The law of diminishing marginal utility explains why

The Law Of Diminishing Marginal Utility

Prior to beginning work on this discussion, read Farah Mohammed’s article, Why Are Diamonds More Expensive Than Water? ( https://daily.jstor.org/diamonds-expensive-water/ ) , as well as Chapter 5 in your textbook, especially Sections 5.1 and 5.3, and respond to the following:

· Describe the relationship between total utility and marginal utility.

· Explain if marginal utility can be negative.

· Examine the diamond-water paradox. Why are diamonds more expensive than water?

· Evaluate the law of diminishing marginal utility.

· Identify some items, explaining your reasoning, that do not follow the law of diminishing marginal utility.

· Evaluate how the law of diminishing marginal utility can explain the diamond-water paradox.

The Law of Diminishing Marginal Utility paper

· Must be three to five double-spaced pages in length (not including title and references pages) and formatted according to APA style

· Must include a separate title page with the following:

o Title of paper

o Student’s name

o Course name and number

o Instructor’s name

o Date submitted

· Must utilize academic voice.

· Must include an introduction and conclusion paragraph. Your introduction paragraph needs to end with a clear thesis statement that indicates the purpose of your paper.

· Must use at least three scholarly, peer-reviewed, and/or other credible sources in addition to the course text.

· Must document any information used from sources in APA style

· Must include a separate references page that is formatted according to APA

Charles O. Cecil/age fotostock/Superstock

Learning Outcomes

After reading this chapter, you should 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.

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110

Section 5.1 Choice, Value, and Utility Theory

Introduction Where you work, where you shop, and all over the world, there are vending machines that supply everything from soft drinks and snacks to emergency footwear and newspapers. If you think about it, you will notice a significant difference between the machines that dispense soft drinks 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 deter- mines consumer choice. Since individual demand curves form the bedrock of microeconomic analysis, we need to consider the factors that underlie them.

The classical approach economists have taken in examining consumer demand involves the concept of measurable utility. We will use this approach to examine some problems and sug- gest some applications for demand analysis. Another approach to consumer demand, indif- ference curve analysis, is more advanced and beyond the scope of this chapter.

5.1 Choice, Value, and Utility Theory The idea that households and firms must make choices because of scarcity is the fundamental notion of economic analysis. We now want to expand on that analysis to consider why con- sumers behave 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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111

Section 5.1 Choice, Value, and Utility Theory

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 philoso- phers 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 Léon Walras, all writing separately, solved the paradox by developing a theory of value in which demand and utility came to the forefront. Their solution played a major role in developing the theory of con- sumer demand.

Another part of the debate underlying the diamond–water paradox was an argument over whether value (or price) was deter- mined by supply or demand. In a famous analogy, Alfred Marshall, the great British economist, said that one could no more say whether supply or demand determined value than one could say which blade of a pair of scissors did the cutting. That is, value (or price) is determined by the interaction of supply and demand.

Economics in Action: Crunch Into Utility Theory

Using the classic cookie, 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. https://www.youtube.com/watch?v=KOUJEyy48qY

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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https://www.youtube.com/watch?v=KOUJEyy48qY
112

Section 5.1 Choice, Value, and Utility Theory

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. Note that in economics, the word utility does not necessarily mean “useful.” There are a number of items in the real world that are not use- ful that give great satisfaction.

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 dif- ferent people, this is a satisfactory measuring device. Such comparisons between people are inappropriate because the number of utils is a subjective measure of a certain 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 soda per day, assign an arbitrary number of utils, say 20. (You can choose any number at all: 1, or 1,000, or 47½.) 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 soda

Cans of soda 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 –2

10 82 –5

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113

Section 5.1 Choice, Value, and Utility Theory

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 = change in total utility

one-unit change in quantity consumed

In Table 5.1 the marginal utility is determined by calculating how much each additional can of soda adds to total utility. For example, the first can of soda adds 20 utils to total utility. The fourth can of soda adds 13 utils to total utility. Marginal utility is found by subtracting the total utility of consuming three sodas from the total utility of consuming that number plus one (67 – 54 = 13).

The 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 consump- tion 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 addition to total utility than the preceding units did. For instance, the seventh soda is expected to provide less additional pleasure than the sixth. This principle is reflected in Table 5.1. Marginal utility falls from 7 utils for the sixth soda 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 sodas per day because the ninth soda has a negative marginal utility.

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114

Section 5.2 Utility and Consumer Behavior

5.2 Utility and Consumer Behavior The 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 Tesla to a Toyota but decide to purchase the Toyota. The explanation for this behavior lies in the relationship between price and utility.

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)

Sodas/day

Total utility

Marginal utility

Sodas/ day

(a)

(b)

Marginal utility (utils)

Figure 5.1: Total and marginal utility

Total utility increases as consumption increases to a certain level, in this case eight sodas 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 that total utility begins to decline, marginal utility becomes negative.

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115

Section 5.2 Utility and Consumer Behavior

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 util- ity. To see how marginal utility and price influence how a consumer maximizes total utility, consider an example with only two goods, cola and pizza. A unit of cola costs $0.50, and a unit of pizza costs $1.00. 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 budget constraint of $13 and see how that amount will be allocated between the two goods to achieve maximum utility.

Suppose, for example, you are considering purchasing a six-pack of soft drinks. You are pre- sented with the three possibilities shown in Table 5.2. Coca-Cola 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 Coca-Cola 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 $0.75 spent on something other than soda 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)

Coca-Cola 30.0 3.75 10

Pepsi 27.0 3.00 12

RC Cola 20.0 2.75 10

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116

Section 5.2 Utility and Consumer Behavior

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 cola (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 cola, the alternative purchase. In other words, the consumer buys two pieces of pizza before buying any cola. The third dollar is spent on cola 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 maxi- mizing total utility, the consumer will spend $5 on 10 cans of cola 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 cola and pizza that will produce more satisfaction (try reducing cola consumption by two cans and increas- ing pizza consumption by one piece, or vice versa).

The consumer’s choices are based on a maximization rule that says that total utility is maxi- mized 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 good A

Price of good A =

Marginal utility of good B

Price of good B This can be written

MUA PA

= MUB PB

Table 5.3: Utility for a consumer of two goods

Cola Pizza

Quantity per week (cans)

Marginal utility, MU (utils)

MU/P (P = $0.50)

Total utility, TU (utils)

Quantity per week (pieces)

Marginal utility, MU (utils)

MU/P (P = $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 24.75 24.75 115.75

5 11 22 65 5 20.25 20.25 136

6 10.75 21.5 75.75 6 18 18 154

7 10.25 20.5 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 6.5 13 126.5 12 9 9 233

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117

Section 5.2 Utility and Consumer Behavior

The marginal utility of a can of cola, when 10 cans per week are consumed, is 8 utils, and the price of a can is $0.50. Thus,

MUcola Pcola

= 8

$0.50 = 16 utils per dollar

For pizza, at the optimum consumption rate, the marginal utility is 16, and the price is $1. Thus,

MUpizza Ppizza

= 16

$1.00 = 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

= MUB PB

= 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 Shandra 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

= MUpizza

Ppizza

doesn’t hold because

10.75

0.50 >

18

1

Shandra isn’t maximizing her utility, because the last dollar she spent on cola yielded more utils than the last dollar she spent on pizza. Shandra should reallocate her consumption out- lays. By giving up a dollar’s worth of pizza, she will lose 18 utils. But she will gain 20.25 utils by spending that dollar on more cola. Her total utility will thus rise by 2 (rounded off), and

10

0.50 <

20.25

1

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118

Section 5.2 Utility and Consumer Behavior

Now suppose the price of good x falls to P2. This change throws the expression out of equi- librium 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 individual consumes more of x, MUx will decline because of the principle of diminishing marginal utility. As consumption moves to x2 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, MUy rises.

By purchasing eight cans of cola and five pieces of pizza, Shandra 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 assuming everything else remains the same. 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

= MUy Py

At this equilibrium, MUx1 corresponds to the consumption of x1 units of good x in Figure 5.2. The price of x1 units is represented by P1 in Figure 5.2.

0

Price

Quantity/ time period

P1

P2

x1 x2

Dx

Figure 5.2: Demand curve for good x

When price falls from P1 to P2, the consumer’s utility maximization is thrown out of equilibrium. Equilibrium will be restored if the consumer increases consumption to x2.

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119

Section 5.2 Utility and Consumer Behavior

Utility-maximizing behavior requires that when the price of good x falls (as from P1 to P2 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 adjust- ments 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 mar- ginal utility. Buying a smaller house, buying one at a less desirable location, and renting are also available alternatives.

A greater problem with utility theory is that it is impossible to measure utility. We have pro- ceeded as if there were a way we could strap a meter to a consumer and exactly measure the utility expected from consuming one more unit, somewhat like measuring temperature 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.

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 when the marginal utility per dollar spent on all goods (and the marginal utility of money) is equal.

• There are 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.

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120

Section 5.2 Utility and Consumer Behavior

Income and Substitution Effects The law of demand, which you studied in Chapter 3, states that as the price of a good or ser- vice declines, the quantity demanded increases, all else being equal. This law is true because of two effects that result from the price decline.

Policy Focus: Progressive Income Taxation—Are Utility Functions Interdependent?

Many noneconomists 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 transferring 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 Jennifer Lawrence than to an unemployed autoworker. In fact, Lawrence might get more satisfaction from being an expert consumer. It is impossible to prove that one individual gets more or less satisfaction from an income increment 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 proved. 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?