krueger is careful to use the term present value. Third, the number given is an average. Some people will benefit more; others will benefit less. Equally, some forms of schooling will generate larger income gains than others. Fourth, Krueger correctly notes that the present value must be compared with the cost of education, but you should remember that the cost of education includes the opportunity cost of lost income.

Table 5.7 "Return on Education" provides some more information on the financial benefits of schooling.US Census Bureau, “Income, Earnings, and Poverty from the American Community Survey,” 2010, table 5, accessed February 24, 2011, http://www.census.gov/hhes/www/poverty/publications/acs-01.pdf. The table shows average income in 2004. There is again evidence of a substantial benefit from schooling. Male college graduates, on average, earned more than $21,000 (68 percent) more than high school graduates, and female college graduates earned more than $16,000 (78 percent) more than high school graduates. The table shows that women are paid considerably less than men and also that the return on education is higher for women.

The presence of such apparently large gains from education helps explain why economists often suggest that education is one of the most important ingredients for the development of poorer countries. (In poorer countries, we are often talking not about the benefit of going to college but about the benefit of more years of high school education.) Moreover, the benefits from education typically go beyond the benefits to the individuals who go to school or college. There are benefits to society as a whole as well.

However, you should be careful when interpreting numbers such as these. We cannot conclude that if you randomly selected some high school graduates and sent them to college, then their income would increase by $17,000. As we all understand, individuals decide whether to go to college. These decisions reflect many things, including general intelligence, the ability to apply oneself to a task, and so on. People who have more of those abilities are more likely to attend—and complete—college.

One last point: we conducted this entire discussion “ignoring the pleasures of going to college.” But those pleasures belong in the calculations. Economics is about not only money but also all the things that make us happy. This is why we occasionally see people 60 years old or older in college. They attend not as an investment but simply because of the pleasure of learning. This is not inconsistent with economic reasoning or our discussion here. It is simply a reminder that your calculations should not only be financial but also include the all the nonmonetary things you care about.

The Effects of Interest Rates on Labor Supply

After you have decided whether or not to go to college and have chosen your career, you will still have plenty of decisions to make involving discounted present value. Remember that you have a lifetime budget constraint, in which the discounted present value of your income, including labor income, equals the discounted present value of consumption.

Your labor income is partly under your control. If you have some choice about how many hours to work, then your individual labor supply curve depends on the real wage, as shown in Figure 5.10 "Individual Labor Supply".Chapter 4 "Everyday Decisions" explains the individual supply of labor. The labor supply curve illustrates the fact that as the real wage increases, you are likely to work more. Labor supply, like the supply of loans that we considered previously, is driven by substitution and income effects. As the real wage increases,

• the opportunity cost of leisure increases, so you have an incentive to work more (substitution effect); and
• you have more income to spend on everything, including leisure, so you have an incentive to consume more leisure and work less (income effect).

Figure 5.10 Individual Labor Supply

An increase in the real wage encourages an individual to work more. The labor supply curve slopes upward.

When you are making a decision about how much to work over many periods of time, your choice is more complicated. How much you choose to work right now depends not only on the real wage today but also on the real wage in the future and on the real interest rate. This is because you work both today and in the future to earn the income that goes into your lifetime budget constraint. If you think it is likely to be harder to earn money in the future, then you will probably decide to work more today. If you think it will be easier to earn money in the future, then you might well decide to work less today.

It is easiest to see how this works with an example. Suppose you are a freelance construction worker in Florida in the aftermath of a hurricane. There is lots of work available, and construction firms are paying higher than usual wages. You realize that you can earn much more per hour of work right now compared to your likely wage a few months in the future. A natural response is to work harder now to take advantage of the unusually high wages.

We can understand your decision in terms of income and substitution effects. The higher wage leads to the usual substitution effect. But because the change in the wage is only temporary, and because you are thinking about your wages over your lifetime, it does not have a large income effect. In this case, therefore, we expect the substitution effect to strongly outweigh the income effect.

Interest rates may also influence your decision about how hard to work. If interest rates increase, then the gains from working today increase as well. If you save money at high interest rates, you can enjoy more consumption in the future. High interest rates, like temporarily high current wages, increase the return to working today compared to working in the future, so you are likely to work more today.

The Demand for Durable Goods

Some of the products we purchase, such as milk or a ticket to a football game, disappear as soon as they are consumed. Other goods last for a long time and are, in effect, consumed over and over. Some examples are a bicycle, a car, and a microwave oven.

Goods that last over many uses are called durable goodsGoods that last over many uses., while those that do not last very long are called nondurable goodsGoods that do not last very long.. There is no hard-and-fast distinction between durable and nondurable goods. Many everyday items, such as plates, books, T-shirts, and downloaded music, are used multiple times. In economic statistics, however, the term durable is reserved for larger items that are bought only occasionally and that typically last for many years. Cars and kitchen appliances are classified as durable goods, but blue jeans and haircuts are not, even though they are not consumed all at once.

Because durable goods last a long time, making decisions about purchasing a durable good requires thinking about the future as well as the present. You must compare the benefits of the durable good over its entire lifetime relative to the cost you incur to pay for the durable now. A durable good purchase is typically a unit demand decision—you buy either a single unit or nothing. For unit demand, your decision rule is simple: buy if your valuation of the good exceeds the price of the good. (Remember that your valuation is the maximum you would be willing to pay for the good.) In the case of durable goods, there is an extra twist: your valuation needs to be a discounted present value.

The idea is that you obtain a flow of services from a durable good. You need to place a valuation on that flow for the entire lifetime of the durable good. Then you need to calculate the discounted present value of that flow of services. If this discounted present value exceeds the price of the good, you should purchase it.

Suppose you are thinking of buying a new car that you expect to last for 10 years. You need to place a valuation on the flow of services that you get from the car each year: for example, you might decide that you are willing to pay $3,000 each year for the benefit of owning the car. To keep life really simple, let us think about a situation where the real interest rate is zero; this is the special case where it is legitimate to add these flows. So the car is worth $30,000 (= $3,000 per year × 10 years) to you now. This means you should be willing to buy the car if it costs less than $30,000, and you should not buy it otherwise.What if you think you might sell the car before it wears out? In this case, the value of the car has two components: (1) the flow of services you obtain while you own it, and (2) the price you can expect to obtain when you sell it. When you buy a durable good, you are purchasing an asset: something that yields some flow of benefits over time and that you can buy and sell. In general, the value of an asset depends on both the benefits that it provides and the price at which it can be traded. We examine these ideas in much more detail in Chapter 10 "Making and Losing Money on Wall Street".

If real interest rates are not zero, then spending on durable goods will depend on interest rates. As interest rates increase, the future benefits of the durable good become smaller, in terms of discounted present value. This means that durable goods become more expensive relative to nondurable goods. Thus the demand for durable goods decreases as interest rates increase.

One way to understand this is to realize that it is often easy to defer the purchase of a durable good. New durable goods are frequently bought to replace old goods that are wearing out. People buy new cars to replace their old cars or new washing machines to replace their old ones. If interest rates are high, you can often postpone such replacement purchases; you decide whether you can manage another year with your old car or leaking washing machine. As a result, spending on durable goods tends to be very sensitive to changes in interest rates.

These examples of discounted present value illustrate one key point: whenever you are making economics decisions about the future—be it what career to follow, when it is best to work hard, or if you should buy a new car—your decisions depend on the rate of interest. Whenever the rate of interest is high, future costs and benefits are substantially discounted and are therefore worth less in present value terms. High interest rates, in other words, mean that you put a lot of weight on the present relative to the future. When the rate of interest decreases, the future should play a larger role in your decisions.

Risk and Uncertainty

Let us begin by making sure we understand what risk and uncertainty mean. (Here we will use the terms more or less interchangeably, although people sometimes reserve the term uncertainty for cases where it is hard to quantify the risks that we face.) Probably the simplest example of risk is familiar to us all: the toss of a coin. Imagine flipping a coin five times. Each time, the outcome will be either a head or a tail. Table 5.8 "Coin-Flipping Experiment" shows an example of such an experiment. In this experiment, the outcome was three heads and two tails. For each flip of the coin, there was uncertainty about the outcome. We did not know ahead of time whether there would be heads or tails. The outcome reported in Table 5.8 "Coin-Flipping Experiment" is only one example. If you were to carry out this experiment right now, you would almost certainly end up with a different outcome.

Coin tosses are special because the flips of the coin are independent of each other (that is, the history of previous tosses has no effect on the current toss of a coin). In Table 5.8 "Coin-Flipping Experiment", the coin was not more likely to come up tails on the third toss because the previous tosses were both heads. Even if you have 100 heads in a row, this does not affect the outcome of the 101st toss of the coin. If you think that the coin is “fair,” meaning that heads and tails are equally likely, then the 101st toss is still just as likely to be heads as tails. By contrast, the likelihood that it will be raining an hour from now is not independent of whether or not it is raining at this moment.

Financial Risk and Expected Value

Some of the risks that we confront are nonfinancial. An example of nonfinancial uncertainty is the risk that you might break your ankle playing basketball or the possibility that your favorite sporting team will win a big game and make you happy. Here, we will focus on financial uncertainty, by which we mean situations where there is money at stake. In other words, we are thinking about risks where you can measure the implications in monetary terms. An obvious example is the money you could win or lose from buying a lottery ticket or playing poker. Another is the money you would have to pay for repairs or medical expenses following a car accident. Another is the gains or losses from buying stocks, government bonds, or other financial assets. Another is the income you would lose if you were laid off from your job.

When we evaluate risky situations, we must have a way of describing the kinds of gambles that we confront. In general, we do this by listing all the possible outcomes together with the likelihood of each outcome. For example, Table 5.9 "Outcomes and Probabilities from a Coin Toss" lists the outcomes and the probabilityThe percentage chance that an outcome will occur. (that is, the likelihood of each outcome) for the experiment of tossing a coin one time.

Think about rolling a normal six-sided die one time and describing outcomes and probabilities.

• We must make sure that we include every outcome. We cannot list as possible outcomes “less than or equal to 2” and “greater than or equal to 4.” Such a list ignores the possibility of rolling a 3.
• We cannot list as possible outcomes “less than or equal to 4” and “greater than or equal to 3.” These categories overlap because a roll of a 3 or a 4 would show up in both categories.
• The outcome “less than or equal to 6” has a probability of 1 because it is certain.
• The outcome “9” has a probability of 0.
• Provided we have a complete list of outcomes (for example “less than or equal to 4” and “greater than or equal to 5”), the probabilities of all the outcomes will always sum to 1. (In this case, the probability of the first outcome is 2/3, and the probability of the second outcome is 1/3.)

Now suppose you are playing a gambling game based on a toss of a coin. If the coin comes up heads, you win $1. If it comes up tails, you win $0. When we look at a situation such as this, we are often interested in how much you would get, on average, if you played the game many times. In this example, it is easy to guess the answer. On average, you would expect to win half the time, so half the time you get $1, and half the time you get nothing. We say that the expected valueThe measure of how much you would expect to win (or lose) on average, if the situation were to be replayed a large number of times. of each flip of the coin is 50 cents.

Table 5.10 "Outcomes and Probabilities from Investment in Internet Venture" gives another example of expected value. Suppose a friend is planning on establishing a small Internet business and asks you to invest $1,000. He tells you (and you believe him) that there is a 50 percent chance that the business will fail, so you will lose your money. There is a 40 percent chance that the business will just break even, so you will get your $1,000 back but nothing more. And there is a 10 percent chance that the business will be very successful, so you will earn $16,000.

In this case, the expected value of the investment is given by the following:

Thus for your investment of $1,000, you could expect to get $2,000 back on average. This seems like a good investment. It is important to remember, though, what “on average” means. You will never actually get $2,000. You will receive either $16,000, $1,000, or nothing. Even though this is a good investment on average, you might still decide that you don’t want any part of it. Yes, you might get the big net gain of $15,000. But there’s also a 50 percent chance that you will be out $1,000. The gamble might seem too risky for you.

Coin tosses are special because it is relatively easy to determine the probability of a head or a tail. This is not the case for all the types of uncertainty you might face. In some cases, financial instruments—such as the mortgage-backed securities that played a big role in the financial crisis of 2007–2009—are so complex that investors find it difficult to assess the probabilities of various outcomes.

We often do a bad job of estimating probabilities. One reason for this is because we are unduly influenced by things that we can easily bring to mind. Psychologists call this the “availability heuristic.” For example, we tend to overestimate certain causes of death, such as car accidents, tornadoes, and homicides, and underestimate others, such as diabetes, stroke, and asthma.See Paul Slovic, Baruch Fischoff, and Sarah Lichtenstein, “Facts versus Fears: Understanding Perceived Risk,” in Judgment under Uncertainty: Heuristics and Biases, ed. Daniel Kahneman, Paul Slovic, and Amos Tversky (Cambridge, MA: Cambridge University Press, 1982), 463–89. We also often do a poor job at using probabilities; in particular, we often put too much emphasis on small probabilities. For example, consider two drugs that are equally effective in treating a disease, but suppose the older drug has a 1 in 10 million chance of having a certain side effect and the newer drug has a 1 in a 100 million chance of having the same side effect. Consumers might view the new drug as much more appealing, even though the side effect was already highly improbable with the older drug.

Diversification of Risk

In many cases, we would like to find some way of getting rid of—at least to some degree—the risks that we face. One way we eliminate risk is through insurance. Sometimes we purchase insurance on the market. Sometimes our employer provides us with insurance. Sometimes the government provides us with insurance. In the following subsections, we look at many different kinds of insurance, including property insurance, unemployment insurance, and deposit insurance.We do not discuss health insurance here. In Chapter 16 "A Healthy Economy", we discuss the provision of health care and the problems of health insurance in detail.

First, though, we need to understand how and why insurance works. Suppose you have a bicycle worth $1,000, and (for some reason) you cannot purchase insurance. You think that, in any given year, there is about a 1 percent chance that your bike will have to be replaced (because it is either stolen or written off in an accident).

Now, in expected value terms, this may not look too bad. Your expected loss from an accident is $0.01 × $1,000 = $10. So on average, you can expect to lose $10 a year. But the problem is that, if you are unlucky, you are stuck with a very big expense. Most of us dislike this kind of risk.

You are complaining about this to a friend, and she sympathizes, saying that she faces exactly (and we mean exactly) the same problem. She also has a bike worth $1,000 and thinks there is a 1 percent chance each year that she will need to replace it. And that’s when you have the brilliant idea. You can make an agreement that, if either one of you has to replace your bikes, you will share the costs. So if you have to replace your bike, she will pay $500 of your costs, and if she has to replace her bike, then you will pay $500 of her costs. It is (almost exactly) twice as likely that you will have to pay something, but if you do, you will only have to pay half as much. With this scheme, your expected loss is unchanged. But you and your friend prefer this scheme because it is less risky; it is much less likely that you will have to make the big $1,000 payout.

We are implicitly assuming here that your chances of having to replace your bike are independent of the chance that she will have to replace her bike. (If you are likely to crash into her, or both of your bikes are stolen, then it is a different story.) There is also still a chance that you will both experience the unlucky 1-in-100 chance, in which case you would both still have to pay $1,000. But the likelihood of this happening is now tiny. (To be precise, the probability of both of you having an accident in the same year is 1 in 10,000 [that is, 0.0001]). This is because the probability that two independent events occur equals the probability of one multiplied by the probability of the other.)

But why stop here? If you can find two more friends with the same problem, then you can make it almost certain that you will have to pay out no more than $250. It is true that you would be even more likely to have to make a payment because you will have to pay if you or one of your friends has to replace his or her bike. But because the payment is now being shared four ways, you will have to pay only 25 percent of the expenses. This is an example of diversificationThe insight that underlies insurance in which people can share their risks., which is the insight that underlies insurance: people share their risks, so it is less likely that any single individual will face a large loss.

Diversification and insurance don’t prevent bad stuff from happening. We live in a world where bicycles are stolen; where houses are destroyed by floods, fires, or storms; where people have accidents or become ill; and so on. There is not a lot we can do about the fact that bad things happen. But we can make the consequences of these bad things easier to deal with. Insurance is a means of sharing—diversifying—these risks.

Continuing with our bicycle insurance example, suppose you could find thousands of friends who would agree to be part of this arrangement. As more and more people join the scheme, it becomes increasingly likely that you have to make a payment each year, but the amount you would have to pay becomes smaller and smaller. With a very large number of people, you would end up very close to a situation where you pay out $10 with certainty each year. Of course, organizing thousands of your friends into such a scheme would present all sorts of practical problems. This is where insurance companies come in.

Insurance companies charge you a premium (an annual payment). In return, they promise to pay you an indemnityIn an insurance contract, a value equal to the full amount of the loss minus the deductible. in the event you suffer a loss. The indemnity is usually not the full amount of the loss. The part of the loss that is not covered is called the deductibleIn an insurance contract, the value not covered in the event of a loss.. In our example, there is no deductible, and the indemnity is $1,000. An insurance company would charge you a premium equal to the expected loss of $10 plus a little extra. The extra payment is how the insurance company makes money. You and everyone else are willing to pay this extra amount in return for the removal of risk.

The idea of diversification can also be applied to investment.We discuss this in Chapter 10 "Making and Losing Money on Wall Street". Think back to our example of your friend with the Internet venture. You might not want to invest $1,000 in his scheme because it seems too risky. But if you had 100 friends with 100 similar (but independent) schemes, you might be willing to invest $10 in each. Again, you would be diversifying your risk.

Different Kinds of Insurance

There are many different kinds of insurance available to you. We briefly discuss some of the most important.

Job Choice

We have already discussed how your choice of career should be based on discounted present value, taking into account the fact that it can be costly to move from one job to another. Your choice of career also reflects how you feel about risk and uncertainty. There are numerous kinds of jobs that differ in many dimensions. When choosing a job, we pay particular attention to wages or salaries, vacation plans, health coverage, and other benefits. We also take into account the job’s riskiness.

The most severe risk is, of course, the risk of death. Every year in the United States several thousand workers suffer fatal work injuries. For most of the last decade, this number has been between about 5,000 and 6,000, or the equivalent of roughly 4 deaths for every 100,000 workers. Figure 5.11 "Work Fatalities in the United States" shows data on work-related deaths in the United States for 2006–9.The data come from Occupational Safety and Health Administration, “Census of Fatal Occupational Injuries,” accessed February 24, 2011, http://stats.bls.gov/iif/oshwc/cfoi/cfch0008.pdf. The Occupational Safety and Health Administration (OSHA) is the federal agency that monitors workplace safety. The fatality rate has generally been declining over time. In the early 1990s, the fatality rate was in excess of 5 deaths for every 100,000 workers; in 2009, the fatality rate was 3.3.

Figure 5.11 Work Fatalities in the United States

Source: US Department of Labor, Occupational Safety and Health Administration, http://stats.bls.gov/iif/oshwc/cfoi/cfch0008.pdf.

The fatality rate in the United States is high relative to many other developed countries. For example, the corresponding rate in England in 2006 was 0.8 per 100,000 workers.See Health and Safety Executive, “Fatal Injury Statistics,” accessed March 14, 2011, http://www.hse.gov.uk/statistics/fatals.htm. Care must be taken when comparing international data because they are not always exactly comparable. Most importantly, European Union statistics exclude road traffic accidents, which account for about 43 percent of US deaths. Correcting for this, the US figures are similar to the European Union average. Figure 5.12 "Work Fatalities in Europe" shows the work-related fatalities for countries in the European Union. Most importantly for the current discussion, the fatality rate varies significantly across jobs. In the United States, “Agriculture and mining recorded the highest fatal work injury rates among the major industry sectors in 2005—32.5 fatalities per 100,000 workers for agriculture and 25.6 fatalities per 100,000 workers for mining.” In the European Union, construction, agriculture, and transportation are the most dangerous sectors.See US Department of Labor Bureau of Labor Statistics, “National Census of Fatal Occupational Injuries in 2005,” accessed March 14, 2011, http://www.bls.gov/iif/oshwc/cfoi/cfnr0012.txt and Health and Safety Executive, “European Comparisons,” accessed March 14, 2011, http://www.hse.gov.uk/statistics/european/fatal.htm.

Figure 5.12 Work Fatalities in Europe

In the European Union, the average work-related fatality rate is lower than in the United States, although some countries—most notably Portugal—have higher rates. The lowest rate in the European Union is in Great Britain.

Source: Health and Safety Executive, Great Britain: http://www.hse.gov.uk/statistics/european/fatal.htm.

The risk of death is not the only job risk. Jobs also differ in terms of their risk of injury. In some cases, these injuries can have a severe impact on a person’s quality of life; in other cases, they may prevent an individual from working in the future. Professional athletes and other performers face the risk of injuries that can end their careers. These individuals sometimes buy insurance to help mitigate some of these risks. In 2006, for example, pop star Mariah Carey purchased a $1 billion insurance policy on her legs after signing up for an advertising campaign (“Legs of a Goddess”) with the Gillette shaving company. Bruce Springsteen’s voice is insured for $5.6 million.See starpulse.com, “Mariah Carey Takes Out $1 Billion Insurance Policy For Her Legs,” accessed March 14, 2011, http://www.starpulse.com/news/index.php/2006/05/30/mariah_carey_takes_out_1_billion_insuran for an account of Ms. Carey’s insurance policy; Paul Bannister, “World's Biggest Insurer Takes on All Risks,” accessed March 14, 2011, http://www.bankrate.com/brm/news/insurance/old-lloyds1.asp, details a number of unusual insurance policies.

Riskier jobs generally pay more. A firm that exposes workers to more risk must compensate them for that risk. A compensating wage differentialThe amount in excess of the normal wage paid to compensate a worker for undesirable aspects of a job. is any difference in pay received by identical workers doing different jobs. (By “identical” we mean workers with comparable education, skills, experience, and so on.) Jobs that are unpleasant or dangerous will typically pay higher wages to compensate workers for the negative aspects of their jobs.

To the extent workers do not like to face risks, jobs that are viewed as riskier tend to pay more on average. For example, a recent study found that nurses who were more likely to be exposed to the AIDS virus (HIV) received higher wages than comparable nurses who were less likely to be exposed.Jeff DeSimone and Edward J. Schumacher, “Compensating Wage Differentials and AIDS Risk” (NBER Working Paper No. 10861, November 2004), accessed March 14, 2011, http://www.nber.org/papers/w10861.

Asset Portfolio Choice

Young people’s portfolios of assets are usually very simple: a typical college student might have only a checking account and a savings account. As you grow older, though, you will typically acquire a broader portfolio. Even if you do not directly purchase assets such as stocks and bonds, you may own them indirectly when you sign up for a pension plan. Because the return on stocks (and other assets) is uncertain, owning these assets is another type of risk you choose to take.

Owning a stock is somewhat like buying a lottery ticket. You pay some money to buy a share of the stock of some company. In return, you may be paid some dividends; at some time in the future, you may sell the stock. But at the time you buy the stock, you don’t know the payments you will receive in the future and you don’t know the future price of the stock. So by purchasing a stock, you are gambling. Whether the gamble is favorable or not depends on the price of the stock, the chance it will pay dividends in the future, and the future price. Choosing how to allocate the assets in a portfolio is a type of gamble we all make.

We cannot completely avoid this kind of gamble. Perhaps you think that putting cash in your mattress would be a way to avoid this risk, but that is not the case. Ultimately you care about what that money can buy in terms of goods and services. The real value of the money held in your mattress depends on the future prices of goods and services, which are not known to you today. The benefit of holding cash depends on the unknown inflation rate.

Buying a Lottery Ticket

Some people, at some times, are eager and willing to engage in risky activities. People engage in extreme sports, where the danger appears to be part of the attraction. People go to Las Vegas or to Monaco to gamble. In many countries, citizens can purchase a wide variety of lottery tickets sold by their governments. This is a form of gambling: you buy a ticket and if you have the lucky number, then you get a (sometimes large) prize. If you do not have the lucky number, your money is gone.

The existence of lotteries and other kinds of gambling seems like a puzzle. If people are risk-averse, then they are supposed to want to get rid of risk. The purchase of a lottery ticket is the exact opposite: you give up a sure thing (the price of the ticket) for an uncertain outcome. Unlike the purchase of insurance, which is a way to avoid risk, buying a lottery ticket is a demand for a gamble. Why do so many people buy lottery tickets? Why do governments sell them?

Do lottery tickets have an expected value that exceeds the cost of the ticket? If the difference is big enough, then even a risk-averse person might want to buy a ticket. Consider a very simply lottery. Suppose there is one fixed prize, and there is a probability that you win the prize. Then your expected gain is just the probability of winning times the prize:

Using this equation, you can determine whether the price for a lottery ticket is high or low. If the price of the ticket exceeds the expected gain from buying the ticket, then the ticket is not a good deal. But if the price is low relative to the expected gain, then you may want to accept the risk and buy the ticket.

Let us look at an example. One US lottery is called Powerball. On February 18, 2006, the prize was worth $365 million to the winner. The chance of getting the jackpot was 1 in 988,172,368.This is based on five balls selected ranging from 1 to 55 and a powerball ranging 1 to 42. See the Powerball site (http://www.usamega.com/powerball-howtoplay.htm) for details on this game. See also the odds calculator at CSGNetwork.com, “The Ultimate Lottery Games Odds Calculator,” accessed March 14, 2011, http://www.csgnetwork.com/oddscalc.html. The expected value of a ticket at that time was the value of the prize times the probability of winning: $\$365\text{ million}\times \frac{\text{1}}{\text{988,172,368}}=\$\text{0}\text{.37—}$far less than the dollar price of the ticket. Despite the huge prize, the price of a ticket far exceeded its expected value.

Another perspective on the lottery is from the viewpoint of the government selling these tickets. Consider the Texas lottery.Texas Lottery home page, accessed March 14, 2011, http://www.txlottery.org/export/sites/default/index.html. The proceeds from the sale of tickets primarily support education. In 2005, about 60 percent of the income from the lottery went to payment for prizes and 28 percent went to a school fund. From the perspective of the Texas state government, selling lottery tickets is a way to fund programs. If the government is to make money on lottery tickets, then those buying the tickets must, on average, be losing money.

In fact, as this discussion suggests, the expected value of a lottery ticket is less—often substantially less—than the cost of the ticket. Why, then, do people buy lottery tickets? One possibility is that they simply enjoy gambling. This means that, at least with respect to these types of gambles, they are risk-loving rather than risk-averse. The pleasure of a lottery ticket is, among other things, the license to dream. Another possibility is that individuals overestimate their chances of winning.

The Gains from Trade from a Single Transaction

Suppose you are interested in buying a car. You go to craigslist in your area and search through offers to sell cars. These offers typically provide lots of information about the product, usually including photos and a price. If you want to inquire about a particular car, you can contact the seller. If you want to buy the car, you can accept the seller’s offer. If you want to negotiate, you can do so as well. To get at the heart of this kind of exchange, let us first take a simple case where there is a single seller and a single buyer.

Economists generally think that individuals make decisions in their own self-interests. If a seller is willing to sell a good at a given price, and a buyer is willing to buy at that price, our presumption is that this exchange makes them both better off. This deceptively simple idea is the very heart of economics: voluntary trade makes both participants better off. The word voluntary matters here. We are supposing that both people freely enter into this trade. If two people make a deal of their own free will and if they are rational, in the sense that they can make decisions in their own best interests, then the deal must make them both better off.

The demand for a car is an example of a unit demand curve because you are deciding whether or not to buy at all rather than how much you should buy.See Chapter 4 "Everyday Decisions" for more discussion. The buyer has a valuation for the good, which represents the most he would be willing to pay for it. For example, suppose you see a used car on craigslist, and your valuation of this car is $3,000. This means that you would be equally happy either having the car and forfeiting $3,000 worth of other goods and services or not having the car. Figure 6.3 "The Buyer’s Valuation" shows what your demand curve looks like in this case. You are choosing to buy either zero units or one unit, so if the price is above your valuation, you do not buy the good, whereas if the price is below your valuation, you buy the car.

Figure 6.3 The Buyer’s Valuation

The buyer follows the decision rule: “Buy if the price is less than the valuation.”

If your valuation were $3,000, then you would, of course, prefer to pay much less. If the car is for sale for $2,990, then it is true that you would be better off buying the car than not, but you won’t get much out of the deal. You would be happier only to the tune of $10 (more precisely, $10 worth of goods and services). If the car is for sale for $2,400, then you will be happier by an amount equivalent to $600 worth of goods and services. On the other hand, if the car were for sale for $3,001, you definitely would not want to buy at that price. Buying the car would actually make you slightly less happy.

The seller also has a valuation of the car. The seller is not willing to sell it at any price. For example, if her valuation is $2,000, she is equally happy keeping the car or not having the car and having an extra $2,000 worth of goods and services. If she can sell the car for more than $2,000, she will be better off. She won’t sell the car for less than $2,000 because then she would be less happy than before. We can show the seller’s willingness to sell in a way analogous to the buyer’s willingness to buy. Figure 6.4 "The Seller’s Valuation" shows that she will not sell the car at a price less than $2,000, but she will sell once the price is greater than $2,000.

By analogy to unit demand, we call this the unit supply curveA supply curve in which the buyer sells either zero units or one unit of a good but no more than one unit.. It tells us the price at which she is willing to sell. Below her valuation, she is unwilling to supply to the market. Above her valuation, she is willing to sell the good. Whereas the buyer’s valuation is the absolute maximum that the buyer is willing to pay, the seller’s valuation is the absolute minimum that the seller is willing to accept.

Figure 6.4 The Seller’s Valuation

The seller follows the decision rule: “Sell if the price is greater than the valuation.”

The buyer’s valuation in our example is larger than the seller’s valuation. This means it is possible to make both the buyer and the seller better off. The mere fact of transferring a good from someone who values it less to someone who values it more is an act that creates value in the economy. We say that there are gains from trade available here.

In this example, therefore, the total surplusA measure of the gains from trade, equal to the buyer’s valuation minus the seller’s valuation. is $1,000. This is the value created in the economy by the simple fact of transferring the car from a seller who values it less to a buyer who values it more. Figure 6.5 "Buyer and Seller Valuations" shows this graphically by combining the unit demand curve and the unit supply curve.

Figure 6.5 Buyer and Seller Valuations

The total surplus from a transaction is equal to the buyer’s valuation minus the seller’s valuation. Graphically, total surplus can be represented as a rectangle. The height of the rectangle is the difference in the valuations. The base of the rectangle is 1 because only one unit is being traded.

The buyer wants the price to be as low as possible, whereas the seller wants the price to be as high as possible. If both agree on a price of $2,100, for example, the buyer gets most of the surplus, and the seller does not get very much. If they agree on a price of $2,900, the situation is reversed: most of the benefit goes to the seller. The distribution of the value created depends on the price. Either way, though, they are both made better off by the trade, and in both cases the total surplus is the same (Figure 6.6 "The Distribution of Total Surplus").

Figure 6.6 The Distribution of Total Surplus

The distribution of surplus between the buyer and the seller depends on the price. A low price means that the buyer will get most of the surplus, while a high price means that the seller will get most of the surplus. The total surplus, however, is the same no matter what the price.

Economic Efficiency

When the buyer purchases the car from the seller, there is a reallocation of society’s resources. Dollars have gone from the buyer to the seller, and the car has gone from the seller to the buyer. Economists have developed a specific criterion, called efficiencyThe basis that economists use for judging the allocation of resources in an economy., for evaluating the way in which resources are allocated in a society.

It is actually easier to understand efficiency by looking at its opposite. Economists say that an allocation of resources is inefficient if there is some way to reallocate those resources that will make some people better off (that is, happier) without making anyone else worse off. For example, think about the situation where the buyer and seller have not traded the car. This allocation is inefficient. The buyer places a greater value on the car than does the seller, so it is inefficient for the car to remain with the seller. Any rearrangement of resources that makes some people better off without making anyone else worse off is welfare improving.

Before the buyer and the seller trade, the allocation of resources is inefficient. However, there are many different trades that make both the buyer and the seller better off. In fact, any trade between a price of $2,000 and a price of $3,000 is welfare improving. The only thing that matters for economic efficiency is that a trade takes place, so the gains from tradeThe total surplus from a trade. can be realized. No matter how the surplus is distributed between the buyer and the seller, the outcome is efficient as long as the trade occurs.

Determining a Price on craigslist

We now know that as long as the buyer’s valuation for a good exceeds the seller’s valuation, there are potential gains from trade. We have not yet explored the mechanisms that allow trade to occur, nor have we explained what determines the price at which trades occur. To begin with, we ignore the possibility of bargaining. Then there are only two steps for selling an item on craigslist:

1. The seller of an item posts a price (makes a take-it-or-leave-it offer).
2. The buyer either accepts or rejects the offer.

If the buyer accepts the seller’s offer, then an exchange is made. But what offer will the seller make? The answer depends on how much the seller knows about the buyer’s valuation of the good. There are two cases to consider:

1. The seller knows the buyer’s valuation. The seller would like her surplus to be as large as possible. If she knows the buyer’s valuation, what should she do? To answer this question, she must put herself in the buyer’s shoes. If she sets a price that is greater than the buyer’s valuation, then the buyer will reject the offer. But as long as the price is less than the buyer’s valuation, the buyer will accept the offer. With this in mind, the seller will set a price slightly less than the buyer’s valuation to capture almost the entire surplus. In our example, the seller should put the car on sale for $2,999. The seller gets $999 worth of surplus, and the buyer gets $1. (Does it matter if the buyer also knows the seller’s valuation? As a matter of pure economic theory, the answer is no. The buyer should be willing to buy provided he is getting some surplus—even if it is very little. After all, something is better than nothing. However, if the buyer knows that the seller is getting a lot of surplus, he may perceive this as unfair and might even choose not to buy out of spite. In reality, sellers often set a lower price, “giving away” some of the surplus to the buyer, to avoid this possibility.Technically, a take-it-or-leave-it offer is an example of an ultimatum game, which is discussed in Chapter 13 "Superstars".)
2. The seller does not know the buyer’s valuation. This case is more likely and also much harder. The seller must trade off two different concerns. If she picks too high a price, then there is a risk of not making a sale at all. But the lower the price, the less surplus she gets in the event of a sale. There is no simple rule to know what price she should set. An economist looking from the outside finds this case more worrying than the first because it is possible that the gains from trade will be missed. If the seller offers a price that is greater than the buyer’s valuation, then—under a take-it-or-leave-it offer—no trade takes place.

The knowledge of the buyer also matters. Suppose that the buyer knows the seller’s valuation. Then he knows that there are possible gains from trade. In this case, it is natural to think that the buyer will try to negotiate with the seller, rather than just accept or reject the seller’s offer. Indeed, if the buyer knows the seller’s valuation, then we have the reverse of the first case. If the buyer offers a price slightly above the seller’s valuation, then the buyer should be able to capture the entire surplus. We summarize this in Figure 6.7 "The Outcomes from a Take-It-or-Leave-It Offer".

In practice, the buyer is also likely to try to negotiate if the seller’s price leaves the buyer with very little surplus. Thus even though craigslist is apparently based on take-it-or-leave-it offers, a great deal of bargaining does in fact take place.

Figure 6.7 The Outcomes from a Take-It-or-Leave-It Offer

Buying on eBay

Suppose you want to purchase something, such as a leather jacket, some cycling gloves, or a cell phone; the list of things that might interest you is endless. On the eBay page, you can search for the exact item you want to buy. Your search must be specific: if you search for “cell phone,” you will find thousands of products. You need to know the exact model of phone you want, and even then you may find multiple items for sale.

Auctions on eBay have several characteristics, including the identity of the seller, the time limit on the auction, the acceptable means of payment, the means of delivery, and the reserve price.

• Seller identity. Unlike when you purchase from a store, you do not get to see the seller on eBay, and you cannot simply walk away with the good. This may concern you. After all, how do you know the seller will actually ship you the good after you have paid? How do you know if the product will work? This is a worry for you, but it is also a worry for any reputable seller. Sellers want you to trust them, so there are mechanisms to allow you to find out about sellers. On the eBay page, you can find detailed information about the seller, including a number—called a feedback score—that indicates the number of positively rated sales by that seller. If you dig a bit deeper, you can even find reviews of the performance of the seller.
• Time remaining in the auction. Online auctions have a fixed time limit. When you go to the auction site for a particular good, you will see the amount of time left in the auction. Much of the action in an auction often comes very near the end of the bidding.
• Means of payment. When you buy a good on eBay, you are not able to simply give the seller some cash. The means of payment accepted by the seller are indicated in the auction information. In many cases, sellers use an electronic payment system, such as PayPal.
• Means of delivery. The seller must have a way of shipping the good to you—perhaps via FedEx or another package delivery service. The auction specifies who pays the cost of shipping.
• Reserve price. The seller will frequently specify a minimum price, called a reserve price. As a potential buyer, however, you will not see the actual reserve price; the only information you will see is whether or not the reserve price has been reached. A natural reserve price for the seller is her valuation of the good. (More precisely, the reserve price would also include the fee that the seller must pay to eBay in the event of a sale. The only reason for a seller to set a higher valuation is if she thinks she might do better trying to auction the good again at some point in the future rather than settling for a low price in the current auction.)

You participate as a buyer in an eBay auction by placing a bid. For some products, you also have an option of clicking “Buy It Now,” where you can purchase the good immediately. In other words, sellers sometimes make a take-it-or-leave it offer as well as offer an auction. To understand the details of the bidding process, look first at the description of how to bid on eBay:

Because participants in an eBay auction are not all present to bid at the same time, eBay bids for you. All you have to do is to tell it how much you are willing to pay, and eBay takes over. This is known as “proxy bidding” or “automatic bidding.”

The exact way in which eBay bids for you is not transparent from this description. It works as follows. Once you input your maximum bid, eBay compares this to the highest existing bid. If your maximum bid is higher than the existing highest bid, then eBay raises the bid by an increment on your behalf. Unless someone bids more, you will win the auction. If someone does bid more (the maximum bid exceeds the highest bid), then you, by proxy, will respond. In this way, the highest bid increases. This process ends with the item going to the bidder with the highest maximum bid. However, the buyer does not pay the amount of the maximum bid. The buyer pays the amount of the next highest bid, plus the increment.

Let us see how this works through an example. Suppose there are two buyers who put in maximum bids of $100 and $120 for a cell phone. Suppose that the increment is $1 and the bidding starts at $50. Because the maximum bids exceed $50, the highest bid will increase by increments of $1 until reaching $100. At this point, the higher of the two maximums, $120, will cause the highest bid to increase by another increment to $101. After this, there is no further action: the other bidder effectively drops out of the auction. The item goes to the buyer who bid $120, and he pays a price of $101 (provided this exceeds the seller’s reserve price).

A Decision Rule for Bidding on eBay

Now that you understand how the auction works, you must decide how to bid. Suppose there is only one auction for the good you want (rather than multiple sellers of similar goods). In this case, there is a remarkably simple decision rule to guide your bidding.

1. Decide on your valuation of the good—that is, the most you would be willing to pay for it.
2. Bid that amount.

This seems surprising. Your first reaction might well be that it is better to bid less than your valuation. But here is the key insight: the amount you actually pay if you win the auction doesn’t depend on your bid. Your bid merely determines whether or not you win the auction.

If you pursue this strategy and win the auction, you will gain some surplus: the amount you pay will be less than the valuation you place on the good. If you don’t win the auction, you get nothing. So winning the auction is better than not winning. If you bid more than your valuation, then there is a chance that you will have to pay more than your valuation. In particular, if the second-highest bidder puts in a bid that exceeds your valuation, then you will lose surplus. So this does not seem like a good strategy. Finally, if you bid less than your valuation, there is a chance that you won’t win the auction even though you value the good more highly than anyone else. Therefore, you will lose the chance of getting some surplus. This is also not a good strategy.

Figure 6.8 "Why You Should Bid Your Valuation in an eBay Auction" illustrates one way of thinking about this. There are two possibilities: either your valuation is bigger than the highest competing bid or your valuation is smaller than the highest competing bid. We don’t have to know anything about how other bidders are making their decisions. Part (a) of Figure 6.8 "Why You Should Bid Your Valuation in an eBay Auction" shows the first case. Here, there is a risk that you will lose out on surplus that you could have received. If you bid below the competing bid, you will lose the auction and hence lose out on the surplus. The surplus is the difference between your valuation and the competing bid, minus the increment.

Figure 6.8 Why You Should Bid Your Valuation in an eBay Auction

These illustrations show why you should always bid your valuation on eBay.

Part (b) of Figure 6.8 "Why You Should Bid Your Valuation in an eBay Auction" shows the case where your valuation is less than the competing bid. Here the risk is that you will win the auction and then regret it. If you bid an amount greater than the competing bid, then you will win the auction, but the amount you will have to pay exceeds your valuation. Your loss is the difference between the competing bid and your valuation, plus the increment.

Although automatic bidding by proxy sounds very fancy, the eBay auction is really the same as “English auctions” that are familiar from television and movies. In an English auction, an auctioneer stands at the front of the room and invites bids. Bidding increases in increments until all but one bidder drops out. The winning bidder pays the amount of his bid. The winning bidder therefore pays an amount equal to the highest competing bid, plus the increment, just as in the eBay auction. The amount that she wins is her valuation minus the price she pays, just as in the eBay auction.

The bidding in an English auction can be exciting to watch; you can also have the excitement of seeing how bids evolve on eBay (at least if you are willing to keep logging on and hitting the “refresh” button). But we could also imagine that eBay could do something simpler. It could carry out a “Vickrey auction,” which is named after its inventor, the Nobel-prize-winning economist William Vickrey. In a Vickrey auction, the auctioneer (1) collects all the bids, (2) awards victory in the auction to the highest bidder, and (3) makes this person pay an amount equal to the second-highest bid.

The Vickrey auction sometimes goes by the more technical name of a second-price sealed-bid auctionAn auction in which all bidders submit a single secret bid to the auctioneer, the winner is the person who submits the highest bid, and the winner pays an amount equal to the second-highest bid.. Most people think this kind of auction sounds very odd when they first hear of it. Why make the winner pay the second-highest bid? Yet it is almost exactly the same as the eBay auction or the English auction. In those auctions, as in the Vickrey auction, the winner is the person with the highest bid, and the winner pays the amount of the second-highest bid (plus the increment). The only difference is that there is no increment in the Vickrey auction; because the increment is typically a very small sum of money, this is a minor detail.

Selling on eBay

Sellers on eBay typically provide information on the product being sold. This is often done by creating a small web page that describes the object and includes a photograph. Sellers also pay a listing fee to eBay for the right to sell products. They also specify the costs for shipping and handling. After the sale is completed, the buyer and the seller communicate about the shipping, and the buyer makes a payment. Then the seller ships the product, pays eBay for the right to sell, and pockets the remainder.

As we mentioned previously, the buyer can provide feedback on the transaction with the seller. This feedback is important to the seller because transactions require some trust. A seller who has built a reputation for honesty will be able to sell more items, potentially at a higher price.

An Economic Perspective on Auctions

As an individual participating in an auction, you have two concerns: (1) whether or not you win and (2) how much you have to pay. As economists observing from outside, there are other perspectives. Auctions play a very valuable role in the economy. They represent a leading way in which goods are bought and sold—that is, they represent a mechanism for trade.

As we have already stated, voluntary trade is a good thing because it creates value in the economy. Every transaction allows a good or service to be transferred from someone who values it less to someone who values it more. The English auction, such as on eBay, is attractive to economists because it does something more. It ensures that the good or the service goes to the person who values it the most—that is, it ensures that the outcome is efficient. It also has the fascinating feature that it induces people to reveal their valuations through their bids.

eBay is just one example of the many auctions you could participate in. There are auctions for all types of goods: treasury securities, art, houses, the right to broadcast in certain ranges of the electromagnetic spectrum, and countless others. These auctions differ not only in terms of the goods traded but also in their rules. For example, firms competing for a contract to improve a local road may submit sealed bids, with the contract going to the lowest bidder to minimize the costs of the project. Of course, other elements of the bid, including the reputation of the bidder, may also be taken into account.

Complications

The eBay auction sounds almost too good to be true. It is easy to understand, brings forth honest bids, and allocates the good to the person who values it the most. Are there any problems with this rosy picture?

Double Oral Auctions

In a double oral auctionA large number of buyers and sellers, each with potentially a different valuation of a good, negotiate with each other, one on one, to try to get a better deal., there is a large number of buyers, each of whom potentially has a different valuation of the good. There is also a large number of sellers, each of whom potentially has a different valuation of the good. Buyers and sellers negotiate with each other, one on one. If they cannot agree to a deal, either party can move on at any time and try to find someone else to bargain with.

Figure 6.9 Trading in a Pit Market

Pit-market traders at work.

© Thinkstock

Until quite recently, auctions such as this were common in many financial markets and commodity markets. These markets sometimes go by the name pit markets because buyers and sellers meet in a frenzy of activity in a trading area called the pit. Traders can hear and see the negotiations of others and often have access to the prices at which deals have been done. This means that both buyers and sellers have lots of information about what price is prevailing in the market.Chapter 10 "Making and Losing Money on Wall Street" has much more to say about these markets.

Economists have also conducted experiments in which they have put people in simulated pit markets to find out how they behave. The result is quite remarkable, but before we explain what happens, we need a framework to help us think about such markets.

Demand: Many Buyers

Suppose we are considering the purchase of a gaming console by a group of buyers. Each potential buyer has his own valuation. Some might be willing to pay as much as $700. Others might be willing to spend much less. After all, how much you are willing to pay for a gaming console depends on your income, how much you like playing, what equipment you currently own, and so on.

Each potential buyer has a unit demand curve like the one we saw in Figure 6.3 "The Buyer’s Valuation". We can add these unit demand curves together to get a picture of demand in the entire market: the market demand curveThe number of units of a good or a service demanded at each price.. For example, suppose only one person is willing to buy if the price is $700. However, suppose there is another buyer with a valuation of $660. If consoles were on sale for $660, then both individuals would want to purchase. At $660, in other words, the quantity demanded is 2. Perhaps the buyer with the next-highest valuation is willing to pay $640. If the price is $640, the quantity demanded is 3. Figure 6.10 "Obtaining the Market Demand Curve" shows what happens when we add together all these unit demand curves. The result is a downward sloping relationship that shows us how many units would be demanded at any given price.

Figure 6.10 Obtaining the Market Demand Curve

We can add together the unit demand curves of different individuals in the economy to get the market demand curve.

Supply: Many Sellers

We saw earlier that each potential seller has a unit supply curve. If the price is less than a seller’s valuation, she will not sell the good, but when the price becomes greater than her valuation, she will be willing to sell. Just as we added together the unit demand curves to get the market demand curve, so too can we add together the unit supply curves to get the market supply curveThe number of units of a good or a service supplied at each price..

In Figure 6.11 "Obtaining the Market Supply Curve", we see that the lowest valuation in the market is $150. There is one seller willing to sell a console at that price. As the price increases, more and more sellers will find the price attractive and will want to sell. For example, there are 11 potential sellers with a valuation less than $350. Thus, at this price, 11 consoles will be supplied to the market.

Figure 6.11 Obtaining the Market Supply Curve

We can add together the unit supply curves of different individuals in an economy to get the market supply curve.

Equilibrium

Figure 6.10 "Obtaining the Market Demand Curve" and Figure 6.11 "Obtaining the Market Supply Curve" tell us the number of buyers willing to buy and the number of sellers willing to sell at each price.

Figure 6.12 "Market Equilibrium" shows what happens if we combine the demand curve and the supply curve on the same diagram. One point jumps out at us: the place where the demand and supply curves meet. In our example, this is at $480 and a quantity of 21 units. At this point, the number of buyers with a valuation greater than the price is the number of sellers with a valuation less than the price. If buyers and sellers were presented with this price, none would find themselves unable to transact. At this price, there is an exact match between the number of buyers and sellers.

Figure 6.12 Market Equilibrium

In this figure, we combine the demand and supply curves to find the equilibrium price and quantity in the market.

EquilibriumThe equilibrium price and the equilibrium quantity in a market. is not only a point on a graph. It is a prediction about a possible outcome in a situation where a large number of buyers and sellers meet with the possibility of trading. It seems plausible that in a situation where a large number of buyers and sellers can meet and trade with each other, most will end up trading at or near the equilibrium priceThe price at which sellers supply the equilibrium quantity and buyers demand the equilibrium quantity..

The equilibrium outcome is plausible because, at any other price, there will be a mismatch of buyers and sellers. Imagine, by contrast, that the buyers and sellers of our example are currently trading at $600, well above the equilibrium price of $480. At this high price, many more people want to sell than want to buy. Buyers would rapidly realize that they are in a strong bargaining position: if many sellers want your business, you can make them compete with each other and force price decreases. In fact, whenever the price is above equilibrium, the mismatch of buyers and sellers will tend to decrease prices.

By similar reasoning, a price of, say, $400 would also result in a mismatch between buyers and sellers. In this case, though, there are more people who want to buy than sell. Sellers can make buyers compete with each other, leading to price increases. At any price below the equilibrium price, prices will tend to increase.

Perfectly Competitive Markets

Economists formalize the intuition we have just developed with the most famous framework in all of economics: supply and demand.The definition is repeated and discussed in more detail in Chapter 8 "Why Do Prices Change?"; we make extensive use of it in other chapters.

Figure 6.13 Supply and Demand

When we have a large number of buyers and sellers of an identical good or service, the equilibrium price and quantity are determined by the intersection of the supply and demand curves.

The position of the demand curve depends on many things, such as income and the prices of other goods. A change in any of these will cause the entire demand curve to shift. Likewise, the position of the supply curve depends on factors such as a supplier’s costs. A change in these will cause the entire supply curve to shift. When one (or both) of the curves shifts, the equilibrium price and quantity change.

Experience with double oral auctions, both in the laboratory and in actual pit markets, tells us that trading will typically settle down close to the equilibrium price within a relatively short period of time. In a situation where there is a large number of people buying and selling an identical good, we say that we have a competitive marketA market that satisfies two conditions: (1) there are many buyers and sellers, and (2) the goods the sellers produce are perfect substitutes.. We expect that most trades will take place at or close to the equilibrium price, and the quantity traded will be approximately equal to the equilibrium quantityThe quantity where the supply and demand curves intersect, so the quantity supplied equals the quantity demanded.. In fact, even when the number of participants in the auction is relatively small, we often find that a double oral auction still gets close to this equilibrium price and quantity. This is the remarkable finding that we mentioned earlier: in a double oral auction, the number of transactions and the prices of these transactions are usually very close to the equilibrium predicted by supply and demandA framework that explains and predicts the equilibrium price and equilibrium quantity of a good..

The Gains from Trade in Equilibrium

Suppose all the transactions in Figure 6.12 "Market Equilibrium" take place at the equilibrium price of $480. What can we say about the surplus received by buyers and sellers? Each individual transaction looks like those we examined in Chapter 6 "eBay and craigslist", Section 6.2 "eBay". The total surplus from any given transaction is equal to the difference between the buyer’s valuation and the seller’s valuation. The buyer surplusA measure of how much the buyer gains from a transaction, equal to the buyer’s valuation minus the price. is the difference between his valuation and $480. The seller surplusA measure of how much the seller gains from a transaction, equal to the price minus the seller’s valuation. is the difference between the price and her valuation. For example, Figure 6.14 "The Gains from Trade in a Single Transaction in Market Equilibrium" shows the gains from trade if a buyer with a valuation of $630 matches up with a seller whose valuation is $230:

and

The transaction generates $400 worth of surplus: $150 goes to the buyer, and $250 goes to the seller.

Figure 6.14 The Gains from Trade in a Single Transaction in Market Equilibrium

Each transaction in the market generates surplus.

We could draw exactly the same diagram for all 21 transactions in the market. If we combine them, we would end up with Figure 6.15 "Surplus in Equilibrium". The total surplus accruing to the buyers is equal to the area below the demand curve and above the price. The total surplus accruing to the sellers is equal to the area above the supply curve and below the price. The total surplus—that is, the total gains from trade in this market—is the sum of the buyer surplus in the market and the seller surplus in the market. The total surplus is therefore the area between the supply curve and the demand curve.

Figure 6.15 Surplus in Equilibrium

If we add the surplus from all trades in the market, supposing that they all take place at $480, we obtain the total surplus in the market.

If you look at Figure 6.15 "Surplus in Equilibrium", something else may become apparent to you. All the gains from trade have been exhausted in the market. If buyers and sellers trade at the market price, then they manage to achieve all the gains from trade that are possible in this market because

• every transaction that has been carried out has created surplus;
• any further transaction would generate negative surplus.

The first statement is true because all trades are voluntary. We can see that the second statement is true by imagining trying to match up another buyer and seller. All the buyers with valuations greater than $480 have now made a purchase. So every remaining potential buyer has a valuation less than $480. All the sellers with valuations less than $480 have now made a sale. So every potential seller has a valuation greater than $480. It follows that there is no mutually beneficial transaction to be carried out.

This is a truly remarkable result. A market where all potential buyers and sellers take as given the equilibrium price allows all the possible gains from trade to be realized. Thus a market is a very effective mechanism for generating an efficient allocation of resources. This is why economists place so much emphasis on markets and “market solutions” to economic problems. Markets allow buyers and sellers to come together to make mutually beneficial trades. Economists believe that, as far as possible, we should create circumstances in which people can meet and carry out voluntary transactions.

Although this argument for markets is very powerful, we must be careful. Buyers and sellers may benefit from trading, but sometimes other people not involved in the transaction may also be affected. For example, suppose you fill up your car with gas at your local gas station. Presumably, you benefit from this transaction—otherwise you wouldn’t have bought the gas. Likewise, the gas station owner benefits from the transaction—otherwise the owner wouldn’t have sold it to you. But your purchase will contribute to smog and air pollution when you drive the car, affecting other people in the vicinity. To the extent that you make a contribution to global climate change, your little transaction has the potential to have an effect—a very tiny effect but an effect nonetheless—on everyone else on the planet. As a more positive example, going to college is presumably a mutually beneficial transaction between you and your school. But many others may eventually benefit from your education as well.In Chapter 14 "Cleaning Up the Air and Using Up the Oil", we consider such uncompensated costs and benefits in detail.

Production Possibilities Frontier for a Single Individual

Inspired by the craigslist posts that we saw earlier, imagine an economy where people care about only two things: web pages and vegan meals. Our first economy has a single individual—we call him Julio—who has 8 hours a day to spend working. Julio can spend his time in two activities: web design and preparing vegan meals. To be concrete, suppose he can produce 1 web page per hour or 2 vegan meals per hour. Julio faces a time allocation problem: how should he divide his time between these activities?We study the time allocation problem in Chapter 4 "Everyday Decisions".

The answer depends on both Julio’s productivity and his tastes. We start by looking at his ability to produce web pages and vegan meals in a number of different ways. Table 6.2 "Julio’s Production Ability" shows the quantity of each good produced per hour of Julio’s time. Julio can produce either 2 vegan meals or 1 web page in an hour. Put differently, it takes Julio half an hour to prepare a meal and 1 hour to produce a web page. These are the technologies—the ways of producing output from inputs—that are available to Julio.

We could write these two technologies as equations:

and

Or we can draw these two technologies (Figure 6.16 "Julio’s Production Ability"). The equations, the figure, and the table are three ways of showing exactly the same information.

Figure 6.16 Julio’s Production Ability

These figures show Julio’s technologies for producing vegan meals and producing web pages.

When we add in the further condition that Julio has 8 hours available each day, we can construct his different possible production choices—the combinations of web pages and vegan cuisine that he can produce given his abilities and the time available to him. The first two columns of Table 6.3 "Julio’s Production Possibilities" describe five ways Julio might allocate his 8 hours of work time. In the first row, Julio allocates all 8 hours to preparing vegan meals. In the last row, he spends all of his time in web design. The other rows show what happens if he spends some time producing each service. Note that the total hours spent in the two activities is always 8 hours.

The third and fourth columns provide information on the number of vegan meals and web pages that Julio produces. Looking at the first row, if he works only on vegan meals, then he produces 16 meals and 0 web pages. If Julio spends all of his time designing web pages, then he produces 0 vegan meals and 8 web pages.

We can also illustrate this table in a single graph (Figure 6.17 "Julio’s Production Possibilities") that summarizes Julio’s production possibilities. The quantity of vegan meals is on the horizontal axis, and the quantity of web pages is on the vertical axis. To understand Figure 6.17 "Julio’s Production Possibilities", first consider the vertical and horizontal intercepts. If Julio spends the entire 8 hours of his working day on web design, then he will produce 8 web pages and no vegan meals (point A). If Julio instead spends all his time cooking vegan meals and none on web design, then he can produce 16 vegan meals and 0 web pages (point B).

Figure 6.17 Julio’s Production Possibilities

Julio’s production possibilities frontier shows the combinations of meals and web pages that he can produce in an 8-hour day.

The slope of the graph is −1/2. To see why, start at the vertical intercept where Julio is producing only web pages. Suppose that he reduces web-page production by 1 page. This means he will produce only 7 web pages, which requires 7 hours of his time. The hour released from the production of web design can now be used to prepare vegan meals. This yields 2 vegan meals. The resulting combination of web pages and vegan meals is indicated as point C. Comparing points A and C, we can see why the slope is −1/2. A reduction of web-page production by 1 unit (the rise) yields an increase in vegan meals production of 2 (the run). The slope—rise divided by run—is −1/2.

Given his technologyA means of producing output from inputs. and 8 hours of working time, all the combinations of vegan meals and web pages that Julio can produce lie on the line connecting A and B. We call this the production possibilities frontierThe combinations of goods that can be produced with available resources.. Assuming that Julio equally likes both web design and vegan meals and is willing to work 8 hours, he will choose a point on this frontier.All of this may seem quite familiar. The production possibility frontier for a single individual is the same as the time budget line for an individual. See Chapter 4 "Everyday Decisions" for more information.

What is the cost to Julio of cooking one more meal? To cook one more meal, Julio must take 30 minutes away from web design. Because it takes 30 minutes to produce the meal, and Julio produces 1 web page per hour, the cost of producing an additional vegan meal is half of a web page. This is his opportunity costWhat you must give up to carry out an action.: to do one thing (produce more vegan meals), Julio must give up the opportunity to do something else (produce web pages). Turning this around, we can determine the opportunity cost of producing an extra web page in terms of vegan meals. Because Julio can produce 1 web page per hour or cook 2 meals per hour, the opportunity cost of 1 web page is 2 vegan meals. The fact that Julio must give up one good (for example, web pages) to get more of another (for example, vegan meals) is a direct consequence of the fact that Julio’s time is scarce.

Could Julio somehow produce more web pages and more vegan meals? There are only two ways in which this could happen. First, his technology could improve. If Julio were able to become better at either web design or vegan meals, his production possibilities frontier would shift outward. For example, if he becomes more skilled at web design, he might be able to produce 3 (rather than 2) web pages in 2 hours. Then the new production possibilities frontier would be as shown in part (a) of Figure 6.18 "Two Ways of Shifting the Production Possibilities Frontier Outward".

Figure 6.18 Two Ways of Shifting the Production Possibilities Frontier Outward

There are two ways in which Julio could produce more in a day: he could become more skilled, or he could work harder.

Alternatively, Julio could decide to work more. We have assumed that the amount of time that Julio works is fixed at 8 hours. Part (b) of Figure 6.18 "Two Ways of Shifting the Production Possibilities Frontier Outward" shows what the production possibilities frontier would look like if Julio worked 10 hours per day instead of 8 hours. This also has an opportunity cost. If Julio works longer, he has less time for his leisure activities.

We have not yet talked about where on the frontier Julio will choose to allocate his time. This depends on his tastes. For example, he might like to have 2 vegan meals for each web page. Then he would consume 4 web pages and 8 meals, as in Figure 6.19 "Julio’s Allocation of Time to Cooking Meals and Producing Web Pages".

Figure 6.19 Julio’s Allocation of Time to Cooking Meals and Producing Web Pages

If Julio likes to consume pages and meals in fixed proportions (2 vegan dishes for every web page), he will allocate his time to achieve the point shown in the figure.

The Production Possibilities Frontier with Two People

If this were the end of the story, we would not have seen the advertisements on craigslist to trade vegan meals or web pages. Things become more interesting and somewhat more realistic when we add another person to our economy.

Hannah has production possibilities that are summarized in Table 6.4 "Production Possibilities for Julio and Hannah". She can produce 1 vegan meal in an hour or produce 1.5 web pages in an hour. Hannah, like Julio, has 8 hours per day to allocate to production activities. In Table 6.4 "Production Possibilities for Julio and Hannah" we have also included their respective opportunity costs of producing web pages and vegan meals.

Table 6.4 "Production Possibilities for Julio and Hannah" reveals that Hannah is more productive than Julio in the production of web pages. By contrast, Julio is more productive in vegan meals. Hannah’s production possibilities frontier is illustrated in Figure 6.20 "Hannah’s Production Possibilities Frontier". It is steeper than Julio’s because the opportunity cost of vegan meals is higher for Hannah than it is for Julio.

Figure 6.20 Hannah’s Production Possibilities Frontier

Hannah’s production possibilities frontier is steeper than Julio’s.

Economists use the ideas of absolute advantageIn the production of a good, one person can produce more of a good in a unit of time than another person. and comparative advantageIn the production of one good, the opportunity cost, as measured by the lost output of the other good, is lower for that person than for another person. to compare the productive abilities of Hannah and Julio.

Both absolute and comparative advantage are relative concepts because they compare two people. In the case of absolute advantage, we compare the productivity of two people for a given good. In the case of comparative advantage, we compare two people and two goods because opportunity cost is defined across two goods (web pages and vegan meals in our example). Comparing Hannah and Julio, we see that Hannah has an absolute advantage in the production of web pages. She is better at producing web pages than Julio. By contrast, Julio has an absolute advantage in the production of vegan meals. Therefore, it is not surprising that Hannah also has a comparative advantage in the production of web pages—the opportunity cost of web pages is lower for her than it is for Julio—whereas Julio has a comparative advantage in vegan meals.

It is entirely possible for one person to have an absolute advantage in the production of both goods. For example, were Hannah’s productivity in both activities to double, she would be better both at both web design and vegan meals. However, her opportunity cost of web pages would be unchanged. Julio would still have a comparative advantage in vegan meals. In general, one person always has a comparative advantage in one activity, while the other person has a comparative advantage in the other activity (the only exception is the case where the two individuals have exactly the same opportunity costs).

Suppose that Hannah’s tastes for vegan meals and web pages are the same as Julio’s: like Julio, Hannah wants to consume 2 meals for every web page. Acting alone, she would work for 2 hours in web design and spend 6 hours cooking, ending up with 3 web pages and 6 meals. But there is something very odd going on here. Julio, who is good at preparing meals, spends half his time on web design. Hannah, who is good at web design, spends three-quarters of her time cooking. Each has to spend a lot of time doing an activity at which he or she is unproductive.

This is where we see the possibility of gains from trade. Imagine that Julio and Hannah join together and become a team. What is their joint production possibilities frontier? If both Julio and Hannah devote their 8 hours of time to the production of web pages, then the economy can produce 20 web pages (8 from Julio and 12 from Hannah). At the other extreme, if both Julio and Hannah devote their 8 hours to cooking vegan meals, then the economy can produce 24 meals (16 from Julio and 8 from Hannah). These two points, which represent specialization of their two-person economy in one good, are indicated by point A and point D in Figure 6.21 "Julio and Hannah’s Joint Production Possibilities Frontier".

Figure 6.21 Julio and Hannah’s Joint Production Possibilities Frontier

Julio and Hannah’s joint production possibilities frontier.

To fill in the rest of their joint production possibilities frontier, start from the vertical intercept, where 20 web pages are being produced. Suppose Julio and Hannah jointly decide that they would prefer to give up 1 web page to have some vegan meals. If Hannah were to produce only 11 web pages, she could free up 2/3 of an hour for vegan meals. She would produce 2/3 of a meal. Conversely, if Julio produced 1 fewer web page, that would free an hour of his time (because he is less efficient than Hannah at web design), and he could create 2 vegan meals. Evidently, it makes much more sense for Julio to shift from web design to cooking (see point B in Figure 6.21 "Julio and Hannah’s Joint Production Possibilities Frontier").

The most efficient way to substitute web design production for vegan meals production, starting at point A, is to have Julio switch from producing web pages to producing vegan meals. Julio should switch because he has a comparative advantage in cooking. As we move along the production possibilities frontier from point A to point B to point C, Julio continues to substitute from web pages to meals. For this segment, the slope of the production possibilities frontier is −1/2, which is Julio’s opportunity cost of web pages.

At point C, both individuals are completely specialized. Julio spends all 8 hours on vegan meals and produces 16 meals. Hannah spends all 8 hours on web design and produces 12 web pages. If they would like to have still more vegan meals, it is necessary for Hannah to start producing that service. Because she is less efficient at cooking and more efficient at web design than Julio, the cost of extra vegan meals increases. Between point A and point C, the cost of vegan meals was 1/2 a webpage. Between point C and point D, the cost of a unit of vegan meals is 1.5 web pages. The production possibilities frontier becomes much steeper. If you look carefully at Figure 6.19 "Julio’s Allocation of Time to Cooking Meals and Producing Web Pages", Figure 6.20 "Hannah’s Production Possibilities Frontier", and Figure 6.21 "Julio and Hannah’s Joint Production Possibilities Frontier", the joint production possibilities frontier is composed of the two individual frontiers joined together at point C.

Gains from Trade Once Again

Figure 6.22 "Julio and Hannah’s Preferred Point" again shows the production possibilities frontier for the Julio-Hannah team: all the combinations of web pages and vegan meals that they can produce in one day, using the technologies available to them.

Figure 6.22 Julio and Hannah’s Preferred Point

Julio and Hannah can benefit from joining forces.

Julio and Hannah have a great deal to gain by joining forces. We know that Julio, acting alone, produces 4 web pages and 8 vegan meals. Hannah, acting alone, produces 3 web pages and 6 vegan meals. The joint total is 7 web pages and 14 vegan meals. In Figure 6.22 "Julio and Hannah’s Preferred Point", we have labeled this as “Total production of Julio and Hannah if they do not form a team.” But look at what they can achieve if they work together: they can produce 9 web pages and 18 vegan meals.

Evidently they both can be better off when they work together. For example, each could get an additional web page and 2 vegan meals. Julio could have 5 web pages and 10 vegan meals (instead of 4 and 8, respectively), and Hannah could have 4 web pages and 8 vegan meals (instead of 3 and 6, respectively).

How do they do this? Julio specializes completely in vegan meals. He spends all 8 hours of his day cooking, producing 16 vegan meals. Hannah, meanwhile, gets to spend most of her time doing what she does best: designing web pages. She spends 6 hours on web design, producing 9 web pages, and 2 hours cooking, producing 2 vegan meals.

The key to this improvement is that we are no longer requiring that Julio and Hannah consume only what they can individually produce. Instead, they can produce according to their comparative advantage. They each specialize in the production of the good that they produce best and then trade to get a consumption bundle that they are happy with. The gains from trade come from the ability to specialize.

It is exactly such gains from trade that people are looking for when they place advertisements on craigslist. For example, the first ad we quoted was from someone with a comparative advantage in fixing furniture looking to trade with someone who had a comparative advantage in dental work. Comparative advantage is one of the most fundamental reasons why people trade, and sites like craigslist allow people to benefit from trade. Of course, in modern economies, most trade does not occur through individual barter; stores, wholesalers, and other intermediaries mediate trade. Although there are many mechanisms for trade, comparative advantage is a key motivation for trade.

Production Possibilities Frontier for a Country

Before we finish with this story, let us try to get a sense of how we can expand it to an entire economy. We begin by adding a third individual to our story: Sergio. Sergio is less efficient than both Julio and Hannah. He has no absolute advantage in anything; he is no better at web design than Hannah, and he is no better preparing vegan meals than Julio. Remarkably, Julio and Hannah will still want to trade with him.

We begin by constructing the production possibilities frontier for these three individuals. The logic is the same as before. Start from the position where the economy produces nothing but web pages (see Figure 6.23 "The Production Possibilities Frontier with Three People", point A). Together, Julio, Hannah, and Sergio can produce a total of 28 web pages in a day. Then we first shift Julio to cooking because he has the lowest opportunity cost of that activity. As before, the slope of this first part of the frontier is −1/2, up to point B. At point B, Julio is producing nothing but vegan meals, and Hannah and Sergio are devoting all of their time to producing web pages. At point B, the economy produces 20 web pages and 16 vegan meals.

Figure 6.23 The Production Possibilities Frontier with Three People

Here we show a production possibilities frontier with three individuals. Notice that it is smoother than the production possibilities frontier for two people.

If they want more vegan meals, who should switch next? The answer is Sergio because his opportunity cost of vegan meals is lower than Hannah’s. As Sergio starts shifting from web design to vegan meals, the frontier has slope −1, and we move from point B to point C. At point C, Sergio and Julio cook meals, and Hannah produces web pages. The number of web pages produced is 12, and there are 24 vegan meals. Finally, the last segment of the frontier has slope −3/2, as Hannah also shifts from web design to vegan meals. At point D, they all cook, with total production equal to 32 meals.

Let us suppose that Sergio, like the others, consumes in the ratio of 2 vegan meals for every web page. If the economy is at point C, the economy can produce 12 web pages and 24 vegan meals. Earlier, we saw that Hannah and Julio could together produce 9 web pages and 18 vegan meals, so bringing in Sergio allows for an extra 3 web pages and 6 vegan meals, which is more than Sergio could produce on his own. Even though Sergio is less efficient than both Julio and Hannah, there are still some gains from trade. The easiest way to see this is to note that it would take Sergio 9 hours to produce 3 web pages and 6 vegan meals. In 8 hours he could produce almost 3 web pages and over 5 vegan meals.

Where do the gains from trade come from? They come from the fact that, relative to Hannah, Sergio has a comparative advantage in vegan meals. Previously, Hannah was devoting some of her time to vegan meals, which meant she had to divert time from web design. This was costly because she is good at web design. By letting Sergio do the vegan meals, Hannah can specialize in what she does best. The end result is that there are extra web pages and vegan meals for them all to share.

Comparing Figure 6.22 "Julio and Hannah’s Preferred Point" and Figure 6.23 "The Production Possibilities Frontier with Three People", you can see that the frontier becomes “smoother” when we add Sergio to the picture. Now imagine that we add more and more people to the economy, each with different technologies, and then construct the frontier in the same way. We would get a smoother and smoother production possibilities frontier. In the end, we might end up with something like Figure 6.24 "The Production Possibilities Frontier with a Large Number of People".

Figure 6.24 The Production Possibilities Frontier with a Large Number of People

As we add more and more people to the economy, the production possibilities frontier will become smoother.

It is easy enough to imagine that Julio, Hannah, and Sergio could all get together, agree to produce according to the principle of comparative advantage, and then share the goods that they have produced in a way that makes them all better off than they would be individually. Exactly how the goods would be shared would involve some kind of negotiation and bargaining among them. Once we imagine an economy with a large number of people in it, however, it is less clear how they would divide up the goods after they were produced. And that brings us full circle in the chapter. It is not enough that potential gains from trade exist. There must also be mechanisms, such as auctions and markets, that allow people to come together and realize these gains from trade.

The Demand Curve Facing a Firm

There will typically be more than one firm that serves a market. This means that the overall demand for a product is divided among the different firms in the market. We have said nothing yet about the kind of “market structure” in which a firm is operating—for example, does it have a lot of competitors or only a few competitors? Without delving into details, we cannot know exactly how the market demand curve will be divided among the firms in the market. Fortunately, we can put this problem aside—at least for this chapter.We look at market structure in Chapter 15 "Busting Up Monopolies". For the moment, it is enough just to know that each firm faces a demand curve for its own product.

When the price of a product increases, individual customers are less likely to think it is good value and are more likely to spend their income on other things instead. As a result—for almost all products—a higher price leads to lower sales.

An example of such a demand curve is

Table 7.1 "Example of the Demand Curve Faced by a Firm" calculates the quantity associated with different prices. For example, with this demand curve, if a manager sets the price at $10, the firm will sell 50 units because 100 − (5 × 10) = 50. If a manager sets the price at $16, the firm will sell only 20 units: 100 − (5 × 16) = 20. For every $1 increase in the price, output decreases by 5 units. (We have chosen a demand curve with numbers that are easy to work with. If you think that this makes the numbers unrealistically small, think of the quantity as being measured in, say, thousands of units, so a quantity of 3 in this equation means that the firm is selling 3,000 units. Our analysis would be unchanged.)

Equivalently, we could think about a manager choosing the quantity that the firm should produce, in which case she would have to accept the price implied by the demand curve. To write the demand curve this way, first divide both sides of the equation by 5 to obtain

Now add “price” to each side and subtract “$\frac{\text{quantity demanded}}{\text{5}}$” from each side:

For example, if the manager wants to sell 70 units, she will need a price of $6 (because 20 − 70/5 = 6). For every unit increase in quantity, the price decreases by 20 cents.

Either way of looking at the demand curve is perfectly correct. Figure 7.5 "Two Views of the Demand Curve" shows the demand curve in these two ways. Look carefully at the two parts of this figure and convince yourself that they are really the same—all we have done is switch the axes.

Figure 7.5 Two Views of the Demand Curve

There are two ways that we can draw a demand curve, both of which are perfectly correct. (a) The demand curve has price on the horizontal axis and quantity demanded on the vertical axis (b). The demand curve has price on the vertical axis, which is how we normally draw the demand curve in economics.

The firm faces a trade-off: it can set a high price, such as $18, but it will be able to sell only a relatively small quantity (10). Alternatively, the firm can sell a large quantity (for example, 80), but only if it is willing to accept a low price ($4). The hard choice embodied in the demand curve is perhaps the most fundamental trade-off in the world of business. Of course, if the firm sets its price too high, it won’t sell anything at all. The choke priceThe price above which no units of the good will be sold. is the price above which no units of the good will be sold. In our example, the choke price is $20; look at the vertical axis in part (b) of Figure 7.5 "Two Views of the Demand Curve".A small mathematical technicality: the equation for the demand curve applies only if both the price and the quantity are nonnegative. At any price greater than the choke price, the quantity demanded is zero, so the demand curve runs along the vertical axis. A negative price would mean a firm was paying consumers to take the product away.

Every firm in the economy faces some kind of demand curve. Knowing the demand for your product is one of the most fundamental necessities of successful business. We therefore turn next to the problem Ellie learned about the demand curve for her company’s drug.

The Elasticity of Demand: How Price Sensitive Are Consumers?

Marketing managers understand the law of demand. They know that if they set a higher price, they can expect to sell less output. But this is not enough information for good decision making. Managers need to know whether their customers’ demand is very sensitive or relatively insensitive to changes in the price. Put differently, they need to know if the demand curve is steep (a change in price will lead to a small change in output) or flat (a change in price will lead to a big change in output). We measure this sensitivity by the own-price elasticity of demandThe percentage change in quantity demanded of a good divided by the percentage change in the price of that good..

Throughout the remainder of this chapter, you will often see −(elasticity of demand). Just remember that this expression always refers to a positive number.

Calculating the Elasticity of Demand: An Example

Go back to our earlier example:

quantity demanded = 100 − 5 × price.

Suppose a firm sets a price of $15 and sells 25 units. What is the elasticity of demand if we think of a change in price from $15 to $14.80? In this case, the change in the price is −0.2, and the change in the quantity is 1. Thus we calculate the elasticity of demand as follows:

1. The percentage change in the quantity is $\frac{1}{25}$ (4 percent).
2. The percentage change in the price is $-\frac{0.2}{15}=\frac{\text{1}}{\text{75}}$ (approximately −1.3 percent).
3. −(elasticity of demand) is $\frac{1/25}{1/75}=3.$

The interpretation of this elasticity is as follows: when price decreases by 1 percent, quantity demanded increases by 3 percent. This is illustrated in Figure 7.6 "The Elasticity of Demand".

Figure 7.6 The Elasticity of Demand

When the price is decreased from $15.00 to $14.80, sales increase from 25 to 26. The percentage change in price is −1.3 percent. The percentage change in the quantity sold is 4. So −(elasticity of demand) is 3.

One very useful feature of the elasticity of demand is that it does not change when the number of units changes. Suppose that instead of measuring prices in dollars, we measure them in cents. In that case our demand curve becomes

quantity demanded = 100 − 500 × price.

Make sure you understand that this is exactly the same demand curve as before. Here the slope of the demand curve is −500 instead of −5. Looking back at the formula for elasticity, you see that the change in the price is 100 times greater, but the price itself is 100 times greater as well. The percentage change is unaffected, as is elasticity.

The Elasticity of Demand for a Linear Demand Curve

The elasticity of demand is generally different at different points on the demand curve. In other words, the market power of a firm is not constant: it depends on the price that a firm has chosen to set. To illustrate, remember that we found −(elasticity of demand) = 3 for our demand curve when the price is $15. Suppose we calculate the elasticity for this same demand curve at $4. Thus imagine that that we are originally at the point where the price is $4 and sales are 80 units and then suppose we again decrease the price by 20 cents. Sales will increase by 1 unit:

1. The percentage change in the quantity is $\frac{1}{80}$ (1.25 percent).
2. The percentage change in the price is $-\frac{0.2}{4}=-\frac{\text{1}}{\text{20}}$ (5 percent).
3. −(elasticity of demand) is $\frac{1/80}{1/20}=\mathrm{0.25.}$

The elasticity of demand is different because we are at a different point on the demand curve.

When −(elasticity of demand) increases, we say that demand is becoming more elastic. When −(elasticity of demand) decreases, we say that demand is becoming less elastic. As we move down a linear demand curve, −(elasticity of demand) becomes smaller, as shown in Figure 7.7 "The Elasticity of Demand When the Demand Curve Is Linear".

Figure 7.7 The Elasticity of Demand When the Demand Curve Is Linear

The elasticity of demand is generally different at different points on a demand curve. In the case of a linear demand curve, −(elasticity of demand) becomes smaller as we move down the demand curve.

Measuring the Elasticity of Demand

To evaluate the effects of her decisions on revenues, Ellie needs to know about the demand curve facing her firm. In particular, she needs to know whether the quantity demanded by buyers is very sensitive to the price that she sets. We now know that the elasticity of demand is a useful measure of this sensitivity. How can managers such as Ellie gather information on the elasticity of demand?

At an informal level, people working in marketing and sales are likely to have some idea of whether their customers are very price sensitive. Marketing and sales personnel—if they are any good at their jobs—spend time talking to actual and potential customers and should have some idea of how much these customers care about prices. Similarly, these employees should have a good sense of the overall market and the other factors that might affect customers’ choices. For example, they will usually know whether there are other firms in the market offering similar products, and, if so, what prices these firms are charging. Such knowledge is much better than nothing, but it does not provide very concrete evidence on the demand curve or the elasticity of demand.

A firm may be able to make use of existing sales data to develop a more concrete measure of the elasticity of demand. For example, a firm might have past sales data that show how much they managed to sell at different prices, or a firm might have sales data from different cities where different prices were charged. Suppose a pricing manager discovers data for prices and quantities like those in part (a) of Figure 7.8 "Finding the Demand Curve". Here, each dot marks an observation—for example, we can see that in one case, when the price was $100, the quantity demanded was 28.

Figure 7.8 Finding the Demand Curve

(a) This is an example of data that a manager might have obtained for prices and quantities. (b) A line is fit to the data that represents a best guess at the underlying demand curve facing a firm.

The straight-line demand curves that appear in this and other books are a convenient fiction of economists and textbook writers, but no one has actually seen one in captivity. In the real world of business, demand curves—if they are available at all—are only a best guess from a collection of data. Economists and statisticians have developed statistical techniques for these guesses. The underlying idea of these techniques is that they fit a line to the data. (The exact details do not concern us here; you can learn about them in more advanced courses in economics and statistics.) Part (b) of Figure 7.8 "Finding the Demand Curve" shows an example. It represents our best prediction, based on available data, of how much people will buy at different prices.

If a firm does not have access to reliable existing data, a third option is for it to generate its own data. For example, suppose a retailer wanted to know how sensitive customer demand for milk is to changes in the price of milk. It could try setting a different price every week and observe its sales. It could then plot them in a diagram like Figure 7.8 "Finding the Demand Curve" and use techniques like those we just discussed to fit a line. In effect, the store could conduct its own experiment to find out what its demand curve looks like. For a firm that sells over the Internet, this kind of experiment is particularly attractive because it can randomly offer different prices to people coming to its website.

Finally, firms can conduct market research either on their own or by hiring a professional market research firm. Market researchers use questionnaires and surveys to try to discover the likely purchasing behavior of consumers. The simplest questionnaire might ask, “How much would you be willing to pay for product x?” Market researchers have found such questions are not very useful because consumers do not answer them very honestly. As a result, research firms use more subtle questions and other more complicated techniques to uncover consumers’ willingness to pay for goods and services.

Ellie decided that she should conduct market research to help with the pricing decision. She hired a market research firm to ask doctors about how they currently prescribed different high blood pressure medications. Specifically, the doctors were asked what percentage of their prescriptions went to each of the drugs on the market. Then they were asked the effect of different prices on those percentages. Based on this research, the market research firm found that a good description of the demand curve was as follows:

quantity demanded = 252 − 300 × price.

Remember that the drug was currently being sold for $0.50 a pill, so

quantity demanded = 252 − 300 × 0.5 = 102.

The demand curve also told Ellie that if she increased the price by 10 percent to $0.55, the quantity demanded would decrease to 87 (252 − 300 × 0.55 = 87). Therefore, the percentage change in quantity is $\frac{87-102}{102}=-\mathrm{14.7.}$ From this, the market research firm discovered that the elasticity of demand at the current price was

$$-\text{(elasticity of demand)}=\frac{\text{percentage change in quantity}}{\text{percentage change in price}}=\frac{14.7}{10}=\mathrm{1.47.}$$

How Do Revenues Depend on Price?

The next step is to understand how to use the demand curve when setting prices. The elasticity of demand describes how quantity demanded depends on price, but what a manager really wants to know is how revenues are affected by price. Revenues equal price times quantity, so we know immediately that a firm earns $0 if the price is $0. (It doesn’t matter how much you give away, you still get no money.) We also know that, at the choke price, the quantity demanded is 0 units, so its revenues are likewise $0. (If you sell 0 units, it doesn’t matter how high a price you sell them for.) At prices between $0 and the choke price, however, the firm sells a positive amount at a positive price, thus earning positive revenues. Figure 7.9 "Revenues" is a graphical representation of the revenues of a firm. Revenues equal price times quantity, which is the area of the rectangle under the demand curve. For example, at $14 and 30 units, revenues are $420.

Figure 7.9 Revenues

The revenues of a firm are equal to the area of the rectangle under the demand curve.

We can use the information in Table 7.1 "Example of the Demand Curve Faced by a Firm" to calculate the revenues of a firm at different quantities and prices (this is easy to do with a spreadsheet). Table 7.2 "Calculating Revenues" shows that if we start at a price of zero and increase the price, the firm’s revenues also increase. Above a certain point, however (in this example, $10), revenues start to decrease again.

Marginal Revenue

Earlier we suggested that a good strategy for pricing is to experiment with small changes in price. So how do small changes in price affect the revenue of a firm? Suppose, for example, that a firm has set the price at $15 and sells 25 units, but the manager contemplates decreasing the price to $14.80. We can see the effect that this has on the firm’s revenues in Figure 7.10 "Revenues Gained and Lost".

Figure 7.10 Revenues Gained and Lost

If a firm cuts its price, it sells more of its product, which increases revenues, but sells each unit at a lower price, which decreases revenues.

The firm will lose 20 cents on each unit it sells, so it will lose $5 in revenue. This is shown in the figure as the rectangle labeled “revenues lost.” But the firm will sell more units: from the demand curve, we know that when the firm decreases its price by $0.20, it sells another unit. That means that the firm gains $14.80, as shown in the shaded area labeled “revenues gained.” The overall change in the firm’s revenues is equal to $14.80 − $5.00 = $9.80. Decreasing the price from $15.00 to $14.80 will increase its revenues by $9.80.

Look carefully at Figure 7.10 "Revenues Gained and Lost" and make sure you understand the experiment. We presume throughout this chapter that a firm must sell every unit at the same price. When we talk about moving from $15.00 to $14.80, we are not supposing that a firm sells 25 units for $15 and then drops its price to $14.80 to sell the additional unit. We are saying that the manager is choosing between selling 25 units for $15.00 or 26 units for $14.80.

Figure 7.11 Calculating the Change in Revenues

If a manager has an idea about how much quantity demanded will decrease for a given increase in price, she can calculate the likely effect on revenues.

Figure 7.11 "Calculating the Change in Revenues" explains this idea more generally. Suppose a firm is originally at point A on the demand curve. Now imagine that a manager decreases the price. At the new, lower price, the firm sells a new, higher quantity (point B). The change in the quantity is the new quantity minus the initial quantity. The change in the price is the new price minus the initial price (remember that this is a negative number). The change in the firm’s revenues is given by

change in revenues = (change in quantity × new price) + (change in price × initial quantity).

The first term is positive: it is the extra revenue from selling the extra output. The second term is negative: it is the revenue lost because the price has been decreased. Together these give the effect of a change in price on revenues, which we call a firm’s marginal revenueThe extra revenue from selling an additional unit of output, which is equal to the change in revenue divided by the change in sales..

Toolkit: Section 31.15 "Pricing with Market Power"

Marginal revenue is the change in revenue associated with a change in quantity of output sold:

$$\text{marginal revenue}=\frac{\text{change in revenue}}{\text{change in quantity}}\text{.}$$

We can write this asFor the derivation of this expression, see the toolkit.

$$\text{marginal revenue}=\text{price}\times \left(1+\frac{\text{percentage change in price}}{\text{percentage change in quantity}}\right)\text{.}$$

Marginal Revenue and the Elasticity of Demand

Given the definitions of marginal revenue and the elasticity of demand, we can write

$$\text{marginal revenue}=\text{price}\times \left(1-\frac{\text{1}}{-\text{(elasticity of demand)}}\right)\text{.}$$

It may look odd to write this expression with two minus signs. We do this because it is easier to deal with the positive number: −(elasticity of demand). We see three things:

1. Marginal revenue is always less than the price. Mathematically, $\left(1-\frac{\text{1}}{-\text{(elasticity of demand)}}\right)<\text{1}\text{.}$ Suppose a firm sells an extra unit. If the price stays the same, then the extra revenue would just equal the price. But the price does not stay the same: it decreases, meaning the firm gets less for every unit that it sells.
2. Marginal revenue can be negative. If –(elasticity of demand) < 1, then $\frac{\text{1}}{-\text{(elasticity of demand)}}>\text{1,}$ and $\left(1-\frac{\text{1}}{-\text{(elasticity of demand)}}\right)<\text{0}\text{.}$ When marginal revenue is negative, increased production results in lower revenues for a firm. The firm sells more output but loses more from the lower price than it gains from the higher sales.
3. The gap between marginal revenue and price depends on the elasticity of demand. When demand is more elastic, meaning −(elasticity of demand) is a bigger number, the gap between marginal revenue and price becomes smaller.

These three ideas are illustrated in Figure 7.12 "Marginal Revenue and Demand". The demand curve shows us the price at any given quantity. The marginal revenue curve lies below the demand curve because of our first observation: at any quantity, marginal revenue is less than price.When a demand curve is a straight line, the marginal revenue curve is also a straight line with the same intercept, but it is twice as steep. The marginal revenue curve intersects the horizontal axis at 50 units: when output is less than 50 units, marginal revenue is positive; when output exceeds 50, marginal revenue is negative. We explained earlier that a linear demand curve becomes more inelastic as you move down it. When the demand curve goes from being relatively elastic to relatively inelastic, marginal revenue goes from being positive to being negative.

Figure 7.12 Marginal Revenue and Demand

The marginal revenue curve lies below the demand curve because at any quantity, marginal revenue is less than price.

Earlier, we showed that when a firm sets the price at $15, −(elasticity of demand) = 3. Thus we can calculate marginal revenue at this price:

$$\text{marginal revenue}=\text{price}\times \left(1-\frac{\text{1}}{-\text{(elasticity of demand)}}\right)=15\left(1-\frac{1}{3}\right)=15\times \frac{2}{3}=10.$$

What does this mean? Starting at $15, it means that if a firm decreases its price—and hence increase its output—by a small amount, there would be an increase in the firm’s revenues.

When revenues are at their maximum, marginal revenue is zero. We can confirm this by calculating the elasticity of demand at $10. Consider a 10 percent increase in price, so the price increases to $11. At $10, sales equal 50 units. At $11, sales equal 45 units. In other words, sales decrease by 5 units, so the decrease in sales is 10 percent. It follows that

$$-\text{(elasticity of demand)}=-\frac{\text{percentage change in quantity}}{\text{percentage change in price}}=1.$$

Plugging this into our expression for marginal revenue, we confirm that

$$\text{marginal revenue}=\text{price}\times \left(1-\frac{\text{1}}{-\text{(elasticity of demand)}}\right)=10\left(1-\frac{1}{1}\right)=10\times 0=0.$$

At $10, a small change in price leads to no change in revenue. The benefit from selling extra output is exactly offset by the loss from charging a lower price.

Figure 7.13 Marginal Revenue and the Elasticity of Demand

The demand curve can be divided into two parts: at low quantities and high prices, marginal revenue is positive and the demand curve is elastic; at high quantities and low prices, marginal revenue is negative and the demand curve is inelastic.

We can thus divide the demand curve into two parts, as in Figure 7.13 "Marginal Revenue and the Elasticity of Demand". At low quantities and high prices, a firm can increase its revenues by moving down the demand curve—to lower prices and higher output. Marginal revenue is positive. In this region, −(elasticity of demand) is a relatively large number (specifically, it is between 1 and infinity) and we say that the demand curve is relatively elastic. Conversely, at high quantities and low prices, a decrease in price will decrease a firm’s revenues. Marginal revenue is negative. In this region, −(elasticity of demand) is between 0 and 1, and we say that the demand curve is inelastic. Table 7.3 represents this schematically.

Table 7.3

−(Elasticity of Demand)	Demand	Marginal Revenue	Effect of a Small Price Decrease
• > –(elasticity of demand) > 1	Relatively elastic	Positive	Increase revenues
−(elasticity of demand) = 1	Unit elastic	Zero	Have no effect on revenues
1 > –(elasticity of demand) > 0	Relatively inelastic	Negative	Decrease revenues

Maximizing Revenues

The market research company advising Ellie made a presentation to her team. The company told them that if they increased their price, they could expect to see a decrease in revenue. At their current price, in other words, marginal revenue was positive. If Ellie’s team wanted to maximize revenue, they would need to recommend a reduction in price: down to the point where marginal revenue is $0—equivalently, where −(elasticity of demand) = 1.

Some members of Ellie’s team therefore argued that they should try to decrease the price of the product so that they could increase their market share and earn more revenues from the sale of the drug. Ellie reminded them, though, that their goal wasn’t to have as much revenue as possible. It was to have as large a profit as possible. Before they could decide what to do about price, they needed to learn more about the costs of producing the drug.

Marginal Cost

Earlier, we showed how a firm’s revenues change when there is a change in quantity that the firm produces. If we also know how a firm’s costs change when there is a change in output, we have all the information we need for good pricing decisions. As with revenues, we scale this change by the size of the change in quantity. Figure 7.14 "Marginal Cost" shows how marginal costThe extra cost of producing an additional unit of output, which is equal to the change in cost divided by the change in quantity. fits into our road map for the chapter.

Figure 7.14 Marginal Cost

When a firm sets a higher price, it sells a smaller quantity and its costs of production decrease.

Table 7.4 "Marginal Cost" shows an example of a firm’s costs. It calculates marginal cost in the last column. We have presented this table with marginal cost on separate rows to emphasize that marginal cost is the cost of going from one level of output to the next. In our example, marginal cost—the cost of producing one more unit—is $10. If you want to produce one unit, it will cost you $60. If you want to produce two units, your must pay an additional $10 in costs, for a total of $70. If you want to produce three units, you must pay the $70 to produce the first two units, plus the additional marginal cost of $10, for a total cost of $80, and so on. Graphically, marginal cost is the slope of the cost line, as shown in Figure 7.15 "An Example of a Cost Function".

Figure 7.15 An Example of a Cost Function

This graph illustrates the cost function for a firm. In this case, the cost function has the equation cost = 50 + 10 × quantity. The cost of producing each additional unit (the marginal cost) is $10.

To emphasize again, only those costs that change matter for a firm’s pricing decision. When a firm considers producing extra output, many of its costs do not change. We can completely ignore these costs when thinking about optimal pricing. This is not to say that other costs don’t matter; quite the contrary. They are critical for a different decision—whether the firm should be in business at all.See Chapter 9 "Growing Jobs". But as long as we are interested in pricing, we can ignore them.

The costs for developing pharmaceutical products are typically quite high. The drug that Ellie was responsible for was first developed in research laboratories, then tested on animals, and then run through a number of clinical studies on human patients. These studies were needed before the Food and Drug Administration in the United States, and equivalent drug safety organizations in other countries, would approve the drug for sale. But these development costs have no effect on marginal cost because they were all incurred before a single pill could be sold.

Surprisingly, this means that even though the drug was very expensive to develop, Ellie’s team—quite correctly—paid no attention to that fact. In determining what price to set, they looked at the price sensitivity of their customers and at marginal cost. They understood that the development costs of the drug were not relevant to the pricing decision. In fact, Ellie’s team had only a very vague idea how much the drug had cost to develop: after all, that development had been carried out by a completely different arm of the company in other parts of the world.

You will often hear the opposite argument. It is common for people to say that pharmaceutical companies charge high prices because it costs so much to develop their drugs. This argument is superficially appealing, but it is completely backward. Pharmaceutical companies don’t charge high prices because they incur large development costs. They are willing to incur large development costs because they can charge high prices.

Estimating Marginal Cost

Estimating marginal cost is generally much easier than estimating demand because the cost side of the business is largely under the control of the firm. The firm’s costs depend on its technology and the decisions made about using that technology. In most medium- or large-sized firms, there is an “operations department” that takes care of the production process. The marketing manager ought to be able to consult with her colleagues in operations and learn about the costs of the firm. Most importantly, even if it is unreasonable to expect an operations manager to know the firm’s entire cost function, the operations manager should have a good idea about marginal cost (that is, should know how much it would cost per unit to scale up operations by a small amount). And that is the information the marketing manager needs for her pricing decisions.

The Markup Pricing Formula

Think about Ellie’s company. If it became more expensive for the company to produce each pill, it seems likely they would respond by raising their costs. Also, we said earlier that their customers are not very sensitive to changes in the price, which should allow them to set a relatively high price. In other words, the profit-maximizing price is related to the elasticity of demand and to marginal cost. These are the two critical ingredients of the pricing decision.

There are three facts about markupThe percentage amount by which price exceeds marginal cost.:

1. Markup is greater than or equal to zero—that is, the firm never sets a price below marginal cost.
2. Markup is smaller when demand is more elastic.
3. Markup is zero when the demand curve is perfectly elastic: −(elasticity of demand) = •.

Ellie’s team looked at their numbers. At the current price, −(elasticity of demand) = 1.47. They learned that the marginal cost was $0.28 per pill, and they were charging $0.50 per pill. Their current markup, in other words, was about 79 percent: 0.5 = (1+ 0.79) × 0.28. But if they applied the markup pricing formula based on the current elasticity of demand, they could charge a markup of 1/0.47 = 2.12—that is, more than a 200 percent markup, leading to a price of $0.87. It was clear that they could do better by increasing their price

A Pricing Algorithm

To summarize, a manager needs two key pieces of information when determining price:

1. Marginal cost. We have shown that the profit-maximizing price is a markup over the marginal cost of production. If a manager does not know the magnitude of marginal cost, she is missing a critical piece of information for the pricing decision.
2. Elasticity of demand. Once a manager knows marginal cost, she should then set the price as a markup over marginal cost. But this should not be done in an ad hoc manner; the markup must be based on information about the elasticity of demand.

Given these two pieces of information, a manager can then use the markup formula to determine the optimal price. Be careful, though. The markup formula looks deceptively simple, as if it can be used in a “plug-and-play” manner—given marginal cost and the elasticity of demand, plug them into the formula and calculate the optimum price. But if you change the price, both marginal cost and the elasticity of demand are also likely to change. A more reliable way of using this formula is in the algorithm shown in Figure 7.19 "A Pricing Algorithm", which is based on our earlier idea that you should find your way to the top of the profit hill. The five steps are as follows:

1. At your current price, estimate marginal cost and the elasticity of demand.
2. Calculate the optimal price based on those values.
3. If the optimal price is greater than your actual price, increase your price. Then estimate marginal cost and the elasticity again and repeat the process.
4. If the optimal price is less than your actual price, decrease your price. Then estimate marginal cost and the elasticity again and repeat the process.
5. If the current price is equal to this optimal price, leave your price unchanged.

Figure 7.19 A Pricing Algorithm

This pricing algorithm shows how to get the best price for a product.

Ellie’s team members were aware that, even though demand for the drug was apparently not very sensitive to price, they should not immediately jump to a much higher markup. They had found that based on current marginal cost and elasticity, the price could be raised. But as they raised the price, they knew that the elasticity of demand would probably also change. Looking more closely at their market research data, they found that at a price of $0.56 (a 100 percent markup), the elasticity of demand would increase to about 2. An elasticity of 2 means that the markup should be 100 percent to maximize profits. Thus—at least if their market research data were reliable—they knew that a price of $0.56 would maximize profits. Ellie recommended to senior management that the price of the drug be raised by slightly over 10 percent, from $0.50 per pill to $0.56 per pill.

Shifts in the Demand Curve Facing a Firm

So far we have looked only at movements along the demand curve—that is, we have looked at how changes in price lead to changes in the quantity that customers will buy. Firms also need to understand what factors might cause their demand curve to shift. Among the most important are the following:

• Changes in household tastes. Starting around 2004 or so, low-carbohydrate diets started to become very popular in the United States and elsewhere. For some companies, this was a boon; for others it was a problem. For example, companies like Einstein Bros. Bagels or Dunkin’ Donuts sell products that are relatively high in carbohydrates. As more and more customers started looking for low-carb alternatives, these firms saw their demand curve shift inward.
• Business cycle. Consider Lexus, a manufacturer of high-end automobiles. When the economy is booming, sales are likely to be very good. In boom times, people feel richer and more secure and are more likely to purchase a luxury car. But if the economy goes into recession, potential car buyers will start looking at cheaper cars or may decide to defer their purchase altogether. Many companies sell products that are sensitive to the state of the business cycle. Their demand curves shift as the economy moves from boom to recession.
• Changes in competitors’ prices. In a business setting, this is a critical concern. If a competitor decreases its price, this means that the demand curve you face will shift inward. For example, suppose that British Airways decides to decrease its price for flights from New York to London. American Airlines will find that its demand curve for that route has shifted inward. Ellie certainly has to worry about this because her company’s product has only a small number of competitors. A change in price of a competing blood pressure drug might make a big difference in the sales and profits of Ellie’s product.

If the demand curve shifts, should a firm change its price? The answer is yes if the shift in the demand curve also leads to a change in the elasticity of demand. In practice, this is likely to be the case, although it is certainly possible for a demand curve to shift without a change in the elasticity of demand. The correct response to a shift in the demand curve is to reestimate the elasticity of demand and then decide if a change in price is appropriate.

Complications

Pricing is a difficult and delicate job, and there are many factors that we have not yet considered:We address some of them in other chapters of the book; others are topics for more advanced classes in economics and business strategy.

• By far the most important problem that we have neglected is as follows: When making pricing decisions, firms may need to take into account how other firms will respond to their decisions. For example, a manager might estimate her firm’s elasticity of demand and marginal cost and determine that she could make more money by decreasing price. That calculation presumes that competing firms keep their prices unchanged. In markets with a small number of competitors, it is instead quite likely that other firms would respond by decreasing their prices. This would cause a firm’s demand curve to shift inward and probably leave it worse off than before.
• We have assumed throughout that a firm has to charge the same price for every unit that it sells. In many cases, this is an accurate description of pricing behavior. When a grocery store posts a price, that price holds for every unit on the shelf. But sometimes firms charge different prices for different units—by either charging different prices to different customers or offering individual units at different prices to the same customer. You have undoubtedly encountered examples. Firms sometimes offer quantity discounts, so the price is lower if you buy more units. Sometimes they offer discounts to certain groups of customers, such as cheap movie tickets for students. We could easily fill an entire chapter with other examples—some of which are remarkably sophisticated.
• Firms can have pricing strategies that call for the price to change over time. For example, firms sometimes engage in a strategy known as penetration pricing, whereby they start off by charging a low price in an attempt to develop or expand the market. Imagine that Kellogg’s develops a new breakfast cereal. It might decide to offer the cereal at a low price to induce people to try the product. Only after it has developed a group of loyal customers would it start setting their prices according to the markup principle.
• Pricing plays a role in the overall marketing and branding strategy of a firm. Some firms position themselves in the marketplace as suppliers of high-end offerings. They may choose to set high prices for their products to ensure that customers perceive them appropriately. Consider a luxury hotel that is contemplating setting a very low price in the off-season. Even though such a strategy might make sense in terms of its profits at that time, it might do long-term damage to the hotel’s reputation. For various reasons, customers often use the price of a product as an indicator of that product’s quality, so a low price can adversely affect a firm’s image.
• Psychologists who study marketing have found that demand is sensitive at certain price points. For example, if a firm increases the price of a product from $99.98 to $99.99, there might be very little effect on demand. But if the price increases from $99.99 to $100.00, there might be a much bigger effect because $100.00 is a psychological barrier. Such consumer behavior does not seem completely rational, but there is little doubt that it is a real phenomenon.
• Throughout this chapter, we have said that there is no difference between a firm choosing its price and taking as given the implied quantity or choosing its quantity and taking as given the implied price. Either way, the firm is picking a point on the demand curve. This is true, but there is a footnote that we should add. A firm’s demand curve depends on what its competitors are doing and, oddly enough, it does make a difference if those competitors are choosing quantities or prices.See Chapter 15 "Busting Up Monopolies" for discussion of this. We should also note that firms often do not know their demand curves with complete certainty. Suppose, for example, that the true demand curve for a firm’s product is actually further outward than a firm expects. If the firm sets the price, it will end up with an unexpectedly large quantity being demanded. If the firm sets the quantity, it will end up with an unexpectedly high price.
• We have focused our attention on the market power of firms as sellers, as reflected in the downward-sloping demand curves they face. Firms can also have market power as buyers. Walmart is such an important customer for many of its suppliers that it can use its position to negotiate lower prices for the goods it buys. Governments are also often powerful buyers and may be able to influence the prices they pay for goods and services. For example, government-run health-care systems may be able to negotiate favorable prices with pharmaceutical companies.

Perfectly Competitive Markets

If you produce a good for which there are few close substitutes, you have a great deal of market power. Your demand curve is not very elastic: even if you charge a high price, people will be willing to buy the good. On the other hand, if you are the producer of a good that is very similar to other products on the market, then your demand curve will be very elastic. If you increase your price even a little, the demand for your product will decrease a lot.

The extreme case is called a perfectly competitive market. In a perfectly competitive market, there are numerous buyers and sellers of exactly the same good. The standard examples of perfectly competitive markets are those for commodities, such as copper, sugar, wheat, or coffee. One bushel of wheat is the same as another, there are many producers of wheat in the world, and there are many buyers. Markets for financial assets may also be competitive. One euro is a perfect substitute for another, one three-month US treasury bill is a perfect substitute for another, and there are many institutions willing to buy and sell such assets.

An individual seller in a competitive market has no control over price. If the seller tries to set a price above the going market price, the quantity demanded falls to zero. However, the seller can sell as much as desired at the market price. When there are many sellers producing the same good, the output of a single seller is tiny relative to the whole market, and so the seller’s supply choices have no effect on the market price. This is what we mean by saying that the seller is “small.” It follows that a seller in a perfectly competitive market faces a demand curve that is a horizontal line at the market price, as shown in Figure 7.20 "The Demand Curve Facing a Firm in a Perfectly Competitive Market". This demand curve is infinitely elastic: −(elasticity of demand) = ∞. Be sure you understand this demand curve. As elsewhere in the chapter, it is the demand faced by an individual firm. In the background, there is a market demand curve that is downward sloping in the usual way; the market demand and market supply curves together determine the market price. But an individual producer does not experience the market demand curve. The producer confronts an infinitely elastic demand for its product.

Figure 7.20 The Demand Curve Facing a Firm in a Perfectly Competitive Market

The demand curve faced by a firm in a perfectly competitive market is infinitely elastic. Graphically, this means that it is a horizontal line at the market price.

Everything we have shown in this chapter applies to a firm facing such a demand curve. The seller still picks the best point on the demand curve. But because the price is the same everywhere on the demand curve, picking the best point means picking the best quantity. To see this, go back to the markup formula. When demand is infinitely elastic, the markup is zero:

so price equals marginal cost:

This makes sense. The ability to set a price above marginal cost comes from market power. If you have no market power, you cannot set a price in excess of marginal cost. A perfectly competitive firm chooses its level of output so that its marginal cost of production equals the market price.

We could equally get this conclusion by remembering that

and that when −(elasticity of demand) is infinite, marginal revenue equals price. If a competitive firm wants to sell one more unit, it does not have to decrease its price to do so. The amount it gets for selling one more unit is therefore the market price of the product, and the condition that marginal revenue equals marginal cost becomes

For the goods and services that we purchase regularly, there are few markets that are truly perfectly competitive. Often there are many sellers of goods that may be very close substitutes but not absolutely identical. Still, many markets are close to being perfectly competitive, in which case markup is very small and perfect competition is a good approximation.

The Supply Curve of a Firm

Table 7.5 "Costs of Production: Increasing Marginal Cost" shows the costs of producing for a firm. In contrast to Table 7.4 "Marginal Cost", where we supposed marginal cost was constant, this example has higher marginal costs of production when the level of output is greater.Total cost in Table 7.5 "Costs of Production: Increasing Marginal Cost" is 50 + 10 × quantity + 2 × quantity².

Figure 7.21 "The Supply Curve of an Individual Firm" shows how we derive the supply curve of an individual firm given such data on costs. The supply curve tells us how much the firm will produce at different prices. Suppose, for example, that the price is $20. At this price, we draw a horizontal line until we reach the marginal cost curve. At that point, we draw a vertical line to the quantity axis. In this way, you can find the level of output such that marginal cost equals price. Looking at the figure, we see that the firm should produce 3 units because the marginal cost of producing the third unit is $20. When the price is $30, setting marginal cost equal to price requires the firm to produce 5.5 units. When the price is $40, setting marginal cost equal to price requires the firm to produce 8 units.

The supply curve shows us the quantity that a firm will produce at different prices. Figure 7.21 "The Supply Curve of an Individual Firm" reveals something remarkable: the individual supply curveHow much output a firm in a perfectly competitive market will supply at any given price. It is the same as a firm’s marginal cost curve. of the firm is the marginal cost curve. They are the same thing. As the price a firm faces increases, it will produce more. Note carefully how this is worded. We are not saying that if a firm produces more, it will charge a higher price. Firms in a competitive market must take the price as given. Instead, we think about the response of a firm to a change in the price.The individual firm’s supply curve is an exact counterpart to something we show in Chapter 4 "Everyday Decisions", where we derive the demand curve for an individual. We show that an individual buys a good up to the point where marginal valuation equals price. From this we can conclude that the demand curve for an individual is the same as the individual’s marginal valuation curve. In Chapter 8 "Why Do Prices Change?", we use an individual firm’s supply curve as the basis for the market supply curve. Likewise, we use the individual demand curve as the basis for the market demand curve. By combining these curves, we obtain the supply-and-demand framework, which we can use to understand changing prices in an economy.

Figure 7.21 The Supply Curve of an Individual Firm

The firm chooses its quantity such that price equals marginal cost, which implies that the marginal cost curve of the firm is the supply curve of the firm.

Market Demand

Figure 8.1 "The Demand Curve of an Individual Household" is an example of a household’s demand for chocolate bars each month. Taking the price of a chocolate bar as given, as well as its income and all other prices, the household decides how many chocolate bars to buy. Its choice is represented as a point on the household’s demand curve. For example, at $5, the household wishes to consume five chocolate bars each month. The remainder of the household income—which is its total income minus the $25 it spends on chocolate—is spent on other goods and services. If the price decreases to $3, the household buys eight bars every month. In other words, the quantity demanded by the household increases. Equally, if the price of a chocolate bar increases, the quantity demanded decreases. This is the law of demand in operation.

One way to summarize this behavior is to say that the household compares its marginal valuation from one more chocolate bar to price. The marginal valuation is a measure of how much the household would like one more chocolate bar. The household will keep buying chocolate bars up to the point where

Figure 8.1 The Demand Curve of an Individual Household

The household demand curve shows the quantity of chocolate bars demanded by an individual household at each price. It has a negative slope: higher prices lead people to consume fewer chocolate bars.

In most markets, many households purchase the good or the service traded. We need to add together all the demand curves of the individual households to obtain the market demand curve. To see how this works, look at Table 8.1 "Individual and Market Demand" and Figure 8.2 "Market Demand". Suppose that there are two households. Part (a) of Figure 8.2 "Market Demand" shows their individual demand curves. Household 1 has the demand curve from Figure 8.1 "The Demand Curve of an Individual Household". Household 2 demands fewer chocolate bars at every price. For example, at $5, household 2 buys 2 bars per month; at $3, it buys 3 bars per month. To get the market demand, we simply add together the demands of the two households at each price. For example, when the price is $5, the market demand is 7 chocolate bars (5 demanded by household 1 and 2 demanded by household 2). When the price is $3, the market demand is 11 chocolate bars (8 demanded by household 1 and 3 demanded by household 2). When we carry out the same calculation at every price, we get the market demand curve shown in part (b) of Figure 8.2 "Market Demand".

Figure 8.2 Market Demand

Market demand is obtained by adding together the individual demands of all the households in the economy.

Because the individual demand curves are downward sloping, the market demand curve is also downward sloping: the law of demand carries across to the market demand curve. As the price decreases, each household chooses to buy more of the product. Thus the quantity demanded increases as the price decreases. Although we used two households in this example, the same idea applies if there are 200 households or 20,000 households. In principle, we could add together the quantities demanded at each price and arrive at a market demand curve.

There is a second reason why demand curves slope down when we combine individual demand curves into a market demand curve. Think about the situation where each household has a unit demand curve: that is, each individual buys at most one unit of the product. As the price decreases, the number of individuals electing to buy increases, so the market demand curve slopes down.See Chapter 4 "Everyday Decisions" and Chapter 6 "eBay and craigslist" for discussions of unit demand. In general, both mechanisms come into play.

• As price decreases, some households decide to enter the market; that is, these households buy some positive quantity other than zero.
• As price decreases, households increase the quantity that they wish to purchase.

When the price decreases, there are more buyers, and each buyer buys more.

Market Supply

In a competitive marketA market that satisfies two conditions: (1) there are many buyers and sellers, and (2) the goods the sellers produce are perfect substitutes., a single firm is only one of the many sellers producing and selling exactly the same product. The demand curve facing a firm exhibits perfectly elastic demand, which means that it sets its price equal to the price prevailing in the market, and it chooses its output such that this price equals its marginal costThe extra cost of producing an additional unit of output, which is equal to the change in cost divided by the change in quantity. of production.At the end of Chapter 7 "Where Do Prices Come From?", we derive the supply curve of a firm in a competitive market. If it were to try to set a higher price, it could not sell any output at all. If it were to set a lower price, it would be throwing away profits. Thus, for a competitive firm, the quantity produced satisfies this condition:

We typically expect that marginal cost will increase as a firm produces more output. Marginal cost is the cost of producing one extra unit of output. The cost of producing an additional unit of output generally increases as firms produce a larger and larger quantity. In part, this is because firms start to hit constraints in their capacities to produce more product. For example, a factory might be able to produce more output only by running extra shifts at night, which require paying higher wages.

If marginal cost is increasing, then we know the following:

• Given a price, there is only one level of output such that price equals marginal cost.
• As the price increases, a firm will produce more.

Indeed, the supply curve of an individual firm is the same as its marginal cost curve.

Figure 8.3 "The Supply Curve of an Individual Firm" illustrates the supply curve for a firm. A firm supplies seven chocolate bars at $3 and eight chocolate bars at $5. From this we can deduce that the marginal cost of producing the seventh chocolate bar is $3. Similarly, the marginal cost of producing the eighth chocolate bar is $5.

Figure 8.3 The Supply Curve of an Individual Firm

A firm’s supply curve, which is the same as its marginal cost curve, shows the quantity of chocolate bars it is willing to supply at each price.

Just as the market demand curve tells us the total amount demanded at each price, the market supply curve tells us the total amount supplied at each price. It is obtained analogously to the market demand curve: at each price we add together the quantity supplied by each firm to obtain the total quantity supplied at that price. If we perform this calculation for every price, then we get the market supply curve. Figure 8.4 "Market Supply" shows an example with two firms. At $3, firm 1 produces 7 bars, and firm 2 produces 3 bars. Thus the total supply at this price is 10 chocolate bars. At $5, firm 1 produces 8 bars, and firm 2 produces 5 bars. Thus the total supply at this price is 13 chocolate bars.

The market supply curve is increasing in price. As price increases, each firm in the market finds it profitable to increase output to ensure that price equals marginal cost. Moreover, as price increases, firms who choose not to produce and sell a product may be induced to enter into the market.A similar idea is in Chapter 6 "eBay and craigslist", where we show how to add together unit supply curves to obtain a market supply curve.

Figure 8.4 Market Supply

Market supply is obtained by adding together the individual supplies of all the firms in the economy.

In general, both mechanisms come into play. The market supply curve slopes up for two reasons:

1. As the price increases, more firms decide to enter the market—that is, these firms produce some positive quantity other than zero.
2. As the price increases, firms increase the quantity that they wish to produce.

When the price increases, there are more firms in the market, and each firm produces more.

Market Equilibrium

In a perfectly competitive market, we combine the market demand and supply curves to obtain the supply-and-demand framework shown in Figure 8.5 "Market Equilibrium". The point where the curves cross is the market equilibrium.The definition of equilibrium is also presented in Chapter 6 "eBay and craigslist". At this point, there is a perfect match between the amount that buyers want to buy and the amount that sellers want to sell. The term equilibrium refers to the balancing of the forces of supply and demand in the market. At the equilibrium price, the suppliers of a good can sell as much as they wish, and demanders of a good can buy as much of the good as they wish. There are no disappointed buyers or sellers.

Figure 8.5 Market Equilibrium

In a competitive market, the equilibrium price and the equilibrium quantity are determined by the intersection of the supply and demand curves.

Because the demand curve has a negative slope and the supply curve has a positive slope, supply and demand will cross once. Both the equilibrium price and the equilibrium quantity will be positive. (More precisely, this is true as long as the vertical intercept of the demand curve is larger than the vertical intercept of the supply curve. If this is not the case, then the most that any buyer is willing to pay is less than the least any seller is willing to accept and there is no trade in the market.)

Table 8.2 "Market Equilibrium: An Example" shows an example of market equilibrium with market supply and market demand at four different prices. The equilibrium occurs at $10 and a quantity of 50 units. The table is based on the following equations:

and

Equations such as these and diagrams such as Figure 8.5 "Market Equilibrium" are useful to economists who want to understand how the market works. Keep in mind, though, that firms and households in the market do not need any of this information. This is one of the beauties of the market. An individual firm or household needs to know only the price that is prevailing in the market.

Reaching the Market Equilibrium

Economists typically believe that a perfectly competitive market is likely to reach equilibrium for several reasons.

• If the prevailing price is different from the equilibrium price, then there will be an imbalance between demand and supply, which gives buyers and sellers an incentive to behave differently. For example, if the prevailing price is less than the equilibrium price, demand will exceed supply. Disappointed buyers might start bidding the price up, or sellers might realize they could charge a higher price. The opposite is true if the prevailing price is too high: suppliers might be tempted to try decreasing prices, and buyers might look for better deals. These are informal stories because the supply and demand curves are based on the idea that firms and consumers take prices as given. Still, the idea that there will be pressure on prices away from equilibrium is a plausible one.
• There is strong support for market predictions in the evidence from experimental markets.In Chapter 6 "eBay and craigslist", we explain that a double oral auction, in which buyers and sellers meet individually and bargain over prices, typically yields results very close to the market outcome in Figure 8.5 "Market Equilibrium".
• The supply-and-demand framework generally provides reliable predictions about the movement of prices.

A Shift in Supply: Beer Prices in Britain

Figure 8.6 A Shift in the Supply Curve of an Individual Firm

An increase in marginal cost leads a firm to produce less output at any given price. This means that a firm’s supply curve shifts upward and to the left.

When we quoted the British newspaper article about beer prices in the chapter introduction, we omitted some sentences. The first sentence reads, in full: “The average price of a pint of beer could hit £4 [pounds sterling] after poor weather forced up the price of hops.” A few sentences later the article states: “Hop farmers have not seen any price rises for years, but the appalling summer has finally forced the prices up.” According to the article, the price of beer is increasing because the price of hops has increased.

This makes intuitive sense, but it is worth understanding the exact chain of reasoning here. Hops are a key ingredient in the production of beer. An increase in the price of hops means an increase in the cost of producing beer. More precisely, the marginal cost of producing beer increases. The typical beer producer decides how much to produce by observing this decision rule:

If marginal cost increases, then, at the existing price, the producer will find that price is now less than marginal cost. To bring price back in line with marginal cost, the producer will have to produce a smaller quantity. In fact, at any given price, an increase in marginal cost leads to a reduction in output (Figure 8.6 "A Shift in the Supply Curve of an Individual Firm"). The supply curve of an individual firm shifts to the left.

The increase in the price of hops affects all firms in the market. Each firm sees an increase in its marginal cost of production, so each firm produces less output at a given price: the shift in supply shown in Figure 8.6 "A Shift in the Supply Curve of an Individual Firm" applies to all firms in the market. Figure 8.7 "A Shift in Market Supply" shows the outcome in the market. Because all the individual supply curves shift to the left, the market supply curve likewise shifts to the left. At any given price, firms supply less beer to the market. From the figure, we see that the higher price of hops leads to an increase in the price of beer and a reduction in the quantity of beer produced and sold.

Figure 8.7 A Shift in Market Supply

An increase in the price of hops causes all beer producers to produce less at any given price. This means that the market supply curve shifts to the left. The consequence is an increase in the equilibrium price and a decrease in the equilibrium quantity.

For the individual producer, what does this mean? The producer sees an increase in marginal cost. In the new equilibrium, the producer also obtains a higher price. However, the increase in price is not as big as the increase in marginal cost. Because the producer sets price equal to marginal cost, each individual brewer still produces less. We show this in Figure 8.8 "The New Equilibrium from the Perspective of an Individual Firm".

1. The price of hops, an input into beer production, has increased, which increases the marginal cost of producing beer.
2. At each given price, beer producers want to supply less beer: the firm supply curve shifts to the left.
3. Because all the individual supply curves shift to the left, the market supply curve also shifts to the left.
4. The beer market reaches a new equilibrium with a higher price and smaller quantity of beer produced and consumed.

Figure 8.8 The New Equilibrium from the Perspective of an Individual Firm

Following the increase in the price of hops, the equilibrium price of beer increases. An individual firm ends up with higher marginal cost but also receives a higher price for beer. Because the increase in price is smaller than the increase in marginal cost, beer production still decreases.

Comparative Statics

The approach that we used here is an illustration of a general technique used by economists to explain changes in prices and quantities and to make predictions about what will happen to market prices.

The most difficult part of a comparative staticsA technique that allows us to describe how market equilibrium prices and quantities depend on exogenous events. exercise is to determine, from the description of the economic problem, which curve to shift—supply or demand. Once you determine which curve is shifting, then it is only a matter of using the supply-and-demand framework to find the new equilibrium. The final step is to compare the new equilibrium point (the new crossing of supply and demand) with the original point. With this comparison, you can predict what will happen to equilibrium prices and quantities when something exogenous changes.

A Shift in Demand

Let us try this technique again. Recall the second story from the chapter introduction about Detroit Tiger merchandise. In that story, we learned that “most shops have marked down jerseys and T-shirts branded with ex-Tigers between 25 and 50 percent.” Figure 8.9 "Shifts in Household Demand" shows the demand of a typical Detroit household’s demand for Granderson shirts. Now that Granderson has left the Tigers for the New York Yankees, the household’s marginal valuation for these shirts is lower. At any given price, a household wants to purchase fewer shirts, so the household’s demand curve shifts to the left.

Figure 8.9 Shifts in Household Demand

A decrease in the marginal valuation of Granderson T-shirts leads a household to demand a smaller quantity at any given price. This means that a household’s demand curve shifts to the left.

We would expect that this shift in demand would apply to most households that contain Detroit Tigers fans. If we now add all the demand curves together, we get the market demand curve. The market demand curve shifts to the left (Figure 8.10 "Shifts in Market Demand"). The end result is that we expect to see a decrease in the price of T-shirts—that is, the retailers put them in the discount bins—and also a decrease in demand.

Figure 8.10 Shifts in Market Demand

The decrease in demand causes both the equilibrium price and the equilibrium quantity of T-shirts to decrease.

Learning about the Slopes of the Supply and Demand Curves

Comparing our beer and T-shirt examples, we see that the quantity demanded decreased in both examples. In the first case, price increased; in the second case, price decreased. We can understand the difference by using the supply-and-demand framework. In the Detroit Tigers example, there is a decrease in the price of shirts and in the quantity sold. This might seem like a violation of the law of demand, which tells us that when price decreases, the quantity demanded increases. The explanation comes directly from Figure 8.10 "Shifts in Market Demand".

• Market demand is downward sloping and obeys the law of demand.
• Both equilibrium price and equilibrium quantity decrease after the departure of Granderson to the New York Yankees.

Curtis Granderson’s move leads to a shift in the demand curve and a movement along the supply curve. The law of demand, by contrast, applies to the movement along a demand curve.

Estimating Demand and Supply Curves

Comparative statics allows us to make qualitative predictions about prices and quantities. Given an exogenous shock in a market, we can determine whether (1) the price is likely to increase or decrease and (2) the quantity bought and sold is likely to increase or decrease. Often, though, we would like to be able to do more. We would like to be able to make some predictions about the magnitudes of the changes.

Figuring out what will happen to equilibrium prices and quantities requires economists to know the shapes of supply and demand. When the supply curve shifts, we need to know about the slope of the demand curve to predict the impact on price and quantity. When the demand curve shifts, we need to know about the slope of the supply curve to predict the impact on price and quantity. More precisely, we need measures of the elasticity of demand and of supply.

How do economists learn about these elasticities? The answer, perhaps surprisingly, is through the logic of comparative statics. For example, suppose the supply curve does not move, but the demand curve shifts around a lot. As the demand curve shifts, we observe different combinations of prices and quantities. Part (a) of Figure 8.11 "Finding the Elasticities of the Supply and Demand Curves" shows this in a supply-and-demand diagram. The different points that we observe are points on the supply curve. If the demand curve shifts but the supply curve does not, we eventually gather data on the supply curve. We can use these data to come up with estimates of the price elasticity of supplyThe percentage change in the quantity supplied to the market divided by the percentage change in price..

Toolkit: Section 31.2 "Elasticity"

The price elasticity of supply equals the percentage change in the quantity supplied divided by the percentage change in price.

Figure 8.11 Finding the Elasticities of the Supply and Demand Curves

Economists estimate the elasticities of supply and demand curves by looking for situations in which one curve is relatively stable while the other one is moving. What we actually observe are the equilibrium points. Movements in the demand curve (a) mean that the equilibrium points trace out the supply curve; movements in the supply curve (b) allow us to observe the demand curve. In most real-life cases, both curves move, and economists use sophisticated statistical techniques to tease apart shifts in supply from shifts in demand.

Part (b) of Figure 8.11 "Finding the Elasticities of the Supply and Demand Curves" shows the opposite case, where demand is stable and the supply curve is shifting. In this case, the data that we observe are different points on the demand curve. We can use this information to estimate the price elasticity of demandThe percentage change in the quantity demanded in the market divided by the percentage change in price., which is the percentage change in the quantity demanded divided by the percentage change in price. It is important to note that we are speaking here about the elasticity of the market demand curve, not the elasticity of the demand curve facing an individual firm.

This sounds straightforward in theory, but it is difficult in practice. Economic data are messy. Typically, both the demand curve and the supply curve are shifting simultaneously. If economists had access to controlled environments, perhaps like a biochemist does, we could “shift the demand curve” and see what happens in the laboratory. Occasionally, we get lucky. Sometimes we can isolate a particular event that we know is likely to shift only one of the curves. This is sometimes called a natural experimentAn exogenous change that can be associated with a shift in either the demand curve only or the supply curve only.. Most of the time, however, we are not so lucky. Economists and statisticians have come up with sophisticated statistical techniques to disentangle shifts in demand and supply in these circumstances.Chapter 7 "Where Do Prices Come From?" discusses how a firm can use a similar technique to learn about the demand curve that it faces. Chapter 11 "Raising the Wage Floor" discusses the difficulties of measuring the demand curve for labor.

Key Takeaways

• Changes in prices come from shifts in market supply, market demand, or both.
• Economists use comparative statics to predict changes in prices. This technique explains how changes in exogenous variables cause shifts in supply and/or demand curves, which lead to changes in prices.

Checking Your Understanding

1. Suppose coffee crops in Brazil are destroyed by inclement weather. What happens to the supply curve for coffee? What happens to the price of coffee and the equilibrium quantity of coffee?
2. The discussion of the Detroit Tigers states that “it’s too soon to tell which Tigers will prove popular at the checkout line.” Suppose that Miguel Cabrera has an excellent season and breaks the home run record. What do you expect will happen to the price and quantity of T-shirts with his name on the back?
3. In our discussion of the demand for beef and mad cow disease, we said that an increase in quantity and a decrease in price require a rightward shift of the supply curve. Draw a diagram to illustrate this case.

Buyer Surplus

Consider the market for chocolate bars, as shown in Figure 8.5 "Market Equilibrium". At the market clearing price, suppliers and demanders of chocolate bars trade the equilibrium quantity of chocolate bars. Imagine first that each household purchases no more than a single chocolate bar at the equilibrium price. For example, if 200 chocolate bars are sold, then 200 separate households bought a chocolate bar. Not all these households are alike, however: some like chocolate bars more than others. Most of them would have, in fact, been willing to pay more than the equilibrium price for the chocolate bar. Their valuation of a chocolate bar is greater than the price.

Any household that would have been willing to pay more than the equilibrium price gets a good deal. For example, suppose the equilibrium price is $5, but a household would have been willing to pay $7. Then that household receives a buyer surplus of $2.See Chapter 6 "eBay and craigslist" for more discussion. This logic extends to the case where households consume more than one unit. The demand curve of a household indicates the maximum amount that a person would pay for each successive unit of a good. The demand curve shows the household’s marginal valuation of a good. The individual household’s demand curve slopes downward because the household is willing to pay less and less for each successive unit—the marginal unit—as the total quantity consumed increases.

In general, we know that a household purchases chocolate bars up to the point where

The household receives no surplus on the very last bar that it purchases because the marginal valuation of that bar equals price. But it receives surplus on all the other bars because its marginal valuation exceeds price for those bars. Diminishing marginal valuation means that the household obtains surplus from all the chocolate bars except the very last one.

Table 8.3 "Calculating Buyer Surplus for an Individual Household" gives an example of a household facing a price of $5. The first column is the quantity, the second is the price, the third is the marginal valuation (the extra value from the last chocolate), the fourth column measures the marginal surplus, and the last column is the total surplus.

The household is willing to buy three chocolate bars because the marginal value of the third bar is exactly equal to the price of $5. (In fact, the household would be equally happy buying either two or three bars. It makes no substantive difference to the discussion, but it is easier if we suppose that the household buys the last bar even though it is indifferent about making this purchase.) The household would not buy four bars because the marginal valuation of the last unit is less than the price, which means the surplus from a fourth chocolate bar would be negative.

The household obtains surplus from the first and second bars that it purchases. The household would have been willing to pay $10 for the first bar but only had to pay $5. It gets $5 of surplus from this first bar. The household would have been willing to pay $8 for the second bar but only had to pay $5. It gets $3 of surplus for this second bar. It gets no surplus from the third bar. So the total buyer surplus for this household is $5 + $3 = $8. Notice that by following the rule “buy until marginal valuation equals price,” the household maximizes its total surplus from the purchase of chocolate bars.

More generally, the buyer surplus for this household is measured by the area under its demand curve (Figure 8.12 "Buyer Surplus for an Individual Household"). For each unit, the vertical difference between the price actually paid for each unit and the price the household would have been willing to pay measures the surplus earned for that unit. If we add the surplus over all units, we get the area between the demand curve and the price.

Figure 8.12 Buyer Surplus for an Individual Household

The buyer surplus is equal to the area between the demand curve and the price.

Seller Surplus

Sellers as well as buyers obtain surplus from trade. Suppose you won a used bicycle that you value at $20. If you can sell that bicycle for $30, you receive a seller surplus of $10—the difference between the price and your valuation of the good. It is worth your while to sell as long as the price is greater than your valuation. When a firm is producing a good for sale, the situation is analogous. If a firm can produce one more unit of a good at a marginal cost of $20, then the firm’s valuation of the good is effectively equal to $20. If the firm can sell that unit for $30, it will receive a surplus of $10. The seller surplus earned by a firm for an individual unit is the difference between price and the marginal cost of producing that unit.

Given the price prevailing in a market, an individual firm in a competitive market will supply output such that the marginal cost of producing the last unit equals the price. The firm follows the rule: increase production up to the point where

The example in Table 8.4 "Calculating Seller Surplus for an Individual Firm" gives the marginal cost of production for each unit and the surplus earned by a firm from producing that unit. If the firm produced only one unit, it would incur a marginal cost of $1, sell the unit for $5, and obtain a surplus of $4. The second unit costs $3 to produce, providing the firm with a surplus of $2. The third unit provides surplus of $1. The fourth unit costs $5 to produce, so the firm earns no surplus on this final unit. So the firm produces four units and obtains a total seller surplus of $7.

This difference between the price of a good and the marginal cost of producing the good is the basis of the seller surplus obtained by a firm. Exactly analogously to a household’s buyer surplus, we measure the seller surplus by looking at the benefit a firm gets from selling each unit, and then we add them together. For each unit, the seller surplus is the difference between the price and the supply curve (remember that the supply curve and the marginal cost curve are the same thing). When we add the surplus for all units, we obtain the area above the supply curve and below the price (Figure 8.13 "Seller Surplus for an Individual Firm").

Figure 8.13 Seller Surplus for an Individual Firm

The seller surplus is the area between the equilibrium price and the firm’s supply curve.

Buyer Surplus and Seller Surplus for the Entire Market

So far we have considered the buyer surplus and seller surplus for an individual household and an individual firm. Because the market demand and supply curves are obtained by adding together the individual demand and supply curves, the same result holds if we look at the entire market. We illustrate this in Figure 8.14 "Surplus in the Market Equilibrium", which shows the total surplus flowing to all households and firms in the market equilibrium. The area below the market demand curve and above the price level is the total buyer surplus. The area above the market supply curve and below the price is the total seller’s (producer’s) surplus.There is one slightly technical footnote we should add. In some circumstances, the seller surplus may not all go to the firm. Instead, it may be shared between the firm and its workers (or other suppliers of inputs to the firm). Specifically, this occurs when increases in the market supply are large enough to cause input prices to change.

Figure 8.14 Surplus in the Market Equilibrium

The total surplus generated in a market is the sum of the buyer surplus and the seller surplus. It is therefore equal to the area below the demand curve and above the supply curve.

Markets and the Gains from Trade

The buyer surplus and the seller surplus tell us something remarkable about market outcome. If we add together the surplus for all buyers and sellers, we obtain the total surplus (gains from trade) in the market. In a competitive market, this is the maximum amount of surplus that it is possible to obtain—that is, exchange in a competitive market exhausts all the gains from trade.

There are two ways of seeing why this is true. First, we can ask what level of output would give us the largest total surplus. You might be able to see by looking at Figure 8.14 "Surplus in the Market Equilibrium", where the equilibrium quantity yields the largest total surplus. Figure 8.15 "Surplus Away from the Market Equilibrium" explains why in more detail. If there are fewer trades, then some surplus goes unrealized: some transactions that would yield positive surplus do not take place. To put it another way, there are buyers whose marginal valuation exceeds the marginal cost of production but who are unable to purchase the good. By contrast, if there are more trades than the equilibrium quantity, then some trades generate a negative surplus. The marginal cost of producing output beyond the competitive level is less than the goods are worth to consumers.

Second, the following things are true at the market equilibrium:

• For each household, the marginal valuation for the last unit equals the price.
• For each firm, price equals the marginal cost for the last unit.

Combining these two pieces of information, we know that each household’s marginal valuation of the last unit is the marginal cost of producing that unit. As quantity increases, marginal valuation decreases and marginal cost increases. Therefore, if more of the good were produced, the marginal cost of the extra units would be higher than the marginal valuation. By the same argument, if fewer units were produced, the reduction in the household’s valuation would be higher than the reduction in cost. So producing one unit more or one unit less would not be beneficial to households and producers. Remember that it is the adjustment of prices that ensures that an economy trades at the point where supply and demand are equal. Price adjustment allows buyers and sellers to obtain all the gains from trade.

Figure 8.15 Surplus Away from the Market Equilibrium

If the quantity traded is less than the equilibrium quantity (a), then some gains from trade go unrealized. If the quantity traded is greater than the equilibrium quantity (b), then some trades generate negative surplus.

Why Markets?

We have been highlighting one of the principal messages in economics: markets are a mechanism to achieve the gains from trade. But are there other ways of achieving the same result? We previously introduced the fiction of an all-knowing, all-powerful central planner. Such a planner tells everyone what they should produce, takes all those goods, and distributes them throughout the economy. The planner tells everybody how much to work at each technology and decides exactly how to distribute all the goods and services that the economy produces.

Should we take this idea seriously or is it only a device to help us think about our theory? The answer is a bit of both. No economy has ever literally been run by a central planner. Historically, though, there have been many examples of so-called planned economies, where government bureaucracies played a major role in deciding what goods and services should be produced. For much of the 20th century, the economy of the Soviet Union operated under such a regime. China also used to be a largely planned economy. North Korea still operates as a largely planned economy.

Neither the Soviet Union nor China enjoyed much economic success under this system. The collapse of the Soviet Union’s economy was a key reason why the country itself collapsed. China eventually changed its system of economic organization to one that gives more primacy to markets. Today, there are very few economies that operate under central planning and none that are significant in global economic terms. However, there are still several economies in which the government plays a significant role in the allocation of resources; so the analysis of the planner remains relevant.

Why were planned economies so unsuccessful? Books have been written on this topic, but there is one key insight. In order to make good decisions—decisions in the interest of individuals in the economy—the planner would need a lot of information. It is simply inconceivable that a planner could have sufficient knowledge about the abilities and skills of different individuals to make good decisions about where and how much they should work. Moreover, the planner also needs to know the tastes of everyone in the economy. Without that knowledge, the planner might instruct them to produce too many chocolate bars or not enough beer. If we think of an economy with millions of inhabitants, all with their own preferences and abilities, it is surely impossible that a planner could be sufficiently well informed to make decisions that are in the interest of all an economy’s inhabitants.

Credit Market

The credit market (or loan market)Where suppliers and demanders of credit meet and trade.—we use the terms loans and credit interchangeably—is where suppliers and demanders of credit meet and trade (Figure 8.16 "Credit Market Equilibrium"). On the supply side are households and firms that, for various reasons, have chosen to save some of their current income. On the demand side are other households, firms, and (in some cases) the government. Households buy houses and cars, so they often need to borrow funds to finance those purchases. Firms seek credit to finance investment, such as the construction of a new production plant. Finally, governments borrow to finance some of their expenditures.

Figure 8.16 Credit Market Equilibrium

This diagram represents the loan or credit market.

The price of credit is the real interest rate, which is a measure of the value of the interest charged on a loan, adjusted for inflation. There are many different markets for credit because there are different kinds of loans in the economy.Chapter 10 "Making and Losing Money on Wall Street" discusses these. Associated with these different credit markets are different interest rates. For simplicity, though, we often suppose that there is a single market for credit.

The demand for credit decreases as the real interest rate increases. When it becomes more expensive to borrow, households, firms, and even governments want fewer loans. The supply of credit by households increases with the real interest rate. When the return on savings increases, households and firms will typically save more and so supply more loans to the market.The response of savings to changes in the real interest rate is discussed more fully in Chapter 5 "Life Decisions".

The news is filled with stories about interest rates increasing and decreasing. You can always use some version of Figure 8.16 "Credit Market Equilibrium" to understand why interest rates are changing. Ultimately, any change in the interest rate is due to a shift in either the supply of credit or the demand for credit. For example, if construction firms anticipate high future demand for housing, they will think that building new homes is a good use of investment funds. They will borrow to finance such construction. The increased demand for credit will shift the demand curve in Figure 8.16 "Credit Market Equilibrium" outward, and interest rates will increase. As another example, if individuals in other countries wish to increase their investment in US assets, this will shift the supply of credit outward, and interest rates will decrease.

Two of the most important players in the credit market are the government and the monetary authority. If the US federal government borrows more, this shifts the demand for credit outward and increases the interest rate. (The government is such a big player in this market that its actions affect the interest rate.) The monetary authority, meanwhile, buys and sells in credit markets to influence the real interest rate in the economy.The actions of the Federal Reserve and other monetary authorities are studied in detail in macroeconomics courses.

Foreign Exchange Market

If you travel abroad, you need to acquire the currency used in that region of the world. If you take a trip to Finland, Russia, and China, for example, you will undoubtedly buy euros, rubles, and yuan along the way. To do so, you need to participate in the foreign exchange marketThe place where suppliers and demanders of currencies meet and trade., trading one currency for another. Foreign exchange markets operate like other markets in the economy. The price—which in this case is called the exchange rateThe price in the foreign exchange market. It measures the price of one currency in terms of another.—is determined by the interaction of supply and demand.

Figure 8.17 "Foreign Exchange Market Equilibrium" shows an example of a foreign exchange market—the market in which US dollars are exchanged for euros. On the horizontal axis, we show the number of euros bought and sold on a particular day. On the vertical axis is the exchange rate: the price of euros in dollars. This market determines the dollar price of euros just like the gasoline market in the United States determines the dollar price of gasoline.

Figure 8.17 Foreign Exchange Market Equilibrium

This diagram represents the foreign exchange market in which euros are bought and sold with US dollars.

On the demand side, there are traders (households and firms) who want to buy European goods and services. To do so, they need to buy euros. This demand for euros expressed in dollars need not come from US households and firms. Anyone holding dollars is free to purchase euros in this market. On the supply side, there are also traders (households and firms) who are holding euros and who wish to buy US goods and services. They need to sell euros to obtain US dollars.

There is another source of the demand for and the supply of different currencies. Households and, more importantly, firms often hold assets denominated in different currencies. You could, if you wish, hold some of your wealth in Israeli government bonds, in shares of a South African firm, or in Argentine real estate. But to do so, you would need to buy Israeli shekels, South African rand, or Argentine pesos. Likewise, many foreign investors hold US assets, such as shares in Dell Computer or debt issued by the US government. Thus the demand and the supply for currencies are influenced by the portfolio choices of households and firms. In practice, the vast majority of trades in foreign exchange markets are conducted by banks and other financial institutions that are adjusting their asset allocation.

In addition to households and firms, monetary authorities also participate in foreign exchange markets. For example, the US Federal Reserve Bank monitors the value of the dollar and may even intervene in the market, buying or selling dollars in an attempt to influence the exchange rate.

If you open a newspaper or browse the Internet, you can quickly find the current price of euros. This price changes all the time in response to changes in the currency’s demand and supply. For example, if you read that the euro is getting stronger, this means that the euro is becoming more expensive: you must give up more dollars to buy a euro. This increase in the price of the euro could reflect either an outward shift in the demand for euros, say as US households demand more goods from Europe, or an inward shift of the euro supply curve if holders of euros are not as willing to sell them for dollars.

Labor Market

In the markets for goods and services, the supply side usually comes from firms. In some cases, buyers are other firms (businesspeople call these B2B transactions), whereas in other cases buyers are households (often called B2C transactions). For the most part, though, households are not on the supply side of these markets. In the labor market, by contrast, firms and households switch roles: firms demand labor and households supply it.

Supply and demand curves for labor are shown in Figure 8.18 "Labor Market Equilibrium". Here the price of labor is the real wage. The real wage measures how much in the way of goods and services an individual can buy in exchange for an hour’s work. It equals the nominal wage (the wage in dollars) divided by the general price level.

The demand for labor comes from the fact that workers’ time is an input into the production process. This demand curve obeys the law of demand: as the price of labor increases, the demand for labor decreases. The supply of labor comes from households that allocate their time between work and leisure activities. In Figure 8.18 "Labor Market Equilibrium", the supply of labor is upward sloping. As real wage increases, households supply more labor. There are two reasons for this: (1) higher wages induce people to work longer hours, and (2) higher wages induce more people to enter the labor force and look for a job.Chapter 11 "Raising the Wage Floor" explains more about nominal wages and real wages, and we study the individual demand for labor in Chapter 9 "Growing Jobs". The decisions underlying labor supply are explained more fully in Chapter 4 "Everyday Decisions".

Figure 8.18 Labor Market Equilibrium

The equilibrium real wage is the price where supply equals demand in the labor market.

As with the other markets, we can use Figure 8.18 "Labor Market Equilibrium" to study comparative statics. For example, if an economy enters a boom, firms see more demand for their products, so they want to buy more labor to produce more product. This shifts the labor demand curve outward, with the result that real wages increase and employment is higher.

Multiple Markets

You have now seen equilibrium in a wide variety of markets: goods (chocolate), loans, foreign exchange, and labor. Actual economies contain hundreds of thousands of markets. Analyzing a single market would be enough if the markets in an economy were not connected, but markets are interrelated in many ways:A topic in advanced studies of economics is the simultaneous equilibrium of all markets. Because all markets are linked, it is necessary to find prices for all goods and services and all inputs simultaneously such that supply equals demand in all markets. This is an abstract exercise and uses lots of mathematics. The bottom line is good news: we can usually expect an equilibrium for all markets.

• Factors that shift the demand in one market may affect other markets as well. For example, an increase in energy costs will raise the marginal costs of firms in all sectors of an economy.
• The demand for one good depends on the prices of others. In the market for coffee, for example, the demand curve depends on the price of goods that are complements to coffee, such as milk, and the prices of goods that are substitutes for coffee, such as tea.
• The supply curve for most goods depends on the prices of inputs, such as labor. The real wage—the price of labor—is determined by the supply and demand for labor. Thus the outcome of the labor market influences the position of the supply curve in almost every other market.
• The income level of households affects the position of the demand curve for most goods and services. But the level of income comes, in part, from the labor market outcome because labor income is part of the income households have to spend.

The following newspaper story from the Singaporean newspaper the Straits Times nicely illustrates linkages across markets.

Look at the last paragraph. First, we are told that a drought has caused a drop in sugarcane production in Thailand. Part (a) of Figure 8.19 "The Sugar Market in Thailand and the Butter Market in Australia" shows this market. We can see that a decrease in sugar production will increase the price of sugar. In this picture we are showing the market in Thailand, so the price is measured in Thai baht.

Figure 8.19 The Sugar Market in Thailand and the Butter Market in Australia

(a) The market for sugar in Thailand is affected by a drought, which has decreased the sugar supply, causing an increase in sugar prices measured in Thai baht. (b) In the Australian butter market, increased demand from China causes the demand curve to shift outward, increasing the price of butter measured in Australian dollars.

We are also told that there has been increased demand for dairy products coming from China. Australia and New Zealand are the major suppliers of dairy products in Southeast Asia. Part (b) of Figure 8.19 "The Sugar Market in Thailand and the Butter Market in Australia" shows the market for butter in Australia. Increased demand from China shifts the demand curve outward, leading to an increase in the price of butter. For this market, we measure the price in Australian dollars.

From the perspective of Singapore bakers, both of these price changes show up as increases in their marginal cost. Moreover, the article reveals that these changes are exacerbated by other factors. Shipping costs have increased, so it also costs more to obtain sugar from Thailand and butter from Australia. And the Australian dollar has appreciated relative to the Singapore dollar, making goods imported from Australia even more expensive.

These are examples of B2B transactions. In fact, there is likely a whole chain of such transactions between, say, the Australian dairy farmer and the Singaporean baker. Farmers sell milk to butter producers, butter producers sell to wholesalers, and wholesalers sell to Singaporean importers and bakeries.

This story also illustrates again the powerful way in which market prices provide information that helps us understand the efficient allocation of resources. Drought in Thailand has reduced the amount of sugar available in the world. Through the magic of a series of prices, one of the results is that people in Singapore are less likely to eat cake for dessert.

Shifts in the Marginal Cost of Production

Figure 8.20 "Finding the Profit-Maximizing Price and Quantity When a Firm Has Market Power" shows how a firm with market power sets its price.This figure is explained more fully in Chapter 7 "Where Do Prices Come From?". To maximize its profits, a firm wants to produce the quantity where marginal revenue equals marginal cost. It sets the appropriate price as a markup over marginal cost.

Figure 8.20 Finding the Profit-Maximizing Price and Quantity When a Firm Has Market Power

A firm with market power faces a downward-sloping demand curve and earns maximum profit at the point where marginal revenue equals marginal cost.

Now what happens if marginal cost increases? Think of a single beer producer and then imagine that the price of hops increases, so the marginal cost of producing an extra unit of output increases. This change in the marginal cost of production leads the brewer to decrease production (Figure 8.21 "An Increase in Marginal Cost"). Marginal cost decreases and marginal revenue increases until the two are again equal.

Figure 8.21 An Increase in Marginal Cost

In response to an increase in marginal cost, a firm now finds it optimal to set a higher price and produce a smaller quantity of beer.

Although Figure 8.21 "An Increase in Marginal Cost" is drawn for a single seller, it captures the common experience and response of all sellers. The increase in the price of hops causes the marginal cost to increase for all brewers, and they all respond by producing less and increasing the price of beer. And this is exactly what we predicted about prices and quantities when we considered an increase in marginal cost in a perfectly competitive market.

Shifts in Demand

Now reconsider the T-shirt example. There may be only a small number of producers who are licensed to produce Detroit Tigers T-shirts. Although there are many different kinds of replica sporting shirts in the world—at least one for each major team in most of the sports you can imagine—these shirts are not all the same. So the market for replica T-shirts—and certainly the market for Granderson T-shirts—is not competitive. The producers of Granderson shirts for the Tigers choose quantities and set prices (see Figure 8.20 "Finding the Profit-Maximizing Price and Quantity When a Firm Has Market Power").

Figure 8.22 "Shifts in Demand and Marginal Revenue" shows the market as seen by one of these producers. Granderson’s move from the Tigers shifts the demand curve inward for the shirts that they produce. This shift in the demand curve also shifts the marginal revenue curve inward. In response, the firm adjusts its output so that marginal revenue again equals marginal cost, choosing its price to match the point on the demand curve at the new quantity produced. Output and price both fall. Again, this is the same prediction that we obtained from the comparative statics of a competitive market.

Figure 8.22 Shifts in Demand and Marginal Revenue

A decrease in demand causes marginal revenue to shift to the left. Marginal cost and marginal revenue intersect at a lower level of output. This lower level of output means marginal cost is lower, so the firm will also decrease its price.

When Is Using Supply and Demand Misleading?

Even when markets are not perfectly competitive, the supply-and-demand framework is usually a good device for predicting what will happen to prices and quantities in a market following a shock. Even if firms have market power, an increase in marginal cost will typically lead to an increase in the price and a decrease in the quantity supplied, just as supply and demand predict. Similarly, an increase in demand will typically lead to an increase in the price and an increase in the quantity supplied, again as predicted by basic supply-and-demand reasoning.

Although the supply-and-demand framework can be used for most situations where markets are not perfectly competitive, we still need to know when it might mislead us.

• Though unlikely, it is possible that an increase in demand will lead to an increase in the price and a decrease in the quantity supplied. This is because it is possible, though unlikely, that an increase in demand will cause marginal revenue to decrease.
• It is possible that an increase in demand will lead to an increase in quantity but a decrease in the price. There are two ways this could happen, both stemming from the fact that a firm sets its price as a markup over marginal cost. First, even if demand is greater, the elasticity of demand could change so as to make the optimal markup. Second, some firms with market power may have decreasing marginal cost.

We also need to recognize that while we may be able to use supply-and-demand intuition for qualitative predictions, it is more difficult to make quantitative predictions when markets are not competitive. We cannot determine supply and demand elasticities as easily when firms have market power. The reason is that one firm’s decisions depend on what other firms are doing. Consider, for example, an increase in marginal cost in the beer industry. We have said that each firm in the market will respond by increasing its price and decreasing its quantity (Figure 8.21 "An Increase in Marginal Cost"). For example, Miller in the United States will set higher prices in response to an increase in the price of hops. But when markets are not perfectly competitive, the story does not stop there. Firms also look at the prices set by their competitors. Miller’s decisions on pricing depend also on the price chosen by Budweiser. If Budweiser sets a higher price as well, then Miller may want to increase its price still further, and so on.How exactly this plays out is a complicated problem, requiring some of the ideas that we introduce in Chapter 15 "Busting Up Monopolies" and Chapter 17 "Cars".

To sum up, the supply-and-demand framework can occasionally mislead when markets are not perfectly competitive. Yet most economists still begin with supply and demand when trying to explain a change in prices or quantities. Then they consider if there are reasons to expect either changes in the elasticity of demand or decreasing marginal cost. If neither of these seems likely, then the simple intuition of supply and demand will almost certainly give the right answer.

Market Demand

With this notation, we represent the demand curve as follows:

α_d, β_d, and γ_d are constants that characterize the effects of prices and income on the quantity demanded. With the restriction that β_d > 0, the demand curve is downward sloping because an increase in p implies a reduction in the quantity demanded. It is natural to assume γ_d > 0, so an increase in income leads to an increase in the quantity demanded. This is represented as a shift in the demand curve.

Market Supply

With this notation, we represent the supply curve as follows:

α_s, β_s, and γ_s are constants that characterize the effects of prices and income on the quantity demanded. With the restriction that β_s > 0, the supply curve is upward sloping because an increase in p leads to an increase in the quantity supplied by all firms. It is natural to assume γ_s > 0, so an increase in the productivity of the current technology leads to an increase in the quantity produced at a given price. This is represented as a shift in the supply curve.

Market Equilibrium

The market is in equilibrium if there is a price and quantity combination, denoted (p*, q*) such that at the price p*, the quantity demanded, and the quantity supplied equal q*. Equilibrium is the simultaneous solution of supply and demand and can be found using the substitution method outlined in the toolkit.

Using q^s = q^d = q*, we can substitute Equation 8.2 into Equation 8.1 yielding:

This is a single equation in a single unknown, p*. Solving the equation for p* implies

The denominator is positive because we have assumed that both β_d and β_s are positive. The numerator is positive as long as the vertical intercept of the demand curve is greater than the vertical intercept of the supply curve: (α_d + γ_sI) > (α_s + γ_dA). This condition, combined with the restrictions on the slopes of supply and demand, is sufficient to guarantee that an equilibrium price exists in the market.

Using this calculation of p* in, say, the supply curve, we find

Grouping the terms into a constant, γ_dI and γ_sA, this becomes

Looking at Equation 8.4 and Equation 8.6, these expressions determine the equilibrium price and the equilibrium quantity depending on the two (exogenous) factors that impact supply and demand: income level I and state of technology A. Though income influences only the position of the demand curve, variations in income influence both the equilibrium price and the equilibrium quantity. The same is true for variations in technology that shift only the supply curve.

The Decisions of a Firm

Firms hire labor to help them produce output. The amount of labor that a firm needs depends on the amount of output that it wants to produce. At the same time, its decision about how much to produce depends on its costs of production, which include the cost of labor. Our task here is to combine these ideas. The decision about how much labor to hire is only one of a large number of choices made by a firm’s managers. Of these, the most fundamental decisions are the following:

• Should a firm be in business at all?
• How much should a firm produce, and what price should its managers set?
• How should a firm produce its desired level of output?

A firm’s managers should actually answer these questions in the reverse order:

1. Managers should first determine the best way to produce output.
2. Then managers need to make a price/output decision. A firm is fundamentally constrained by the desires of the market. If managers choose the price of output, they must accept whatever sales are demanded by consumers at that price. If they choose the level of output, they can only charge the price that the market will bear for that quantity. In other words, a firm’s managers must choose a point on the demand curve facing a firm.
3. Then, and only then, can a firm’s managers decide if it is worth being in business at all. An existing firm can stay in the market or exit, thus destroying jobs. Potential new firms can enter the market and create jobs.

We follow this logic in our discussion.

The Production Function

A firm possesses a means of turning inputs into outputs. For example, Starbucks produces, among other things, grande vanilla low-fat decaf lattes. This drink is an example of a Starbucks output. The list of inputs that Starbucks needs to produce this product is much too long to write out in full but includes the following:

• Water, coffee beans, milk, vanilla syrup, paper cups, lids, and electricity
• An espresso machine
• The time of the barista—the person making the drink
• Starbucks’ “blueprints” (that is, the instructions for how to make a grande vanilla low-fat decaf latte)

This list doesn’t include any of the “back office” aspects of Starbucks’ operations, such as accounting, payroll, or the logistics of sourcing coffee beans and delivering them to individual stores. Other firms, of course, would have a very different list of inputs. So if we want to talk in abstract terms about the production of a firm, we need a description of production that could apply not only to Starbucks but also to General Motors, IKEA, your local computer repair store, and a manufacturer of paper clips. Therefore, we group inputs into broad categories called factors of productionThe inputs used in a firm’s production process, primarily physical capital, labor hours, raw materials, and technology..

You can think of raw materials as the things that are transformed in the production process. In our Starbucks example, these include milk, coffee beans, and electricity. Labor refers to the time of the employees who work at a firm, so the time put in by a Starbucks’ barista counts as labor. Capital refers to goods that are used to help with production but are not used up in the process. The espresso machine is one of Starbucks’ capital goods; others are the tables and chairs in the café.

Starbucks’ technologyA means of producing output from inputs.—which we also think of as a factor of production—is the knowledge that allows it to take all these inputs and turn them into an output—the final product that people actually want to buy. It is this knowledge that ultimately lies behind Starbucks’ existence as a firm. Included in the technology are the managerial skills that allow Starbucks to operate effectively.

Figure 9.5 The Technology of a Firm

The production function combines a firm’s physical capital stock, labor, raw materials, and technology to produce output. Technology is the knowledge (the blueprints) that a firm possesses, together with managerial skills.

We represent the production process of a firm schematically in Figure 9.5 "The Technology of a Firm". Our description is quite general and can apply to nearly any kind of firm—for example, a lawyer’s office, Walmart, a university, and a child’s lemonade stand. Most people find it easiest to visualize a production function in terms of physical manufacturing, such as a production line for automobiles. Think of a firm’s capital as factory buildings and machinery; its labor as the workers on the production line; and its raw materials as the steel, plastic, and glass that it purchases.

A Production Function That Uses Only Labor

We summarize the technological possibilities of a firm using a production functionA description of how much output a firm can produce as it varies its inputs., which is a description of how much output a firm can produce as it varies its inputs. Even though a typical firm’s production function contains many different inputs, we can understand most of the key features of the production function using an example where labor is the only factor of production. Although there are few goods or services that literally require no inputs other than labor, there are many services that are highly labor intensive, such as babysitting, housecleaning, and personal training at a gym.

To be concrete, think about housecleaning and suppose it has the following production function:

output = productivity × hours of labor input,

where we think of productivity as just some number. If output measures clean houses, and if it takes 5 hours of labor to produce one clean house, then productivity is 0.2, and the production function is

output = 0.2 × hours of labor input.

The production function tells us the level of output of a firm for given levels of labor input. Labor input is the total hours of labor time used by a firm. At this point, we are not distinguishing between hours worked per person and the number of people working, so a firm with 8 employees each working 20 hours per week has the same weekly labor input as a firm with 4 employees each working 40 hours per week. Table 9.1 "Production Function for Housecleaning" lists the amount of output that a housecleaning firm can obtain from various levels of input. We call this a linear production function because its graph is a straight line, as shown in Figure 9.6 "A Linear Production Function".

Table 9.1 Production Function for Housecleaning

Labor Input (Hours)	Output (Clean Houses)
0	0
1	0.2
2	0.4
3	0.6
4	0.8
5	1
10	2
15	3
20	4
25	5
30	6
35	7
40	8

Figure 9.6 A Linear Production Function

A production function shows the maximum amount of output produced, given a level of labor input.

The marginal product of laborThe amount of extra output produced from one extra hour of labor input. is the amount of extra output produced from one extra hour of labor input and is defined as

$$\text{marginal product of labor}=\frac{\text{change in output}}{\text{change in labor input}}\text{.}$$

When the production function is linear, the marginal product of labor is constant. It is equal to the number we labeled productivity in our original production function.

In most cases, the marginal product of labor is not constant. To understand why, imagine you are managing a Starbucks outlet. You already have the machines to produce espresso, and you have lots of coffee beans on hand. You also have 500 square feet of space for making coffee and charging customers. But you still need labor. If you have no barista to operate the espresso machine, then you will have no output. If you hire one worker, you will be able to serve coffee to people. Adding the first worker will increase output considerably. However, that person must not only make the coffee but also clear the tables and handle the cash register. Adding a second worker to help with the register and clear tables will increase output even more. Now suppose you keep increasing the number of workers in the 500 square feet of space. After the third or fourth worker, they will start to bump into each other, and the barista will start to be very annoyed and unproductive. In other words, because one of your inputs—the amount of available space—is fixed, each additional worker contributes less and less to output. We call this the diminishing marginal product of laborThe idea that each additional hour of labor input contributes a smaller and smaller amount to output..

Table 9.2 "Production Function for Coffee with a Diminishing Marginal Product of Labor" is an example of a production function with a diminishing marginal product of labor. In creating this table, the labor input is changed while holding all other inputs (the size of the café, the number of espresso machines, etc.) fixed.

Table 9.2 Production Function for Coffee with a Diminishing Marginal Product of Labor

Labor Input (Hours)	Output (Cups of Coffee)	Marginal Product of Labor
0	0
1	10	10
2	14.1	4.1
3	17.3	3.2
4	20	2.7
5	22.4	2.4
…
10	31.6	1.6
15	38.7	1.3
20	44.7	1.1
25	50.0	1.0
30	54.8	0.9
35	59.2	0.9
40	63.2	0.8

The marginal product of labor is shown in the third column. For the first few entries, you can calculate it directly from the table because you can easily determine how much output changes from one row to the next. For example, the marginal product of the third hour of labor is 17.3 – 14.1 = 3.2. Finding the marginal product of, say, the 40th unit of labor from the table is trickier because the table doesn’t tell us how much we can produce with 39 hours of labor. Looking back at the formula for the marginal product of labor, however, we can calculate it:

$$\text{marginal product of labor}=\frac{\text{change in output}}{\text{change in labor input}}=\frac{63.2-59.2}{40-35}=\frac{4}{5}=\mathrm{0.8.}$$

We illustrate this production function in Figure 9.7 "A Production Function with a Diminishing Marginal Product of Labor". Notice that while the slope of the production function is always positive, the slope decreases as the labor input increases.

Figure 9.7 A Production Function with a Diminishing Marginal Product of Labor

This production function exhibits diminishing marginal product of labor: as more labor is added to a firm, output increases at a decreasing rate.

Toolkit: Section 31.17 "Production Function"

The production function is a description of how much output a firm can produce as it varies its inputs. Typically, we suppose that the production function exhibits the following:

• Positive marginal product of labor
• Diminishing marginal product of labor

The first property means that adding more labor into production means more output—that is, the slope of the production function is positive. The second property explains how the marginal product of labor varies as labor input increases. Though the marginal product of labor is always positive, it will generally decrease as more labor is added to a production process. That is why the second property is called diminishing marginal product of labor. (It is technically possible that the marginal product of labor could even become negative. But because a firm would never pay for workers when they decrease output, we never expect to see a firm operating with a negative marginal product of labor.)

The Cost Function

Now that we have a way of describing a firm’s ability to produce goods, we are well on our way to understanding how a firm produces output. This then allows us to understand how much it will cost a firm to produce different levels of output. Our next goal is to describe these costs. The total cost of producing some specified level of output represents the cost of acquiring all the inputs needed.

To see how this works, let us determine the costs for our earlier housecleaning example. Recall that the production function is

Suppose that housecleaners can be hired at $10 per hour:

The cost of two clean houses is $100, the cost of three clean houses is $150, and so on.

More generally, suppose we take the linear production function and divide both sides by the level of productivity. We get

The cost of a single hour of labor is given by the wage. Thus we can write

This is the cost function of a firm, which is illustrated in Figure 9.8 "The Cost Function". Pay careful attention to the axes in Figure 9.6 "A Linear Production Function" and Figure 9.8 "The Cost Function". Figure 9.6 "A Linear Production Function" has hours of labor on the horizontal axis and output on the vertical axis. Figure 9.8 "The Cost Function" has output on the horizontal axis and costs (= labor hours × wage) on the vertical axis.

Figure 9.8 The Cost Function

The cost function shows the cost of producing different levels of output.

Marginal Cost

The cost function in Figure 9.8 "The Cost Function" is linear. Because the production function has a constant marginal product of labor, the cost function displays constant marginal cost. What about the case in which the production function has a diminishing marginal product? Then additional labor provides less and less output. Turning this around, it follows that producing each additional unit of output requires more and more labor. We show this in Figure 9.9 "The Cost Function with a Decreasing Marginal Productivity of Labor". In this figure, the marginal cost is increasing, so the cost function gets steeper as we produce more output.

Toolkit: Section 31.14 "Costs of Production"

You can review the definition of marginal cost in the toolkit.

Figure 9.9 The Cost Function with a Decreasing Marginal Productivity of Labor

If a firm’s technology exhibits a diminishing marginal product of labor, the cost function will increase at an increasing rate.

We show the marginal cost curve in Figure 9.10 "The Marginal Cost Function". In this example, marginal cost is a straight line, but this need not be the case in general.

Figure 9.10 The Marginal Cost Function

If a firm’s technology exhibits a diminishing marginal product of labor, then the marginal cost will increase as output increases.

Marginal cost depends on the following:

• The cost of inputs into the production process
• The productivity of the inputs into the production process

If the costs of inputs increase, then the marginal cost is higher is well. If the productivity of the inputs into the production function is higher, then the marginal cost is lower. In fact, marginal cost can be written as

$$\text{marginal cost}=\frac{\text{wage}}{\text{marginal product of labor}}\text{.}$$

We can see from this equation that when the marginal product of labor decreases, the marginal cost of production increases. We see also that an increase in the cost of inputs—in this case an increase in wages—leads to an increase in the marginal cost of production.