CHAPTER
21
The Theory of Consumer
Choice
Goals
in this chapter you will
See how a budget constraint represents the choices a consumer
can afford
Learn how indifference curves can be used to represent a
consumer’s preferences
Analyze how a consumer’s optimal choices are determined
See how a consumer responds to changes in income and changes
in prices
Decompose the impact of a price change into an income effect
and a substitution effect
Apply the theory of consumer choice to three questions about
household behavior
Outcomes
after accomplishing
these goals, you
should be able to
Draw a budget constraint on a graph if you are given the value of
income and the prices of the goods
Explain why indifference curves must slope downward if the two
products considered are “goods”
Explain the relationship between the relative prices and the
marginal rate of substitution between two goods at the consumer’s
optimum
Shift the budget constraint when the price of a good increases
Demonstrate the income and substitution effect on a graph using
indifference curves and budget constraints
Show why someone’s labor-supply curve might be backward
sloping
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Chapter 21 The Theory of Consumer Choice
Strive for a Five
The theory of consumer choice is a topic tested on the AP microeconomics test. The
following areas are of specific importance:
■■ Maximizing utility
■■ Income effect
■■ Substitution effect
■■ The concept of utility and marginal utility
Although the budget constraint graph and indifference curve are also included in this
chapter and are useful and pertinent to the study of economics in general, they are not
included on the AP exam. Please check with your instructor to confirm which topics and
chapters will be covered in your course.
Key Terms
■■
■■
■■
■■
■■
Normal good—A good for which an increase in income raises the quantity demanded
Inferior good—A good for which an increase in income reduces the quantity demanded
Income effect—The change in consumption or spending that results when a price
change moves the consumer to a higher or lower indifference curve
Substitution effect—The change in consumption that results when a price change
moves the consumer along a given indifference curve to a point with a new marginal
rate of substitution
Giffen good—A good for which an increase in the price raises the quantity demanded
Chapter Overview
Context and Purpose
Chapter 21 is the first of two unrelated chapters that introduce you to some advanced
topics in microeconomics. These two chapters are intended to whet your appetite for
further study in economics. Chapter 21 is devoted to an advanced topic known as the
theory of consumer choice.
The purpose of Chapter 21 is to develop the theory that describes how consumers
make decisions about what to buy. So far, we have summarized these decisions with the
demand curve. We now look at the theory of consumer choice, which underlies the
demand curve. After developing the theory, we apply the theory to a number of questions
about how the economy works.
Chapter Review
Introduction Chapter 21 develops the theory that describes how consumers make
decisions about what to buy. So far, we have summarized these decisions with the demand
curve. We now look at the theory of consumer choice, which underlies the demand curve.
After developing the theory, we apply the theory to the following questions:
■■ Do all demand curves slope downward?
■■ How do wages affect labor supply?
■■ How do interest rates affect household saving?
The Budget Constraint: What the Consumer Can Afford
A budget constraint is the limit on the consumption bundles that a consumer can afford
(given the consumer’s income and the prices of the goods the consumer wishes to buy).
On a graph that measures the quantity of a consumption good on each axis, a budget
constraint is a straight line connecting the maximum amounts that could be purchased
Chapter 21 The Theory of Consumer Choice
of each commodity given the prices of each commodity and the consumer’s income. For
example, if a consumer has income of $1,000 and the price of Pepsi is $2 per pint, the
maximum amount of Pepsi that could be purchased is $1,000/$2 = 500 pints. If the price
of pizza is $10, the maximum amount of pizza that could be purchased is $1,000/$10 =
100 pizzas.
The slope of the budget constraint is the relative price of the two goods. In this case since
a pizza costs five times what a pint of Pepsi costs, the consumer can trade one pizza for
five pints of Pepsi. If the quantity of Pepsi is plotted on the vertical axis and the quantity
of pizza on the horizontal axis, the slope of the budget constraint (rise/run) is 5/1, which
equals the price of pizza divided by the price of Pepsi or $10/$2 = 5. Since the budget
constraint always slopes downward or negatively, we often ignore the negative sign.
Preferences: What the Consumer Wants
A consumer’s preferences can be represented with indifference curves. If two bundles of
commodi­ties suit a consumer’s tastes equally well, the consumer is indifferent between
them. Graphically, an indifference curve is a curve that shows consumption bundles that
give the consumer the same level of satisfaction. When drawn on a graph that measures the
quantity consumed of each good on each axis, an indifference curve must be downward
sloping because if consumption of one good is reduced, the consumption of the other
good must be increased for the consumer to be equally happy. The slope at any point on
an indifference curve is known as the marginal rate of substitution or MRS. The MRS is
the rate at which a consumer is willing to trade one good for another while main­taining a
constant level of satisfaction.
There are four properties of indifference curves:
■■ Higher indifference curves (further from the origin) are preferred to lower ones
because people prefer more goods rather than fewer.
■■ Indifference curves are downward sloping because if consumption of one good is
reduced, the consumption of the other good must be increased for the consumer to
be equally happy.
■■ Indifference curves do not cross because it would suggest that a consumer’s
preferences are contradictory.
■■ Indifference curves are bowed inward because a consumer is willing to trade a greater
amount of a good for another good if they have an abundance of the good they are
trading away and they are willing to trade a lesser amount of a good for another good
if they have very little of the good they are trading away.
When it is easy to substitute two goods for each other, indifference curves are bowed
inward very little. When it is difficult to substitute two goods for each other, indifference
curves are bowed inward a great deal. This is demonstrated by two extreme cases:
■■ Perfect substitutes: two goods with straight-line indifference curves. An example of
perfect sub­stitutes is nickels and dimes—two nickels for each dime.
■■ Perfect complements: two goods with right-angle indifference curves. An example of
perfect complements is right shoes and left shoes—additional shoes that don’t come in
pairs do not in­crease satisfaction.
Optimization: What the Consumer Chooses
When we combine the budget constraint and the consumer’s indifference curves, we
are able to de­termine the amount of each commodity that the consumer will buy.
The consumer will try to reach the highest indifference curve subject to remaining on
the budget constraint. The point where an indifference curve just touches the budget
constraint determines the optimum amount of purchases of each good. At the optimum,
the indifference curve is tangent to the budget constraint and the slope of the indifference
curve and the budget constraint are the same. Thus, the consumer chooses consump­tion
of the two goods so that the marginal rate of substitution (slope of the indifference curve)
equals the relative price of the two goods (slope of the budget constraint). At the optimum,
the trade-off between the goods that the consumer is willing to make (slope of the
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indifference curve) is equal to the trade-off between the goods that the market is willing to
make (slope of the budget constraint).
An alternative way to describe preferences and optimization is with the concept of
utility. Utility is an abstract measure of the happiness or satisfaction a consumer receives
from consuming a bundle of goods. Therefore, an indifference curve is actually an
“equal-utility” curve. The marginal utility of a good is the increase in utility one gets from
consuming an additional unit of that good. Goods exhibit diminishing marginal utility as
more of any good is consumed. Since the marginal rate of substitution (the slope of the
indifference curve) is the trade-off between two goods that the consumer is willing to
make, it must also equal the marginal utility of one good divided by the marginal utility of
the other good. Therefore, for two goods X and Y, at the optimum:
MRS = Px/Py = MUx/MUy
or,
MUx/Px = MUy/Py.
At the optimum, the marginal utility of a dollar spent on X must be equal to the
marginal utility of a dollar spent on Y. Similarly, one can say that, at the optimum, the
indifference curve is tangent to the budget constraint.
Suppose the income of the consumer were to increase. Because the consumer can now
consume more of both goods and because the relative price of the two goods remains
unchanged, an increase in income shifts the budget constraint outward in a parallel fashion.
The consumer can now reach a new optimum on a higher indifference curve. It is most
common that the consumer will choose to consume more of both goods. Thus, a normal
good is a good for which an increase in income raises the quantity demanded. Alternatively,
an inferior good is a good for which an increase in income reduces the quantity
demanded. Bus rides are an inferior good.
Suppose the price of one of the goods were to fall. If the consumer allocates all of his
income to the good whose price has fallen, the consumer can buy more of that good.
If the consumer allocates all of his income to the good whose price is unchanged, the
maximum amount he can purchase remains unchanged. This causes the budget constraint
to rotate outward. That is, the budget constraint only shifts outward on the axis of the
good whose price has fallen. The consumer can now reach a new optimum on a higher
indifference curve.
The impact of a change in the price of a good can be decomposed into two effects: an
income ef­fect and a substitution effect. The income effect is the change in consumption
that results when a price change moves the consumer to a higher or lower indifference
curve. The substitution effect is the change in consumption that results when a price
change moves the consumer along a given indiffer­ence curve to a point with a new
marginal rate of substitution. Graphically, the substitution effect is the change in
consumption that results from the change in relative prices, which rotates the budget line
along a given indifference curve. The income effect is the change in consumption that
results from the parallel shift in the budget constraint to the new optimum on the new
indifference curve.
A demand curve can be derived from the consumer’s optimizing decisions that result
from the consumer’s budget constraint and indifference curves. The combined income and
substitution effect shows the total change in quantity demanded from a change in the price
of a good. When these val­ues are plotted on a price/quantity graph, the points form the
consumer’s demand curve.
Three Applications
■■ Do all demand curves slope downward? Theoretically, demand can sometimes slope
upward. If an increase in the price of an inferior good has a larger income effect than
substitution effect (the good is very strongly inferior), then an increase in the price
of the good would cause the quantity demanded to rise. A Giffen good is a good
for which an increase in the price raises the quantity demanded. Giffen goods are
extremely rare. Evidence suggests that rice in China may be a Giffen good.
Chapter 21 The Theory of Consumer Choice
■■
How do wages affect labor supply? The theory of consumer choice can be applied to the
allocation decision between work (to afford consumption goods) and leisure. In this
case, the two goods are consumption and leisure. The maximum amount of leisure is
the number of hours available. The maximum amount of con­sumption is the number
of hours available times the wage. The individual’s indifference curves determine an
optimum amount of leisure and consumption. Suppose the wage were to rise. The
substitution effect induces more consumption and less leisure (more work). However,
if both leisure and consumption are normal goods, the income effect suggests that the
individual will wish to have both more consumption and more leisure (less work). If
the substitution effect out­weighs the income effect, an increase in wages will increase
the quantity of labor supplied and labor supply is upward sloping. If the income effect
outweighs the substitution effect, an increase in wages will decrease the quantity
of labor supplied and labor supply slopes backward. Evi­dence that the workweek is
getting shorter suggests that the income effect is very strong and the labor supply
curve bends backward when measured over long periods of time. Evidence on the
behavior of lottery winners and people who receive large bequests suggests that, at
high-income levels, the labor-supply curve is backward sloping.
■■
How do interest rates affect household saving? The theory of consumer choice can be
applied to the decision of how much income to consume today and how much
to save for tomorrow. In this case, we measure consumption when young on the
horizontal axis and consumption when old on the vertical axis. A person can consume
all of his earnings when young and have nothing when old, or consume nothing
when young, save all of his income, earn interest on the sav­ing, and consume a
greater amount when old. A person’s preferences determine the optimal amounts of
consumption in each period. If the interest rate rises, the budget constraint becomes
steeper because the maximum possible consumption when old increases. When the
interest rate rises, the substitution effect suggests that the consumer should increase
consumption when old and decrease consumption when young (save more) because
consumption when old has become relatively cheaper. However, if consumption in
both periods is a normal good, the income effect suggests that the individual should
consume more in both periods (save less). If the substitution effect outweighs the
income effect, an increase in the interest rate will cause the individual to save more. If
the income effect outweighs the substitution effect, an increase in the interest rate will
cause the individual to save less. Evidence on this issue is mixed, so there is no clear
recom­mendation for public policy toward the taxation of interest.
Conclusion: Do People Really Think This Way?
Although consumers may not literally make decisions in the manner suggested by the
theory of consumer choice, the model of consumer choice describes a process that permits
economic analysis. The theory is useful in many applications.
Helpful Hints
1. We have noted that the slope of the budget constraint is equal to the relative prices
of the two goods represented on the graph. However, which price should we put
in the numerator and which price should we put in the denominator of the slope?
Place the price of the good represented on the horizontal axis in the numerator and
the price of the good represented on the vertical axis in the denominator of the
slope. For example, if the quantity of popcorn is measured on the hori­zontal axis and
the quantity of candy bars is measured on the vertical axis, and if the price of a bag
of popcorn is $2 while the price of a candy bar is $1, then two candy bars can be
exchanged for one bag of popcorn. The slope of the budget constraint is $2/$1 or 2.
(Again, the slope of the budget constraint is always negative so we often ignore the
sign.)
2. A mapping of an individual’s preferences generates an infinite set of indifference
curves. Each indifference curve divides the commodity space into three areas—points
preferred to those on the indifference curve (points outside the indifference curve
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Chapter 21 The Theory of Consumer Choice
or away from the origin), points inferior to the indifference curve (points inside the
indifference curve or toward the origin), or points of equal satisfaction as those on the
indifference curve (points on the indifference curve). Although there are an infinite set
of indifference curves, it is customary to represent on a graph only those indifference
curves that are tangent to a budget constraint, and thus, only those indiffer­ence curves
that determine an optimum.
3. The slope of the indifference curve is the marginal rate of substitution, which is the
marginal utility of one good compared to the marginal utility of the other good. The
slope of the budget constraint is equal to the relative prices of the two goods. Because
at the optimum, the indifference curve is tangent to the budget constraint, it follows
that at the optimum the relative prices of the two goods equal the relative marginal
utilities of the two goods. Thus, at the optimum, the additional utility gained by the
consumer from an additional dollar’s worth of one good is the same as the additional
utility gained by the consumer from an additional dollar’s worth of the other good.
That is, at the optimum, the consumer cannot increase his total satisfaction by mov­ing
expenditures from one good to the other good.
Self-Test
Multiple-Choice Questions
1. Just as the theory of the competitive firm provides a more complete understanding of
supply, the theory of consumer choice provides a more complete understanding of
a. demand.
b. profits.
c. production possibility frontiers.
d. wages.
e. income.
2. The goal of the consumer is to
a. maximize utility.
b. minimize expenses.
c. spend more income in the current time period than in the future.
d. spend less income in the current time period than in the future.
e. spend an equal amount of income in the current time period and in the future.
3. Which of the following equations corresponds to an optimal choice point?
(i) MRS = PX/PY
(ii) MUX/MUY = PX/PY
(iii) MUX/PX = MUY/PY
(iv) MUX/PY = MUY/PX
a. (i) only
b. (i), (ii), and (iii) only
c. (ii) and (iv) only
d. (iii) and (iv) only
e. (i), (ii), (iii), and (iv)
Chapter 21 The Theory of Consumer Choice
4. The relationship between the marginal utility that Wendy gets from eating hamburgers
and the number of hamburgers she eats per month is as follows:
Hamburgers
Marginal Utility
1
2
3
4
5
6
20
16
12
8
4
0
Wendy receives 3 units of utility from the last dollar spent on each of the other goods
she consumes. If hamburgers cost $4 each, how many hamburgers will she consume
per month if she maximizes utility?
a. 2
b. 3
c. 4
d. 5
e. 6
5. Jeffrey spends all of his income on warm-up suits and running shoes, and the price of
a pair of shoes is four times the price of a warm-up suit. In order to maximize total
utility, Jeffrey should
a. buy four times as many warm-up suits as pairs of running shoes.
b. buy four times as many pairs of running shoes as warm-up suits.
c. buy both items until the marginal utility of a pair of running shoes is four times
the marginal utility of a warm-up suit.
d. buy both items until the marginal utility of a warm-up suit is four times the
marginal utility of a pair of running shoes.
e. buy equal amounts of warm-up suits and running shoes.
6. Jane is maximizing total utility while consuming food and clothing. Her marginal
utility from food is fifty, and her marginal utility from clothing is twenty-five. If
clothing is priced at $10 per unit, the price of food per unit must be
a. $2.00
b. $2.50
c. $5.00
d. $20.00
e. $25.00
7. The consumer’s optimal choice is the one in which the marginal utility per dollar
spent on good X is
a. equal to the marginal utility per dollar saved on good X.
b. greater than the marginal utility per dollar spent on good Y.
c. equal to the marginal utility per dollar spent on good Y.
d. less than the marginal utility per dollar spent on good Y.
e. is the greatest.
8. When economists describe preferences, they often use the concept of
a. markets.
b. income.
c. utility.
d. prices.
e. opportunity cost.
9. As more units of an item are purchased, everything else equal, marginal satisfaction
from consuming additional units will tend to
a. decrease at the same rate for all consumers.
b. decrease but at different rates for different people.
c. increase at the same rate for all consumers.
d. increase but at a decreasing rate for all consumers.
e. increase but at an increasing rate for all consumers.
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Chapter 21 The Theory of Consumer Choice
10. If John’s marginal utility derived from the consumption of another candy bar is 1 and
the price of the candy bar is $1.50, then
a. this is the last candy bar John will purchase as the marginal utility is less than the
price.
b. the opportunity cost of the candy bar is less than $1.50.
c. if John purchases and consumes the candy bar, his total satisfaction will go down
because the marginal utility is less than the price.
d. John should not purchase the candy bar.
e. there is not enough information to determine if John will or will not purchase
the candy bar.
11. A normal good is one in which
a. the average consumer chooses to consume at a normal level.
b. the average consumer chooses to consume the good over other similar goods.
c. an increase in income increases consumption of the good.
d. an increase in income decreases consumption of the good.
e. an increase in income has no effect on the consumption of the good.
12. A good is an inferior good if the consumer buys less of it when
a. his income rises.
b. the price of the good rises.
c. the price of a substitute good falls.
d. his income falls.
e. the price of the good falls.
Free Response Questions
1. Explain the difference between inferior and normal goods. As a developing economy
experiences increases in income (measured by GDP), predict what would happen to
demand for inferior goods.
2. Jim enjoys consuming both coffee and rolls. The following table lists the satisfaction he
receives from each and their prices.
Marginal Utility Received
from the last unit consumed
Price
Coffee
10
$2
Rolls
20
$5
Jim is considering buying more coffee or more rolls. Which one should he buy next?
Explain.
Chapter 21 The Theory of Consumer Choice
Solutions
Multiple-Choice Questions
1. a TOP: Consumer choice
2. a TOP: Optimization
3. b TOP: Optimization
4. b TOP: Optimization
5. c TOP: Optimization
6. d TOP: Optimization
7. c TOP: Optimization
8. c TOP: Utility
9. b TOP: Marginal utility
10. e TOP: Marginal utility
11. c TOP: Normal goods
12. a TOP: Inferior goods
Free Response Questions
1. Normal goods are those for which consumption increases as income rises. Inferior goods are those for which
consumption decreases as income rises. We would expect the demand for inferior goods to decrease as
developing countries experience increases in income.
TOP: Inferior goods | Normal goods
2. Jim should buy more coffee. His marginal utility per dollar spent on coffee is 10/$2 or 5. His marginal utility
per dollar spent on rolls is 20/$5 or 4. To maximize satisfaction, he should allocate his next purchase toward
the item with the highest marginal utility per dollar spent. In this case, that is coffee.
TOP: Consumer choice
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