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k Learning Objectives
By the end of the chapter, you will be able to:
• Discuss the importance of utility in explaining consumer choice.
• Derive an individual demand curve for a good based on the equation for maximizing total utility and the principle of diminishing marginal utility.
• Apply utility theory to explanations of consumer behavior.
• Identify and describe the concept of consumer surplus.
• Describe how advertising attempts to increase utility.
Demand and Consumer Choice
5
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Section 5.1 Choice, Value, and Utility Theory CHAPTER 5
Introduction
Consider this. . . Where you work, where you shop, and most certainly in the stu-dent union there is a vending area. In that area there are most likely coin-operated machines that supply everything from soft drinks, to snacks, to newspapers. If you think about it, you will notice a significant difference between the machines that dispense soft drinks or snacks and those that dispense newspapers. After you have deposited the requisite amount of money, the food and drink machines provide a single can or package through a chute of some sort, while the newspaper machine allows you to open a door and take one paper from a stack. Why? Are readers more honest than eaters?
This chapter will help provide an answer to this puzzle. To do this we will look at what determines consumer choice. Since individual demand curves form the bedrock of micro- economic analysis, we need to consider the factors that underlie them.
The first approach economists took in examining consumer demand, the classical approach, involved the concept of measurable utility. We will use this approach to examine some problems and suggest some applications for demand analysis. The second approach to consumer demand, indifference curve analysis, is discussed in an appendix to this chapter.
5.1 Choice, Value, and Utility Theory
T he idea that households and firms must make choices because of scarcity is the fun-damental notion of economic analysis. We now want to expand on that analysis to consider why consumers behave in the way they do. Why does a person demand a certain good or service? An obvious answer is that the good or service is expected to satisfy some need or desire of the consumer.
Economists’ view of consumer choice is based on five assumptions about the psychology of consumer behavior:
1. Consumers (or households) must make choices because they have limited income and are forced to choose which of their many wants to satisfy.
2. Consumers make rational choices when they make these consumption decisions. That is, they weigh costs and benefits and make the decision that gives them the most satisfaction.
3. Consumers make these choices with imperfect information. In other words, they don’t know (with certainty) all the attributes of the goods they are choosing to consume.
4. As increasing amounts of a good are consumed, the additional satisfaction gained from an additional unit becomes smaller.
5. Many goods have qualities that make them satisfactory substitutes for other goods.
All of these statements may seem simple and obvious, but they will enable us to draw some powerful conclusions about the nature of demand.
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Section 5.1 Choice, Value, and Utility Theory CHAPTER 5
The History of Utility Theory: The Diamond-Water Paradox
In the early development of economic theory, economists often posed questions that they then debated. One of the popular debate topics was what determined value. Adam Smith wrote that value could mean either “value in use” or “value in exchange.” He posed (in 1776) what became known as the diamond-water paradox:
The things that have the greatest value in use have frequently little or no value in exchange; and on the contrary, those which have the greatest value in exchange have frequently little value in use. Nothing is more valuable than water, but it will purchase scarce anything; scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it. (Smith)
The diamond-water paradox was the problem that classical economists used when they argued that value in use could not determine price (value in exchange). Diamonds, although less useful than water, are more expensive than water. The dialogue about the diamond- water paradox went on for a long time. Many famous mathematicians, economists, and philosophers took part in the debate. The confusion over the diamond-water paradox arose in part over disagreement as to what the term useful meant. In the 1870s, William Stanley Jevons, Carl Menger, and Leon Walras, all writing separately, solved the paradox by develop- ing a theory of value in which demand and utility came to the forefront. Their solution played a major role in developing the theory of consumer demand.
Another part of the debate underlying the diamond-water paradox was an argument over whether value (or price) was determined by supply or demand. In a famous analogy, Alfred Marshall, the great Brit- ish economist, said that you could no more say whether supply or demand determined value than you could say which
Economics in Action: Crunch Into Utility Theory Using the classic potato chip, this video bites straight into utility theory, to help us understand the total amount of satisfaction one gains from a product despite the diminishing marginal utility. Check out the following clip provided by MindBites at http://www.youtube.com/watch?v=PZJR9EemtjQ.
Ingram Publishing/Thinkstock
The diamond-water paradox argues that value in use cannot determine price. Diamonds, for example, are arguably less useful than water but are more expensive than water.
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Section 5.1 Choice, Value, and Utility Theory CHAPTER 5
blade of a pair of scissors did the cutting. That is, value (or price) is determined by the interaction of supply and demand.
We’ll consider the influence of demand on value first and leave supply for later chapters. Demand theorists use the notion of utility. If a consumer wants a good or service, then that good or service has utility for that person. Utility is the satisfaction a consumer receives from consuming a good or service. The same good may have a great deal of utility for one person and none or very little for some other person. Like beauty, utility is in the eye (or mind) of the beholder.
Total Utility and Marginal Utility
A good unit for the measurement of utility, like the pound or gallon or mile, does not exist. Since utility is unique to the individual, however, an arbitrary (and imaginary) unit called the util can be employed. As long as no attempt is made to compare the number of utils of different people, this is a satisfactory measuring device. Such comparisons between people are inappropriate because the number of utils is a subjective measure of a cer- tain individual’s satisfaction and as such is not subject to meaningful comparisons. (Some people prefer the beach to the mountains!)
A relationship that expresses a person’s desire to consume differing amounts of a good is called a utility function. For example, suppose you try to construct your utility function for a certain brand of soft drink. First, choose a convenient time period, such as a day. Then, for one unit (one can) of Coke per day, assign an arbitrary number of utils, say 20. (You can choose any number at all: 1, or 1,000, or 47 1/2.) Ask yourself, if I get 20 utils from one can, how many would I get if I consumed two cans per day? Suppose, after much reflection, you say 38. Ask yourself the same question about three cans per day, four, five, six, and so on. You use these figures to construct a utility schedule, as shown in Table 5.1.
Table 5.1: Utility schedule for Coke
Cans of Coke per day Total utility (utils) Marginal utility (utils)
1 20 20
2 38 18
3 54 16
4 67 13
5 77 10
6 84 7
7 88 4
8 89 1
9 87 22
10 82 25
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Section 5.1 Choice, Value, and Utility Theory CHAPTER 5
Marginal utility (MU) is the amount of utility that one more or one less unit consumed adds to or subtracts from total utility. It is the change in satisfaction provided by one more or one less unit of consumption. The formula for marginal utility is
MU 5 change in total utility
change in quantity consumed
In Table 5.1, the marginal utility is determined by calculating how much each additional can of Coke adds to total utility. For example, the first can of Coke adds 20 utils to total utility. The fourth can of Coke adds 13 utils to total utility. Marginal utility is found by subtracting the total utility of consuming three Cokes from the total utility of consuming that number plus one (67 2 54 5 13).
Principle of Diminishing Marginal Utility
The important feature of the schedule shown in Table 5.1 is that, although the total utility becomes larger the more you consume per day (up to a point), the increases to total utility from each additional unit consumed become smaller. The fact that additional, or marginal, utility declines as consumption increases is called diminishing marginal utility.
The principle of diminishing marginal utility states that the greater the level of con- sumption of a particular good in a given time period, the lower the marginal utility of an additional unit. As you consume more units of a good, the later units yield less of an addi- tion to total utility than the preceding units did. For instance, the seventh Coke is expected to provide less additional pleasure than the sixth Coke. This principle is reflected in Table 5.1. Marginal utility falls from 7 utils for the sixth Coke to 4 utils for the seventh.
Figure 5.1(a) shows the total utility curve plotted from Table 5.1. Figure 5.1(b) shows the marginal utility curve that corresponds to the table. Note that when the total utility curve reaches its maximum, marginal utility is zero. Thereafter each additional unit contributes a negative marginal utility; thus, total utility will be decreased. In Table 5.1, total utility reaches a maximum at eight Cokes per day because the ninth Coke has a negative mar- ginal utility.
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Section 5.1 Choice, Value, and Utility Theory CHAPTER 5
Figure 5.1: Total and marginal utility
Total utility increases as consumption increases to a certain level—in this case 8 Cokes per day—and then it declines. When total utility is increasing, marginal utility is declining, illustrating the principle of diminishing marginal utility. At the point where total utility begins to decline, marginal utility becomes negative.
0
10 20 30 40 50 60 70 80 90
100
2
–2 –4 –6
4 6 8
10 12 14
20 18 16
1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Total Utility (Utils)
Cokes/Day
Total Utility
Marginal Utility
Cokes/ Day
(a)
(b)
Marginal Utility (Utils)
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Section 5.2 Utility and Consumer Behavior CHAPTER 5
5.2 Utility and Consumer Behavior
T he concepts of utility and price can be combined to show how consumers make choices in the marketplace. Consumers are confronted with a range of items and also a range of prices. A consumer may not necessarily choose based solely on which item has the greatest utility; price and the consumer’s income are also important factors. In other words, consumers don’t always buy their first choice. You may prefer a Porsche to a Chevrolet but decide to purchase the Chevrolet. The explanation for this behavior lies in the relationship between price and utility.
Suppose, for example, you are considering purchasing a six-pack of soft drinks. You are presented with the three possibilities shown in Table 5.2. Coke is your first choice because to you it yields the most utility. But the relevant question is not which soft drink has the most utility, but rather which has the most utility per dollar. Therefore, you choose to buy a six-pack of Pepsi. This choice implies that the extra satisfaction of Coke over Pepsi is not worth $0.75, but the extra satisfaction of Pepsi over RC Cola is worth $0.25. There are other things you can do with the extra $0.75. You are saying that $.75 spent on something other than Coke will yield more additional utils than the difference between the utility of Coke and the utility of Pepsi, but that $0.25 spent on other goods will not yield more utils than spending it on Pepsi instead of RC Cola.
Table 5.2: Hypothetical utility-per-dollar comparison
Choice Marginal utility (utils) Price (dollars) Marginal utility per dollar (utils)
Coke 30.0 3.00 10
Pepsi 27.0 2.25 12
RC Cola 20.0 2.00 10
Thus, in deciding how to spend your money, you look at marginal utility per dollar rather than marginal utility alone. You do this because money is the common measure of what you have to give up. Dollars can be used to buy any available good. So for each dollar you spend, you want to choose the item with the highest utility per dollar. In doing so, you economize by getting the most satisfaction per dollar.
Maximizing Total Utility
The self-interest assumption maintains that individuals will act to maximize their total utility. To see how marginal utility and price influence how a consumer maximizes total utility, consider an example with only two goods, Coke and pizza. A unit of Coke costs $0.50 and a unit of pizza costs $1. The consumer’s utility schedules for the two goods are presented in Table 5.3. The consumer has a given amount of income, called a budget constraint. A budget constraint is a given level of income that determines the maximum amount of goods that may be purchased by a consumer. Let’s allow this consumer a bud- get constraint of $13, and see how that amount will be allocated between the two goods to achieve maximum utility.
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Section 5.2 Utility and Consumer Behavior CHAPTER 5
Table 5.3: Utility for a consumer of two goods
Coke Pizza
Quantity per week (cans)
Marginal utility, MU (utils)
MU/P (P 5 $.50)
Total utility, TU (utils)
Quantity per week (pieces)
Marginal utility, MU (utils)
MU/P (P 5 $1.00)
Total utility, TU (utils)
1 15 30 15 1 32 32 32
2 14 28 29 2 31 31 63
3 13 26 42 3 28 28 91
4 12 24 54 4 24¾ 24¾ 115¾
5 11 22 65 5 20¼ 20¼ 136
6 10¾ 21½ 75¾ 6 18 18 154
7 10¼ 20½ 86 7 17 17 171
8 10 20 96 8 16 16 187
9 9 18 105 9 14 14 201
10 8 16 113 10 12 12 213
11 7 14 120 11 11 11 224
12 6½ 13 126½ 12 9 9 233
The first dollar will be allocated to pizza because a dollar’s worth of pizza (one piece) yields 32 utils of satisfaction compared with 29 utils for a dollar’s worth of Coke (two cans). The next dollar will also be spent on pizza because it yields 31 utils, which is still greater than the first dollar’s worth of Coke, the alternative purchase. In other words, the consumer buys two pieces of pizza before buying any Coke. The third dollar is spent on Coke because the 29 utils of satisfaction gained from purchasing two cans are greater than the 28 utils that are yielded by a third piece of pizza. The process continues until the entire income of $13 is spent. In maximizing total utility, the consumer will spend $5 on ten cans of Coke and $8 on eight pieces of pizza. This allocation produces 300 utils of satisfaction—the maximum total utility that can be purchased with $13 of income. You cannot find a different combination of Coke and pizza that will produce more satisfaction (try reducing Coke consumption by two cans and increasing pizza consumption by one piece, or vice versa).
The consumer’s choices are based on a maximization rule that says that total utility is maximized when the last dollar spent on good A yields the same utility as the last dollar spent on good B. In algebraic form, total utility is maximized when
Marginal utility of of good A
Price of good A 5
Marginal utility of of good B
Price of good B
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Section 5.2 Utility and Consumer Behavior CHAPTER 5
This can be written
MUA PA
5 MUB
PB
The marginal utility of a can of Coke, when ten cans per week are consumed, is 8 utils, and the price of a can is $0.50. Thus,
MUcola Pcola
5 8
$0.50 5 16 utils per dollar
For pizza, at the optimum consumption rate, the marginal utility is 16, and the price is $1. Thus,
MUpizza Ppizza
5 16
$1.00 5 16 utils per dollar
Of course, individuals don’t spend all their income on goods. Sometimes individuals hold money as they do any other commodity. Including money (symbolized by $), the equation for maximization of utility is
MUA PA
5 MUB
PB 5
MU$ P$
Utility maximization is the process by which a consumer adjusts consumption, given a bud- get constraint and a set of prices, in order to attain the highest total amount of satisfaction. The equation above is an expression for utility maximization. It includes all commodities, even money. This equation says that in order to maximize total utility, the marginal utilities per dollar of all goods consumed have to be equal and also have to equal the marginal utility of money. If this is not the case, a change in the consumption pattern can produce more satis- faction for a given budget constraint. This equation is just a formal way of saying that people allocate their income so as to yield the most satisfaction possible. When utility is being maxi- mized, the additional satisfaction from any use of a dollar will equal the additional satisfac- tion from any other use of that dollar. When this is not the case, the consumer can reallocate personal income from one good to another and gain more satisfaction.
To see how a given consumption pattern can be adjusted to achieve maximum utility, look again at Table 5.3. Let’s give Susan an income of $9 and say that she uses it to buy $3 worth of cola and $6 worth of pizza. The expression
MUcola Pcola
5 MUpizza
Ppizza
doesn’t hold because
10 34 0.50
. 18 1
Susan isn’t maximizing her utility because the last dollar she spent on cola yielded more utils than the last dollar she spent on pizza. Susan should reallocate her consumption outlays.
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Section 5.2 Utility and Consumer Behavior CHAPTER 5
By giving up a dollar’s worth of pizza, she will lose 18 utils. But she will gain 20 1/4 utils by spending that dollar on more cola. Her total utility will thus rise by 2 (rounded off), and
10 0.50
. 20 14
1
By purchasing eight cans of cola and five pieces of pizza, Susan is maximizing utility with a $9 budget constraint.
Marginal Utility and the Law of Demand
Utility theory makes it possible to derive a consumer’s demand curve for a good (good x). Suppose there are only two goods, x and y. Remember, demand curves are drawn using the ceteris paribus assumption. That is, income, tastes, and the prices of all other goods (good y) are held constant. The consumer is initially in equilibrium, maximizing utility when
MUx Px
5 MUy
Py
At this equilibrium, MU xl corresponds to the consumption of x
1 units of good x in Figure
5.2. The price of x 1 units is represented by P
1 in Figure 5.2.
Figure 5.2: Demand curve for good x
When price falls from P 1 to P
2 , the consumer’s utility maximization is thrown out of equilibrium.
Equilibrium will be restored if the consumer increases consumption to x 2 .
0
Price
Quantity/ Time Period
P1
P2
x1 x2
Dx
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Section 5.2 Utility and Consumer Behavior CHAPTER 5
Now suppose the price of good x falls to P 2 . This change throws the expression out of
equilibrium because the denominator on the left side is now smaller, making the left side of the expression larger.
To get back into equilibrium, the consumer has to lower the value of the left side of the expression and/or raise the value of the right side. How can this be done? If the indi- vidual consumes more of x, MU
x will decline because of the principle of diminishing mar-
ginal utility. As consumption moves to x 2 on Figure 5.2, the marginal utility of good x falls.
Furthermore, consuming more of x will mean some reduction in the consumption of y. As consumption of y falls, MU
y rises.
Utility-maximizing behavior requires that when the price of good x falls (as from P 1 to
P 2 in Figure 5.2), the consumer will increase consumption of x. Since this is necessary for
utility maximization, it demonstrates that the demand curves of individuals must have a negative slope. That is, the lower the price of a good, the greater the quantity demanded.
Problems With Utility Theory
There are two major problems with a demand theory based on utility. The first problem is that some goods are not divisible. The second, more serious problem is that utility cannot be measured.
The theory works well enough to describe the consumption of certain kinds of goods, such as soft drinks or pizzas. When the good being consumed is an automobile or a home, however, it is difficult to talk about additional units because the purchase is “lumpy.” It is very difficult to consume a part of a house or a part of a car, but it is common to consume part of a six-pack of cola.
This problem with utility theory is really not a major flaw. Consumers can still make adjustments with most lumpy purchases. Consider a house as an example. Suppose the consumer decides after the purchase that the house is too large and that other purchases would yield more marginal utility. Over time, expenditures on the house can be lowered by a lessening of routine maintenance so that more can be spent on the other goods that yield a higher marginal utility. Buying a smaller house, buying one at a less desirable loca- tion, and renting are also available alternatives.
A greater problem with utility theory is that it is impossible to measure utility. We have proceeded as if there were a way we could strap a meter to a consumer and exactly mea- sure the utility expected from consuming one more unit, somewhat like measuring tem- perature or blood pressure. This is, of course, not possible. But before you reject utility theory as useless, remember that it is a theoretical tool. It really isn’t that important for the theory of demand to be able to measure utility. The purpose of utility theory is to develop a better understanding of why and how quantity demanded will change when prices change.
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Section 5.2 Utility and Consumer Behavior CHAPTER 5
Check Point: Utility Theory • Assumptions of model
Individual has budget constraint Individual gets utility from consumption Marginal utility diminishes as consumption rises
• Maximization Utility is maximized where the marginal utility per dollar spent on all goods (and the mar-
ginal utility of money) is equal • Testable implications
Quantity demanded is inversely related to price, ceteris paribus As the price of good rises, the demand for substitutes will increase, ceteris paribus As income rises, the demand for normal goods will increase, ceteris paribus
Policy Focus: Progressive Income Taxation—Are Utility Functions Interdependent? Many non-economists believe that money and income are subject to diminishing marginal utility. This idea is one of the main arguments (but certainly not the only one) for a progressive income tax. A progressive tax takes a larger percentage of dollars from those earning high incomes because for them a dollar’s marginal utility is thought to be low. A smaller percentage of dollars is taken from those taxpayers earning lower incomes because for them a dollar’s marginal utility is thought to be much higher. This argument assumes that it is possible to measure utility and to make interpersonal utility comparisons. Such comparisons are attempts to measure the utility of one individual relative to that of another. One way to avoid directly comparing utilities for different people is to assume that individuals all have the same utility schedule for given levels of income. With these two assumptions, proponents of the progressive income tax argue that society can maximize total utility by taking income away from high-income individuals who have lower marginal utilities of income and transfer- ring it to low-income individuals who have higher marginal utilities of income.
Those who apply principles of individual utility maximization to a society as a whole are on very shaky ground, however. First, economists generally believe that interpersonal utility comparisons are not feasible. People are different. There is no way you can prove that an additional $100 of income gives less satisfaction to actress Angelina Jolie than to an unemployed auto worker. In fact, Ms. Jolie might get more satisfaction from being an expert consumer. It is impossible to prove that one individual gets more or less satisfaction from an increment to income than any other individual does.
A second and more fundamental problem with this analysis is that it assumes a diminishing marginal utility for income, or goods and services in general. This proposition cannot be proven. The principle of diminishing marginal utility, you will remember, states that the marginal utility of a particular good declines as consumption is increased. Increased income, however, represents an increase in the consumption of all goods. If wants are insatiable, there is no reason to believe that the principle of diminishing marginal utility holds for money or income. Even so, it is probably the case that most people think that income has diminishing marginal utility. What do you think?
There may be other arguments for progressive income taxes. Progressive income taxes may offset more regressive sales or property taxes to create an overall proportional tax system. In other cases, where income is very unequally distributed, the only substantial source of revenue (continued)
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Section 5.3 Some Applications of Utility Theory CHAPTER 5
Income and Substitution Effects
The law of demand, which you studied in Chapter 3, states that as the price of a good or service declines, the quantity demanded increases, ceteris paribus. This law is true because of two effects that result from the price decline.
The first effect is called the substitution effect. When the price of a good (or service) falls, the good becomes less expensive relative to all other goods. As a result, consumers pur- chase more of it because it has become a better substitute for other goods as it has become cheaper. Steaks and ground beef provide a good example. As the price of steak falls, more people will switch from ground beef to steaks.
The second effect of a price decline is called the income effect. When the price of a good or service falls, ceteris paribus, the consumer’s real income, or purchasing power, rises. That is, after buying the same amount as before (of the good for which price has fallen), the consumer has more income left over. With this higher real income, more of all normal goods will be consumed. Thus, the consumption of the good whose price declined also will increase (if it is a normal good). Income and substitution effects, along with diminish- ing marginal utility, explain why demand curves slope down from left to right.
5.3 Some Applications of Utility Theory
You have practiced and observed utility maximization in your own life even though you may not have thought of it in the formal language of economics. Suppose, for example, you are organizing the beer concession for a fund-raising event. There are two ways to run the concession: you can charge an admission fee to the event and then allow unlimited consumption, or you can charge a set price for each beer, say $2.50 per glass. Utility theory predicts different levels of consumption for these two alternatives and thus different requirements for planning the supply. In the first case, beer drinkers will consume beer until the marginal utility per glass is zero because the price per addi- tional glass is zero. In the second case, beer drinkers will consume beer until the marginal utility per glass equals the marginal utility of $2.50. You can predict, then, that there will be more drunken, rowdy behavior if the party is financed by an admission charge.
If you don’t agree with this analysis, reflect back on parties you have observed. Were the most rowdy ones the pay-as-you-go type or the admission type? With the growing awareness of alcohol abuse on campus, student organizations on some campuses have outlawed keg beer parties (“all you can drink”) and required that they be replaced with
for the government to tap may be income taxes on the very wealthy. There may be subjective inter- pretations of what is equitable or fair that go way beyond the scope of economics. All economics has to say on the subject is that diminishing marginal utility is not a valid argument for progressive income taxation.
Policy Focus: Progressive Income Taxation (continued)
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Section 5.3 Some Applications of Utility Theory CHAPTER 5
can-only beer parties (pay by the can). These campus rule-setters understand diminishing marginal utility whether they know it or not.
This example may seem insignificant because the consumption of beer isn’t a very earth- shaking issue. Let’s change the good from beer to medical services. If the government were to provide free national health care, what do you predict would happen to the con- sumption of these services? People would consume them until the marginal utility of the last unit is zero. This is exactly what tends to happen with a prepaid or tax-financed health care system.
Take, for example, the health care reform undertaken by the state of Massachusetts in 2006. Building on a long history of reform efforts, Massachusetts created near-universal health care for state residents. Fast forwarding six years later, what was the result? First, by 2010 the percentage of uninsured individuals in Massachusetts was just 6.3 percent, compared to the national average of 18.4 percent. (Henry J. Kaiser Family Foundation, 2012) Although the number of visits to hospitals and community health centers increased,
as expected, these additional visits were primarily for adults receiving preventative care. According to a report by the Kaiser Family Foundation, “The number of unnecessary emer- gency room visits and hospital inpatient stays fell, suggesting improvements in health care delivery” (Henry J. Kaiser Fam- ily Foundation, 2012, 5). It is important to recognize that util- ity theory was able to predict an increase in the consumption of health care services, but not necessarily the type of services, which means that it only helps us to understand one aspect of such a policy change.
The Diamond-Water Paradox Explained
Adam Smith (and others) argued that utility (and thus demand) could not be a determinant of price because diamonds, while less useful than water, are more expensive than water. The paradox disappears if we distinguish between total utility and marginal utility. The total utility of water is high. However, since there is a great deal in existence and large quanti- ties are consumed, its marginal utility is low. The total utility of diamonds, on the other hand, is relatively low. However, since diamonds are rare, their marginal utility is high. Price, then, is determined by marginal utility, not total utility. Economists say that marginal utility determines value in exchange (price) and that total utility determines value in use. Price, then, is related to scarcity through utility. If something has a low marginal utility at all quantities consumed, it will have a low price, regardless of how scarce it is. If something is relatively scarce and has a high marginal utility, it will be valuable and thus expensive.
iStockphoto/Thinkstock
Utility maximization is practiced and observed in everyday life. For example, utility theory can help predict what might happen if the government were to provide free national health care.
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Section 5.4 Consumer Surplus and Utility CHAPTER 5
Shopping for Bargains
Economists have used the concept of utility-maximizing behavior to analyze shopping behavior. The idea is that a buyer will search for bargains until the expected savings in value or utility equals the cost of continued searching.
Several predictions can be made from this theory. The first is that the larger the amount individuals expect to save, the longer they will continue to search. In other words, the big- ger the item in terms of your budget, the more you will shop around. You will search lon- ger for a good price on a car than for a good price on a loaf of bread. You might even buy bread at a convenience store, where you know the price is higher, to save some shopping time. The second prediction is that, in percentage terms, the variation in prices for bigger budget items should be smaller than the variation in prices for smaller budget items. The search process will drive high-price sellers of large items out of business or force them to reduce their prices. The third prediction is that where search costs are higher, price dif- ferences between sellers could be higher without driving the high-priced sellers out of business. Have you ever noticed that prices of gasoline are higher near freeways than in towns? Utility-maximizing theory can explain this phenomenon. Users of freeways are going somewhere, often in a hurry. Their search costs are high. They therefore do less shopping around and as a result pay higher prices.
The Internet plays an important role by drastically reducing search costs, which may also have an impact on prices and buying behavior. For example, according to a study by Chiou and Pate (2010), online auctions exhibit substantially less price dispersion than documented in physical stores and other online markets. They also find evidence of greater search by price-sensitive shoppers, which generally leads to lower prices for all goods on the Internet.
5.4 Consumer Surplus and Utility
Consumers often benefit in a market economy because they are able to purchase a good or service by sacrificing something that is worth less to them than the value of what they receive. Consumer surplus is the extra utility derived from a purchase that has a value to the consumer greater than the market price. Utility theory provides a measure of consumer surplus.
Consider the demand curve for a single consumer (or group of homogeneous consumers) in Figure 5.3. At price P
1 the individual will consume Q
1 units of the good. According to
Economics in Action: Follow Your Cravings The Khan Academy explains marginal utility through chocolate bars and fruits. As an individual craves more chocolate and fruit, she or he will consider the satisfaction of each product individually and against each other. When price gets involved, marginal utility helps the individual decide how to gain the most “bang for the buck.” Follow the link to the Khan Academy (http://www.khanacademy.org), and then do a search for the video "Marginal Utility."
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Section 5.5 Advertising, Marketing, and Demand CHAPTER 5
the theory of utility-maximizing behavior, the marginal utility of the last unit purchased is equal to the price of the unit. This means that the marginal utility of each previous unit purchased was greater than price P
1 . The consumer would have been willing to pay
higher prices for those previous units, so at the market price of P 1 the consumer receives
a bonus in terms of utility on all units but the last one. The total purchase is worth more to the consumer than the total amount (price times quantity) that is paid. This extra util- ity gained is called consumer surplus and is represented by the shaded area in Figure 5.3. Consumer surplus will be an important concept when we study monopoly. The next Global Outlook box describes an application of consumer surplus in international trade.
Figure 5.3: Consumer surplus
The consumer surplus is the shaded area above the price P 1 and below the demand curve.
5.5 Advertising, Marketing, and Demand
T he theory developed in this chapter explains a great deal about demand and con-sumer equilibrium. It does not say anything about the role of advertising and mar-keting. Advertising and marketing are difficult topics for economists to deal with because economic analysis usually assumes that consumers are informed, rational utility maximizers who know their own tastes and preferences. Advertising and marketing are not, however, inconsistent with those basic assumptions.
0
Price
Consumer Surplus
Quantity/ Time Period
P1
Q1
D
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Section 5.5 Advertising, Marketing, and Demand CHAPTER 5
Advertisers spend a great deal of time trying to alter consum- ers’ tastes and perceptions. If enough tastes and perceptions can be changed that the aver- age consumer’s utility from the firm’s product can be increased, more will be demanded. Changes in tastes do not mean that the consumer is not ratio- nal. Even without advertising, tastes would change over time with changes in age, education, and other factors. Some tastes even change regularly with the change of season.
Advertisers also spend some time generating information for consumers about prices. This behavior of advertisers fits with the description of consumers’ search behavior. If the cost of getting information falls, the cost of the search falls and consumers will do more searching. As a consequence, they may alter their purchasing patterns and buy from sell- ers offering lower prices.
Much advertising is directed toward making consumer demand more in-elastic by con- vincing buyers that similar products are not satisfactory substitutes for the one being advertised. In other words, the advertiser attempts to widen the spread between the util- ity of its product and the utility of potential substitutes. From what you have learned in this chapter, you can see that if this strategy succeeds, an advertiser can charge a higher price for its product without losing many sales.
Shi Wei/Getty Images
Advertisers spend a great deal of time trying to alter consumers’ tastes and perceptions. Much advertising is directed toward making consumer demand more inelastic by convincing buyers that other products are not satisfactory.
Global Outlook: Pity the Poor Japanese Consumer! Japan places high tariffs on food products to protect an efficient and powerful political lobby in Japan. The Organization for Economic Co-operation and Development (OECD) calculates that over 45 percent of the value of Japan’s farm production comes from trade barriers or domestic subsidies. In addition to tariffs, Japan has additional rules that make imports of other vegetables and fruits both difficult and expensive for exporters. (United States Department of Agriculture, Economic Research Service, 2012)
American beef ranchers, rice farmers, and citrus growers complain bitterly to the U.S. government about these tariffs. In fact, U.S. producers of goods that the Japanese export to the United States use these high tariffs in Japan as an argument that the United States should impose tariffs on Japa- nese goods to create a “level playing field.” Let’s examine the effect of Japanese tariffs on Japanese consumers.
Tariffs have many effects. They reduce the efficiency of resource allocation. They redistribute income between countries and between producers and consumers within countries. They (continued)
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Section 5.5 Advertising, Marketing, and Demand CHAPTER 5
raise revenue for the countries that impose them. All of the economic effects of tariffs are important and will be discussed in the chapter on international trade. It is possible, however, to use the concept of consumer surplus developed in this chapter to see how tariffs affect the well-being of Japanese consumers.
In Figure 5.4, S d is the domestic supply curve and S
w is the world supply curve. World supply is per-
fectly elastic at the world price P f . Consumers are demanding quantity Q, of which quantity A is sold
by domestic producers and quantity Q - A is imported. The triangle formed by S w , D, and the vertical
axis represents consumer surplus. What happens if the government imposes a tariff equal to t? The price rises by the amount of the tariff to P
t , creating a new world supply curve, S’
w Consumers now
purchase quantity B from domestic producers and C - B from foreign producers. Consumer surplus is now represented by the triangle formed by S’
w , D, and the vertical axis. There has been a reduction
in consumer surplus equal to the difference between the two triangles, or the shaded area. What this example demonstrates is that a tariff permits domestic producers to sell more of a product at a higher price and that government revenues rise by the amount of the tariff times the imported quantity. However, consumers experience a decline in consumer surplus.
Figure 5.4: Tariffs and consumer surplus
Consumer surplus before the tariff is equal to triangle P f P
N b. The loss of consumer surplus is area
P f P
t ab.
0
Price
Quantity/ Time Period
Pf Sw
Sd
S′wPt
PN
Q
a
b
CBA
D
±
Global Outlook: Pity the Poor Japanese Consumer! (continued)
(continued)
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Key Points CHAPTER 5
Summary
Consider again. . . You should now be able to explain why the vending machine technology is different for newspapers than it is for food and drink. It surely has nothing to do with technology. It would be easy to have the paper delivered to you in the same way a pack of Skittles comes out of the machine. The explanation is in marginal utility analysis. Newspaper companies know that for most people the marginal utility of the second paper is zero—maybe even negative because you have to get rid of it. So most people will be honest. Have you ever taken a second paper when you only paid for one? If you did, perhaps the reason was that you anticipated that you would have to share the paper and as a result the second paper had positive utility. It is easy for newspapers to “trust” the honesty of people because the second unit of what they sell is “worthless.”
Key Points
1. Total utility is the total amount of satisfaction expected from consuming an item. Marginal utility is the change in total utility from consuming one more or one less unit of a good.
2. Consumers, in deciding among items, choose those items with the highest mar- ginal utility per dollar. An individual maximizes total utility by consuming all items so that their marginal utilities per dollar spent are equal. When the price of a good or service falls, the quantity demanded increases because of income effects and substitution effects.
3. Marginal utility determines value in exchange (price) and total utility determines value in use.
4. Consumer surplus is the extra utility derived from a purchase that has a value to the consumer that is greater than the price paid. In this sense consumer surplus is bonus utility to the consumer.
5. If advertising can change tastes and perceptions, the utility a consumer gets from the advertised product will increase.
The citizens that suffer the most from Japanese tariffs on beef, rice, and citrus are Japan’s own domestic consumers. The problem is that they are not an effective lobbying group, while Japanese farmers are. Given what we know about economics, what would we expect to see? In recent years, a small but growing number of Japanese consumers and businesses are doing what economics would predict: abandoning their loyalty to expensive, premium-grade homegrown rice and switch- ing to cheaper alternatives from China, Australia, and the United States (Tabuchi, 2012). If this trend continues, the downward pressure on domestic prices may lead Japanese farmers to rethink their strategy.
Global Outlook: Pity the Poor Japanese Consumer! (continued)
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Critical Thinking and Discussion Questions CHAPTER 5
Key Terms
budget constraint A given level of income that determines the maximum amount of goods that may be purchased by a consumer.
consumer surplus The extra utility derived from a purchase that has value to the con- sumer greater than the market price.
diamond-water paradox The fact that diamonds, although less useful than water, are more expensive than water. That is, things with the greatest value in exchange (price) often have little value in use.
income effect An increase in demand for a good (or service) when its price falls, ceteris paribus, because the household’s real income rises and the consumer buys more of all normal goods.
marginal utility (MU) The amount of utility that one more or one less unit of consumption adds to or subtracts from total utility.
principle of diminishing marginal utility The fact that the additional utility declines as quantity consumed increases. Less sat- isfaction is obtained per additional unit as more units are consumed.
substitution effect An increase in the quantity demanded of a good (or services) because its price has fallen and it becomes a better substitute for all other goods.
util An arbitrary unit used to measure individual utility.
utility The satisfaction that a consumer receives from consuming a good or service.
utility function A relationship expressing a consumer’s desire to consume differing amounts of a good.
utility maximization The process by which a consumer adjusts consumption, given a budget constraint and a set of prices, in order to attain the highest total amount of satisfaction.
Critical Thinking and Discussion Questions
1. How is the diamond-water paradox useful in explaining the difference between a useful good and a good that has utility?
2. What is diminishing marginal utility and why is it important? 3. How does the presence of a budget constraint limit the maximum utility possible? 4. What is consumer surplus and how is it related to utility? 5. The topics in this chapter discuss rational consumer behavior. Is it ever rational
to be irrational? 6. How does the presence of outlet stores impact consumer surplus? 7. If the developers of the Microsoft Surface tablet use flashy advertising to increase
sales, how are they trying to impact consumer utility? 8. The marginal utility of one good is 3 and the price is $4.00 and the marginal util-
ity of another good is 6 and its price is $2.00. According to consumer choice based on the maximization rule is the consumer maximizing utility? Explain.
9. Observers of the wealthy often comment on the fact that they tend to waste a lot of things, like food, but are very careful in their use of time. Is this irrational behavior?
10. If your rent doubles in one year, what happens to your budget constraint? How would this change the quantity and types of goods you purchase?
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Critical Thinking and Discussion Questions CHAPTER 5
11. What would you expect to happen to a normal consumer’s total utility for steak if the Surgeon General confirmed a link between the consumption of beef and certain cancers?
12. When restaurants offer “all-you-can-eat” buffets, they typically have restrictions. What restrictions might they want to impose and how are these related to utility theory?
13. If the government wanted to propose a more progressive tax system, how could they try to use the concept of diminishing marginal utility in their argument?
14. Does advertising increase or decrease the utility you receive from consuming cer- tain goods? Is this good or bad? Should certain types of advertising be regulated by the government?
15. How would a university policy to make food on campus more affordable for stu- dents impact the university’s utility? Are there other positive outcomes?
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Chapter 5 Appendix: Indifference Analysis: An Alternative Approach
to Consumer Choice
T he marginal utility theory discussed in this chapter has the drawback that it requires precise numerical values to be assigned to alternatives (cardinal utility). A later innovation in the economic theory of choice was based on ordinal utility. Ordinal utility requires only that the utility of the choices can be ranked. Instead of saving, “The next slice of pizza has 30 units of util- ity,” or, “The next Coke has 25 units of utility,” the consumer needs only to be able to say, “I prefer another slice of pizza to another Coke.”
In the late 1800s, Italian economist Vilfredo Pareto and British economist F.Y. Edgeworth, working separately, developed an approach to analyzing consumer behavior based on ordinal utility—indif- ference analysis. It wasn’t until 1939, when Nobel Prize-winning British economist Sir John Hicks published his classic book, Value and Capital, that this technique became popular with economic theorists and teachers. The theory swept the economics profession, and, for a while, marginal utility analysis fell into disrepute.
Pareto, Edgeworth, Hicks, and others were not trying to discredit utility theory; rather, they were proposing an alternative way of viewing consumer behavior. The major improvement of their the- ory is that it does not require the measurement of units of utility. All that is necessary is that con- sumers be able to rank bundles of goods in the order, from low to high, in which they prefer them.
5.1A Indifference or Preference
I ndifference and preference seem better than marginal utility for describing the way consumers actually make decisions. Individuals make choices between bundles, or collections, of goods. For example, you might choose between four tickets to a football game and two tickets to a concert. In indifference analysis, the consumer is viewed as making choices between collections of goods and services. The only assumption is that the consumer is able to state preferences for differ- ent collections or to profess indifference between some of them. In other words, confronted with a choice between going to a movie and going to a football game, the consumer might rank the football game as the preferred choice. Or the consumer might say, “I don’t have a preference. I’m indifferent to the two choices.”
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Section 5.1A Indifference or Preference CHAPTER 5 APPENDIX
Suppose Mary is considering different combinations of cans of Coke and slices of pizza, as indicated in Table 5.1A. Combination A consists of 16 cans of Coke and 3 slices of pizza, and combination B consists of 12 cans and 4 slices. When these two combinations are offered to Mary, she states that neither combination A nor combination B is preferred over the other. They are equal in the amount of satisfaction she expects to derive. Therefore, she is indifferent between the two. Offering Mary the choice among combinations C, D, and E yields the same response—indifference. Mary has indicated that all five combinations of pizza and Coke yield the same amount of satisfaction. These five combinations comprise an indifference set for her.
Table 5.1A: Mary’s indifference set
Combination Good x (cans of Coke) Good y (slices of pizza)
A 16 3
B 12 4
C 0 5
D 8 7
E 6 9
An indifference set can be represented graphically by an indifference curve. An indiffer- ence curve corresponding to the indifference set in Table 5.1A is shown in Figure 5.1A. An indifference curve shows all combinations of two goods (or services) among which a consumer is indifferent.
Indifference curves are negatively sloped because for a consumer to be in-different, all points on the curve must represent equal amounts of utility. If more of one good is added to the combination, some of the other must be removed. Each combination represents a trade-off. In Mary’s case, if combination B has more pizza than combination A, it must have less Coke, since the combinations yield the same level of satisfaction. If one combina- tion had more pizza and more Coke than any other, or if it had more of one without hav- ing less of the other, it would be preferred. The consumer would no longer be indifferent. This is yet another way of saying that more is preferred to less.
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Section 5.1A Indifference or Preference CHAPTER 5 APPENDIX
Figure 5.1A: Indifference curve
An indifference curve represents combinations of two goods among which the consumer is indifferent. All combinations on the same indifference curve give the same level of satisfaction.
The indifference set represented by a higher indifference curve is preferred to that repre- sented by a lower indifference curve. As Mary moves from I
1 to I
2 to I
3 to I
4 in Figure 5.2A,
she receives more satisfaction. Such a series of indifference curves is called an indiffer- ence map. Every individual consumer has such a map, and movement to a higher curve on the map represents a gain in utility.
0
10
7.5
5
2.5
2015105
Good y (Pizza)
Good x (Coke)
D
C
B
A
E
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Section 5.1A Indifference or Preference CHAPTER 5 APPENDIX
Figure 5.2A: Indifference map
An indifference map is a set of indifference curves, each corresponding to a different level of satisfaction. Higher curves on the map represent higher levels of satisfaction.
The shape of the typical indifference curve for two goods will be somewhat convex with respect to the origin. The convexity means that as a consumer gets more units of one good and fewer units of the other, it takes more and more units of the more abundant good to compensate for the loss of one unit of the good that is becoming more scarce. For example, at Point A in Figure 5.3A, the individual is consuming relatively large amounts of good y and small amounts of good x. In order to compensate for a reduction in consumption of 1 unit of y, the person would only require 2 units of x in order to be satisfied with such a trade. At Point B, however, since less of y and more of x are being consumed compared to Point A, it will take a larger quantity of x (5 units) to compensate for the loss of 1 unit of y. At Point C, the person is consuming a large amount of x and very little y. To give up 1 unit of y, 20 more units of x would be needed to have the same utility as before.
0
Good y (Pizza)
Good x (Coke)
I4
I3
I2 I1
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Section 5.2A Diminishing Marginal Rates of Substitution CHAPTER 5 APPENDIX
Figure 5.3A: Convexity feature of indifference curves
A typical indifference curve is convex to the origin. This convexity means that it takes increasingly larger amounts of the abundant good to compensate for losses of the good that is becoming more scarce.
Why do economists expect such preference relations to hold? First, most of us would agree that this is the way we would behave in such a trade-off situation. Second, the oppo- site conclusion seems highly unlikely. It would say that the less you had of a good, the less you would want of it relative to other goods, and the more you had of a good, the more valuable additional units of it would become. Indifference curves reflect the concept of diminishing marginal utility for two goods without assigning numerical values to utility.
5.2A Diminishing Marginal Rates of Substitution
T he trade-off ratio along an indifference curve is called the marginal rate of substitu-tion (MRS). The marginal rate of substitution of x for y, MRSxy shows the willing-ness of the consumer to substitute between goods x and y: MRSxy 5
number of units of y given up
number of units of x gained
0
10
9
8
7
6
5
4
3
2
1
7060
20
5040302010 1575
5
1
1
1
2
Good y
Good x
C
B
A
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Section 5.3A Budget Constraints CHAPTER 5 APPENDIX
In Figure 5.3A, the MRS xy
at Point A is 1/2. That is, 1 unit of y must be sacrificed to gain 2 units of x. At Point B, the MRS
xy is 1/5, and at Point C it is 1/20. The declining value of
MRS xy
is a reflection of the principle of diminishing marginal rates of substitution. That is, as more of one good (x) is substituted for the other good (y), the value of good x in terms of good y declines.
5.3A Budget Constraints
A n indifference map makes it possible to compare points representing combina-tions of two goods to determine whether the consumer prefers one such combina-tion or feels indifferent among several. All points on any single indifference curve are equivalent to each other in utility, even if utility cannot be measured numerically. Points on indifference curves located to the right and above other indifference curves are preferred combinations.
Which combinations are actually attainable for the consumer? The answer depends on the income available and on the prices of the goods. Keep in mind that the consumer faces prices that are determined in markets and cannot influence them. Income constrains the consumer from buying all that might be desired. The income is the budget constraint and, when drawn on the indifference map, is called the budget line.
We limit the analysis to two goods (you could think of one of them as “all other goods”). Again assume that Mary can consume either slices of pizza or cans of Coke. Suppose she has a disposable income (DI) of $10.00 and pizza (good y) and Coke (good x) sell for $1.00 and $0.50, respectively, per unit. The construction of the budget line is illustrated in Figure 5.4A. If she spends her entire income (DI) on pizza, she can buy 10 slices. This number is determined by dividing income by the price of the good:
DI Py
5 $10.00 $1.00
5 10 slices of pizza
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Section 5.3A Budget Constraints CHAPTER 5 APPENDIX
Figure 5.4A: Budget line
A budget line graphically depicts the consumption combinations that are attainable with a given level of income. Any combination above the line is unattainable.
Thus, 10 is the y-intercept. The x-intercept is calculated in the same manner:
DI Px
5 $10.00 $0.50
5 20 cans of Coke
A straight line connecting the two points that represent buying all good y (pizza) or all good x (Coke) shows all possible combinations that Mary can purchase with a given income level of $10. For example, $10 will buy 5 slices of pizza and 10 Cokes or 6 slices of pizza and 8 Cokes. Any combination outside (above) the line is unattainable at that income level. It is outside her budget constraint. In other words, the budget line is the dividing line between those combinations that are attainable and those that are unattain- able at a given level of prices and a given level of income.
0
=10= $10
$1
Good y (Pizza)
Good x (Coke)
DI
P1 Unattainable Combinations
Attainable Combinations
=20= $10
$50
DI
Px
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Section 5.4A Changes in Income and Changes in Price CHAPTER 5 APPENDIX
5.4A Changes in Income and Changes in Price
T he budget line is developed holding prices and income constant. How do changes in income and prices affect the budget line? An increase in income means that more of both goods can be purchased, if prices stay the same. A doubling of income means that twice as much of both goods can be purchased, if prices remain constant. An increase in income is represented by a parallel outward shift of the budget line. A decrease in income is represented by a parallel inward shift of the budget line. Such shifts are shown in Figure 5.5A.
Figure 5.5A: The effect of income changes on budget lines
An increase in income is represented by an outward parallel shift of the budget line. A decrease in income is represented by an inward parallel shift of the budget line.
A change in the price of one good affects the maximum amount of that good that can be purchased, but does not affect the maximum amount of the other good that can be purchased. If the price of cola rises and Mary spends all her income on pizza, the price rise has no effect on the amount of pizza purchased. A price rise, then, will only affect the intercept of the budget line with the axis for the good that has experienced the price rise. Such a change is shown in Figure 5.6A. A price rise for good x from P
x1 to P
x2 causes
the x-intercept of the budget line to move closer to the origin, reflecting the fact that
0
Good y
Good x
DI
Py
Increase in Income
Decrease in Income
DI
Px
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Section 5.4A Changes in Income and Changes in Price CHAPTER 5 APPENDIX
less of good x can now be purchased with constant income. A decrease in the price of good x from P
x1 to P
x3 means more of good x can be purchased. The x-intercept of the
budget line moves away from the origin, reflecting increases in the potential consump- tion of good x.
Figure 5.6A: The effect of price changes on budget lines
An increase in the price of one good changes the slope of the budget line because if all disposable income is spent on that good, less of it can be purchased. As a result, the intercept of the budget line will shift closer to the origin. The opposite holds for a decrease in price.
Price changes cause the slope of the budget line to change. The slope of the budget line is Dy/Dx. Note that the slope is the negative of the ratio of the y-intercept to the x-intercept, or
DI Py
DI Px
5 Px Py
The slope of the budget line changes when the ratio of the prices of the two goods changes. A change in income, on the other hand, represents no change in relative prices. In that case, the slope of the budget line remains the same, but it shifts as described above.
0
Good y
Good x
DI
Py
Decrease in Price of x
Increase in Price of x
DI
Px 1
DI
Px 2
DI
Px 3
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Section 5.5A Maximization of Consumer Satisfaction CHAPTER 5 APPENDIX
5.5A Maximization of Consumer Satisfaction
Adding a budget line to an indifference map makes it possible to demonstrate maxi-mization of consumer satisfaction. In Figure 5.7A, at Point A, the budget line is tangent to indifference curve I 2 . Any point on I
3 , such as Point B, is preferred to
Point A because higher indifference curves represent higher levels of utility. However, Point B is not attainable because it is outside the budget line. Point C on I
1 is attainable, but
a point on I 2 is also attainable, and any point on I
2 represents more satisfaction than any
point on I 1 . The consumer wants to reach the highest attainable indifference curve. The
highest attainable curve will be one that is tangent to the budget line because no higher curve can be reached with the given income and prices. In this example, the consumer is maximizing utility, or is in equilibrium, at Point A on indifference curve I
2 .
Figure 5.7A: Maximization of consumer satisfaction
An individual maximizes consumer satisfaction at the point where the budget line is tangent to the highest attainable indifference curve.
You should remember from geometry that two curves that are tangent have equal slopes at the point of tangency. At the point of tangency between the indifference curve and the
0 20
= 20
15105
20
15
=10
5
Good y
Good x
DI
Py
DI
Px
A
B
C
I3
I2 I1
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Section 5.5A Maximization of Consumer Satisfaction CHAPTER 5 APPENDIX
budget line, the marginal rate of substitution is equal to the ratio of the price of x to the price of y. That is,
MRSxy 5 Px Py
This expression means that the marginal rate of substitution expresses the willingness of the consumer to trade a certain amount of x for a certain amount of y, and the slope of the budget line reflects the market’s willingness to trade a certain amount of x for a certain amount of y. The impersonal forces of the market impose the relative prices on the con- sumer, so the consumer adjusts consumption amounts in such a way that his or her trade- off is the same as the trade-off in the market.
Suppose you are consuming 15 units of y and 5 units of x (you are at Point A in Figure 5.8A). According to your indifference curve (I
1 ), you would be willing to give up 5 units
of y if you received 2 additional units of x. The market, however, is willing to give you 5 units of x in exchange for 5 units of y (note Point B). You would probably consume less y and more x. In fact, you would be able to increase your utility by moving in the direction of the tangency of some higher indifference curve with the budget line.
Figure 5.8A: Tangency once again
Lower indifference curves that are within the budget constraint represent lower levels of utility than the highest, but still attainable, indifference curve.
0 2015105 7
20
15
10
5
Good y
Good x
A
B
I2
I1
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Section 5.5A Maximization of Consumer Satisfaction CHAPTER 5 APPENDIX
Consumer Reaction to Income Changes
The best feature of indifference curve analysis is that it allows us to analyze the reaction of consumers to price and income changes. Using the indifference map and the budget line, we can trace the adjustment process that takes place when a household experiences a change in income. In Figure 5.9A, for example, if the household’s income is represented by the budget line DI
1 and x and y sell for P
x and P
y , respectively, the optimal utility is at Point
A. A decrease in income is represented by budget line DI 0 , and two increases in income
are represented by budget lines DI 2 and DI
3 . The respective optimal positions represent-
ing tangencies of these budget lines with an indifference curve are Points B, C, and D. Connecting Points A, B, C, and D generates an income-consumption curve. This curve shows how consumption of the two goods changes as income changes. Recall the discus- sion of the income elasticity of demand in the preceding chapter. The income elasticities of both good x and good y in Figure 5.9A are positive because consumption of both goods increases as income increases. (Remember that a positive income elasticity indicates that a good is a normal good. An inferior good has a negative income elasticity since, in that case, as income increases, consumption of the good decreases.)
Figure 5.9A: Income changes and the income-consumption curve
An income-consumption curve traces the response of consumption combinations to changes in income.
0
Good y
Good x
Income-Consumption Curve
D
C
A
B
Px
DI0
Py
DI0
Py
DI1
Py
DI2
Py
DI3
Px
DI1 Px
DI2 Px
DI3
I1
I2
I3
I4
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Section 5.5A Maximization of Consumer Satisfaction CHAPTER 5 APPENDIX
Figure 5.10A shows a case where one commodity, good x, is a normal good for a house- hold until its income reaches DI
3 When income increases above DI
3 , the household buys
less of x. So x is a normal good up to Point A and then becomes an inferior good as the income-consumption curve bends backward. There is nothing derogatory about the term inferior. A daily newspaper might be considered an inferior good for some buyers. As income falls, a person may buy the paper more often because it is a less expensive form of entertainment and also because it offers job listings. Remember, also, that a normal good to some people may be an inferior good to others.
Figure 5.10A: Income-consumption curve for an inferior good
The income-consumption curve for an inferior good bends backwards, indicating that less of the good is consumed as income increases beyond a certain level.
Consumer Reaction to Price Changes
Let’s look at how the optimal consumption combination will be affected by price changes. Initially, the consumer is at the point of maximum utility (Point A in Figure 5.11A). As the price of x falls from P
x1 to P
x2 , the budget line rotates out to intersect the x-axis at DI/P
x2 ,
and the consumer now has a new optimum at Point B on indifference curve I 2 . Another
decrease in price to P x3
allows the consumer to reach a still higher indifference curve, I
3 , and a new optimum at Point C. Connecting the Points A, B, and C produces a price-
consumption curve. This curve shows how consumption changes when relative prices change.
0
Good y
Good x
Income-Consumption Curve
A
Px
DI1
Py
DI1
Py
DI2
Py
DI3
Py
DI4
Py
DI5
I5
I4
I3
Px
DI2 Px
DI3 Px
DI4 Px
DI5
I2I1
ama80571_05_c05_131-168.indd 165 1/28/13 9:49 AM
Section 5.6A Indifference Analysis and the Law of Demand CHAPTER 5 APPENDIX
Figure 5.11A: Price-consumption curve
A price-consumption curve depicts how consumption changes when relative prices change.
The theory behind this change in consumption patterns relies on the income and substi- tution effects again. When the price of a good falls, there are two forces at work to cause the consumer to increase purchases of that good. First, when the price of a good falls, the market trade-off between this good and other goods (or the substitution rate) changes. This part of the response to a price change is the substitution effect. Second, the consumer has a larger real income, meaning that with the same nominal income, more of both (or all) goods can be purchased (and will be purchased as long as the good is not an inferior good). This part of the response to a price change is the income effect.
5.6A Indifference Analysis and the Law of Demand
Indifference analysis can be used to derive a consumer’s demand curve and demon-strate the law of demand. This demonstration is a ceteris paribus experiment in which the price of one good is changed. Part (a) of Figure 5.12A shows an indifference map and a budget line for goods x and y. The consumer is at an optimum at Point A. At Point A, the individual consumes x
1 units of good x at a price of P
x1 . Price and quantity demanded
of good x are plotted in part (b). Now suppose the price of x falls to P x2
. As before, this
0
Good y
Good x
Price-Consumption Curve
C B
A
Px 1
DI
Py
DI
Px 2
DI
Px 3
DI
I1
I2
I3
ama80571_05_c05_131-168.indd 166 1/28/13 9:49 AM
Section 5.6A Indifference Analysis and the Law of Demand CHAPTER 5 APPENDIX
decline in price causes the budget line to rotate outward. A new optimum is reached at Point B, where the new budget line is tangent to indifference curve I
3 . The change in price
has caused the quantity demanded to increase from x l to x
2 , as shown in part (b). The line
connecting two price-quantity points in part (b) is a demand curve for good x, and it has the usual negative slope.
Figure 5.12A: Deriving a demand curve
When the price of good x decreases, the consumer can reach a higher indifference curve. This increased consumption of good x at a lower price means that the demand curve must have a negative slope.
0
Good y
(a)
Good x
B
A
Px 1
DI
Py
DI
Px 2
DI
I1
I2
I3
I4
0
Price/ Unit
(b)
Quantity/Time Period
B
A
x1
Px 1
Px 2
x2
Dx
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Key Terms CHAPTER 5 APPENDIX
Key Terms
income-consumption curve A curve that uses parallel budget lines to show changes in consumer equilibrium when income changes.
indifference analysis An approach to analyzing consumer behavior based on ranking the utility of choices relative to one another.
indifference curve A plot of all combina- tions of goods that the consumer is indif- ferent among.
indifference map A set of indifference curves. Higher curves on the map repre- sent higher levels of utility.
indifference set Any number of combi- nations of goods among which the indi- vidual consumer is indifferent (has no preference).
marginal rate of substitution (MRS) The trade-off ratio along an indifference curve.
price-consumption curve A curve that shows changes in consumer equilibrium when the price of one good on an indiffer- ence curve changes.
principle of diminishing marginal rates of substitution The fact that as more of one good is consumed, more and more of the other must be given up to maintain indifference between the two.
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