Chapter 7Utility Maximization

In this chapter, the law of diminishing marginal utility is developed, which leads into a detailed discussion of the theory of consumer choice. The numerical illustrations of the utility maximizing rule should be viewed as a pedagogical technique, rather than an attempt to portray the actual choice making process of consumers. When this illustration is explained by “order of purchase,” the brief algebraic summary of consumer equilibrium should pose no great difficulties for most students. The Last Word concludes the chapter with a discussion of how society might use this theory to reduce criminal behavior.

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Key Terms• Law of diminishing marginal utility• Utility• Total utility• Marginal utility• Rational behavior• Budget constraint• Utility maximizing rule• Income effect• Substitution effect

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Law of Diminishing Marginal Utility• Law of diminishing marginal utility• As consumption of a good or service

increases, the marginal utility obtained from each additional unit of a good or service decreases

• Explains downward sloping demand curve

LO1

Although consumers’ wants, in general, are insatiable, wants for specific commodities can be fulfilled. The more of a specific product that consumers obtain, the less they will desire more units of that product. Theory of consumer behavior uses the law of diminishing marginal utility to explain how consumers allocate their income.

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Terminology

• Utility is the satisfaction one gets from consuming a good or service• Not the same as usefulness• Subjective• Difficult to quantify

LO1

Utility is a subjective notion in economics, referring to the amount of satisfaction a person gets from consumption of a certain item. Utility and usefulness are not the same thing. Items that are essentially useless can provide a lot of utility.

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Total Utility and Marginal Utility• Util is one unit of satisfaction or pleasure• Total utility is the total amount of

satisfaction• Marginal utility is the extra satisfaction

from an additional unit of the good• MU = ΔTU/ΔQ

LO1

Utility is measured in utils. Total utility is the total amount of satisfaction one gets from the consumption of a single product or a combination of products. Total utility can be derived by adding up the utils of successive units consumed. Marginal utility refers to the extra utility a consumer gets from one additional unit of a specific product. In a short period of time, the marginal utility derived from successive units of a given product will decline. This is known as diminishing marginal utility.

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Total Utility and Marginal Utility Continued

0

10

20

30

1086420-2

1 2 3 4 5 6 7

1 2 3 4 5 6 7

Tota

l util

ity (u

tils)

Mar

gina

l util

ity (u

tils)

(2)Total

Utility,Utils

(3)Marginal

Utility,Utils

01234567

010182428303028

10

8

6

4

2

0

-2

Total Utility

TU(1)TacosConsumedPer Meal

MU

]]]]]]]

LO1

Curves TU and MU are graphed from the data in the table. As more of a product is consumed, total utility increases at a diminishing rate, reaches a maximum, and then declines. Marginal utility, by definition, reflects the changes in total utility. Thus, marginal utility diminishes with increased consumption, becomes zero when total utility is at a maximum, and is negative when total utility declines. As shown by the shaded rectangles, marginal utility is the change in total utility associated with each additional taco. Or, alternatively, each new level of total utility is found by adding marginal utility to the preceding level of total utility.

Theory of Consumer Behavior

• Rational behavior• Preferences• Budget constraint• Prices

LO2

Rational behavior is the assumption that the consumer tries to use his or her money income to derive the greatest satisfaction from it.

Each consumer has clear cut preferences for certain goods and services available in the market and has some idea of how much marginal utility they might get from purchasing and consuming additional units.

At any point in time the consumer has a limited, fixed amount of money to spend.

Every good has a price and prices are unaffected by amounts purchased by the consumer. Goods and services have prices and are scarce relative to the demand for them.

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Utility Maximizing Rule

• Utility maximizing rule• Consumer equilibrium• Consumer allocates his or her income so

that the last dollar spent on each product yields the same amount of extra (marginal) utility

• Algebraically,MU of product A MU of product B

Price of A Price of B=

LO2

A consumer is in equilibrium when utility is “balanced (per dollar) at the margin.” When this is true, there is no incentive to alter the expenditure pattern unless tastes, income, or prices change. When using the utility maximizing rule, it is important to express the marginal utility of the good as marginal utility per dollar spent since the two goods probably have different prices. Therefore, we can’t just compare utilities otherwise it’s like comparing apples to oranges. So, we have to find the marginal utility per dollar by dividing the marginal utility of the good by the price of the good.

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Numerical ExampleThe Utility-Maximizing Combination of Apples and Oranges Obtainable with an Income of $10

(2)Apple (Product A):

Price = $1

(3)Oranges (Product B):

Price = $2

(1) Unit of Product

(a)Marginal Utility,

Utils

(b)Marginal Utility

per dollar(MU/Price)

(a)Marginal Utility,

Utils

(b)Marginal Utility

per dollar(MU/Price)

First 10 10 24 12

Second 8 8 20 10

Third 7 7 18 9

Fourth 6 6 16 8

Fifth 5 5 12 6

Sixth 4 4 6 3

Seventh 3 3 4 2

LO2

It is assumed in this table that the amount of marginal utility received from additional units of each of the two products is independent of the quantity of the other product. For example, the marginal utility schedule for apples is independent of the number of oranges obtained by the consumer. When determining whether to buy the apples or oranges, we will compare the marginal utility per dollar.

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Decision-Making Process

Sequence of Purchases to Achieve Consumer Equilibrium

Choice Number Potential Choices

Marginal Utility

per Dollar Purchase DecisionIncome

Remaining

1 First AppleFirst Orange

1012

First orange for $2 $8 = $10 - $2

2 First AppleSecond Orange

1010

First apple for $1 and Second orange for $2

$5 = $8 - $3

3 Second AppleThird Orange

89

Third orange for $2 $3 = $5 - $2

4 Second AppleFourth Orange

88

Second apple for $1and Fourth orange for $2

$0 = $3 - $3

LO2

This illustration shows how consumers must choose among alternative goods with their limited money incomes. As long as one good provides more utility per dollar than another, the consumer will buy more of the first good; as more of the first product is bought, its marginal utility diminishes until the amount of marginal utility per dollar just equals that of the other product. This table summarizes the step-by-step decision making process the rational consumer will use to reach the utility maximizing combination. The algebraic statement of this utility-maximizing state is that the consumer will allocate income in such a way that: MU of apples/price of apples = MU of oranges/price oranges

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Deriving the Demand Curve

$2

1

4

6

QuantityDemanded

Price per Orange

Pric

e pe

r ora

nge

0

$1

$2

4 6

Quantity demanded of oranges

DO

LO3

At a price of $2 the consumer represented by the data in the table maximizes utility by purchasing 4 oranges. The decline in the price of oranges to $1 disrupts the consumer’s initial utility-maximizing equilibrium. The consumer restores equilibrium by purchasing 6 rather than 4 oranges. Thus, a simple price-quantity schedule emerges, which creates two points on a downsloping demand curve.

Income and Substitution Effects• Income effect• The impact a price change has on a

consumer’s real income• Substitution effect• The impact a price change has on a

product’s relative expensiveness

LO4

The substitution effect and income effect work simultaneously. The income effect is the impact that a price change has on a consumer’s real income and, consequently, on the quantity demanded of the good. If the price of a good falls, income is freed up and can be used to buy more of both, or either, good under consideration. The income effect is shown by the fact that a decline in price expands the consumer’s real income and the consumer can purchase more of this and other products until equilibrium is once again attained for the new level of real income.

The substitution effect is the impact that a change in a product’s price has on its relative expensiveness and on the quantity demanded. If the price of a product falls, this decreases its relative expensiveness and thus the consumer will now substitute more of this good for the other. When the price of an item declines, the consumer will no longer be in equilibrium until more of the item is purchased and the marginal utility of the item declines to match the decline in price. More of this item is purchased rather than another relatively more expensive substitute.

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Applications and Extensions

• New products• iPad• Diamond-water paradox• Opportunity cost and time• Medical care purchases• Cash and noncash gifts

LO5

The first touchscreen tablet computer, the iPad, was a new product enormously popular with consumers and perceived by them as having a greater marginal utility to price ratio than other alternative products. This resulted in a major shift in demand for the new product as consumers attempted to increase their total utility.

Why do some goods that are essential to life have low prices and goods that are not essential to life have high prices? The marginal utility of the last unit of water consumed is small because we consume a lot of water. The marginal utility of the last diamond is large because we consume few diamonds.

Time also has a value, so this must be considered in decision making and utility maximization. When time is considered, consumer behavior appears to be much more rational. Highly skilled people, like doctors, earn high wages and therefore incur a higher opportunity cost whenever they use their time in some other way. They are more likely to buy goods over the internet and pay higher prices for things that will save them time. Unskilled workers or retirees have low opportunity costs for their time and therefore will use time to search out ways to save money. They are more likely to search for bargains and take longer trips if it saves them money. Foreigners observe that Americans waste material goods but conserve time. This could be because our high productivity makes our time more valuable than many of the goods we waste.

With medical care purchases we pay an upfront fixed charge each month and this charge is not affected by the amount we consume. The additional marginal benefit is higher than the marginal cost of additional use. This explains why we use so much more than if we had to pay full price.

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Noncash gifts result in a loss of utility and we then take action to maximize our utility, such as taking it back and exchanging it, etc. Noncash gifts may yield less utility to the receiver than a cash gift of equal monetary value because the noncash gift may not match the receiver’s preferences. Individuals know their own preferences better than the gift giver.

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Criminal Behavior

• The criminal attempts to maximize his or her total utility

• Compares the marginal benefit with the marginal cost of the unlawful activity

• Most people find the costs too high• For others, society imposes additional

costs such as fines and imprisonment• Potential to reduce crime by increasing the

cost of crime

The cost of criminal activity consists of the guilt one may feel, supplies and tools needed for the crime, and foregone income from lawful activity. These costs are too high for most people. However, for those who find their benefit of crime exceeds these costs of crime, many may be further deterred due to the costs society levies on lawbreakers; namely, fines and possible imprisonment. Economic analysis provides ideas to reduce crime that include ways to increase the cost of crime further. This could be achieved by raising the “guilt” costs through family, educational, and religious efforts; increasing the direct costs that criminals bear by using more sophisticated security systems; increasing the cost incurred from the foregone income due to criminal activity with more educational and training opportunities; adding more police to raise the probability of being caught; and imposing higher penalties on those who are caught. Any one or all of these could thwart crime by raising the marginal cost of that activity to the point that it exceeds the marginal benefit.

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