Managerial Economics

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Managerial Economics and Strategy

Third Edition

Chapter 4

Consumer Choice

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Managerial Problem

Paying Employees to Relocate

How can a manager use consumer theory to optimally compensate employees who are transferred to other cities?

Solution Approach

Managers can assess the items employees consume in the original location and entice them to relocate by offering a compensation that allows them to consume basically the same in the new location. However, these packages usually overcompensate employees. To avoid costly overcompensation, managers may use the theory of consumer choice.

Empirical Methods

Individual preferences determine the satisfaction people derive from the goods and services they consume.

Consumers face constraints or limits on their choices, particularly because their budgets limit how much they can buy.

Consumers seek to maximize the level of satisfaction they obtain from consumption, subject to the constraints they face (“do the best with what they have”).

Learning Objectives (1 of 2)

4.1 Consumer Preferences

Predict consumer choices using underlying properties of consumer preferences

4.2 Utility

Summarize a consumer’s preferences using a utility function

4.3 The Budget Constraint

Explain how prices and income limit what a consumer can purchase

Learning Objectives (2 of 2)

4.4 Constrained Consumer Choice

Show how consumers maximize their utility given prices and limited income

4.5 Deriving Demand Curves

Derive demand curves from underlying consumer preferences

4.6 Behavioral Economics

Discuss the role of behavioral biases in consumer choice

4.1 Consumer Preferences (1 of 6)

A consumer faces choices involving many goods and must allocate his or her available budget to buy a bundle of goods.

Would ice cream or cake make a better dessert? Is it better to rent a large apartment or rent a single room and use the savings to pay for concerts?

How do consumers choose the bundles of goods they buy?

One possibility is that consumers behave randomly and blindly choose one good or another without any thought.

Another is that they make systematic choices.

To explain consumer behavior, economists assume that consumers have a set of tastes or preferences that they use to guide them in choosing between goods.

These tastes differ substantially among individuals. For example, three out of four European men prefer colored underwear, while three out of four American men prefer white underwear.

4.1 Consumer Preferences (2 of 6)

Properties of Consumer Preferences

4.1 Consumer Preferences (3 of 6)

Properties of Consumer Preferences

Completeness

When a consumer faces a choice between any two bundles of goods, only one of the following is true. The consumer might prefer the first bundle to the second, or the second bundle to the first, or be indifferent between the two bundles. Indifference is allowed, but indecision is not.

Transitivity

If a is strictly preferred to b and b is strictly preferred to c, it follows that a must be strictly preferred to c. Transitivity applies also to weak preference and indifference relationships.

More is better

All else being the same, more of a good is better than less. This is a nonsatiation property.

4.1 Consumer Preferences (4 of 6)

Preference Maps

A preference map is a complete set of indifference curves that summarize a consumer’s tastes.

An indifference curve is the set of all bundles of goods that a consumer views as being equally desirable.

Panel c of Figure 4.1 shows three of Lisa’s indifference curves:

In this figure, the indifference curves are parallel, but they need not be.

Preferences and Indifference Curves

Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin.

There is an indifference curve through every possible bundle.

Indifference curves cannot cross.

Indifference curves slope downward.

Figure 4.1 Bundles of Pizzas and Burritos That Lisa Might Consume

4.1 Consumer Preferences (5 of 6)

Willingness to Substitute Between Goods

4.1 Consumer Preferences (6 of 6)

Willingness to Substitute Between Goods

The Marginal Rate of Substitution (M R S) is the rate at which a consumer can substitute one good for another while remaining on the same indifference curve.

If pizza is on the horizontal axis in Figure 4.3 (a), Lisa’s marginal rate of substitution of burritos for pizza is M R S = ΔB/ΔZ, where ΔB is the number of burritos Lisa will give up to get ΔZ more pizzas while staying on the same indifference curve.

The indifference curves in Figure 4.3 (a) are convex or “bowed in” toward the origin. This willingness to trade fewer burritos for one more pizza reflects a diminishing marginal rate of substitution.

Curvature of Indifference Curves

Convex indifference curves reflect imperfect substitutes (panel a in Figure 4.3 and panel c in Figure 4.4).

Straight-line indifference curves reflect perfect substitutes, goods that are essentially equivalent for the consumer (Panel a, Figure 4.4).

Right-angle indifference curves reflect perfect complements, goods consumed only in fixed proportions (Panel b, Figure 4.4).

Figure 4.3 Marginal Rate of Substitution

Figure 4.4 Perfect Substitutes, Perfect Complements, and Imperfect Substitutes

4.2 Utility (1 of 2)

Utility Functions

Our consumer behavior model assumes that consumers can compare bundles of goods and take the one with the greatest satisfaction.

If we knew the utility function—the relationship between utility measures and every possible bundle of goods—we could summarize the information in indifference

maps succinctly. Lisa’s utility function

Utility functions do not exist in any fundamental sense.

If you ask your mother what her utility function is, she would be puzzled. However, she could easily answer: “Do you want one scoop of ice cream with two pieces of cake or two scoops of ice cream with one piece of cake?” Also, she may not know how much more she prefers one bundle to the other.

Ordinal and Cardinal Utility

Ordinal utility if we know only a consumer’s relative rankings of bundles.

Cardinal utility if we know absolute numerical comparisons.

Most of our discussion of consumer choice in this chapter holds if utility has only ordinal properties. We care only about the relative utility or ranking of the two bundles.

4.2 Utility (2 of 2)

Marginal Utility (M U)

Marginal utility is the slope of the utility function as we hold the quantity of the

other good constant,

Given Lisa’s utility function

Lisa’s marginal utility from

increasing her consumption of pizza from 4 to 5 in Figure 4.5 is

Using calculus: If

Marginal Rates of Substitution (M R S)

The M R S depends on the negative of the ratio of the marginal utility of one good to the marginal utility of another good.

Lisa’s M R S depends on the negative of the ratio of the M U of pizza to

the M U of burritos,

Figure 4.5 Utility and Marginal Utility

4.3 The Budget Constraint (1 of 3)

Consumers maximize their well-being subject to constraints, and the most important is the budget constraint.

The budget constraint or budget line shows the bundles of goods that can be bought if the entire budget is spent on those goods at given prices.

In Figure 4.6, Lisa’s budget constraint is p B B + p Z Z = Y, where p B B and p Z Z are the amounts she spends on burritos and pizzas.

How many burritos can Liza buy?

Lisa can afford to buy more burritos B only if her income Y increases, the prices of burritos and pizza (p B, p Z) falls, or she buys fewer pizzas Z.

In Figure 4.6, p B = $2, p Z =$1, Y = $50. So,

4.3 The Budget Constraint (2 of 3)

The opportunity set is all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint.

In Figure 4.6, the opportunity set is all those bundles of positive Z

and B such that

Slope of the Budget Line

It is determined by the relative prices of the two goods and is called the

marginal rate of transformation

In Figure 4.6, Lisa’s

She can “trade” an extra pizza

for half a burrito or give up two pizzas to obtain an extra burrito.

Using calculus, If

Figure 4.6 The Budget Line

4.3 The Budget Constraint (3 of 3)

Effects of a Change in Price on the Opportunity Set

If the price of pizza doubles but the price of burritos is unchanged, the budget line swings in toward the origin (Figure 4.7a).

The new budget line is steeper and lies inside the original one. Unless Lisa only wants to eat burritos, she is unambiguously worse off, she can no longer afford the combinations of pizza and burritos in the shaded “Loss” area.

Effects of a Change in Income on the Opportunity Set

If the consumer’s income increases, the consumer can buy more of all goods.

A change in income affects only the position and not the slope of the budget line.

If Lisa’s income increases and relative prices do not change, her budget line shifts outward (away from the origin) and is parallel to the original constraint (Figure 4.7b)

Figure 4.7 Changes in the Budget Line

4.4 Constrained Consumer Choice (1 of 4)

The Consumer’s Optimal Bundle

The optimal bundle must lie on an indifference curve that touches the budget line but does not cross it.

So, M R S = M R T

For the case of Lisa that only consumes pizza Z and burritos B,

M R S = M R T becomes

Rearranging terms,

In words, the marginal utility per dollar spent on pizza is equal to the marginal utility per dollar spent on burritos.

Thus, Lisa maximizes her utility if the last dollar she spends on pizza gets her as much extra utility as the last dollar she spends on burritos. If the last dollar spent on pizza gave Lisa more extra utility than the last dollar spent on burritos, Lisa could increase her happiness by spending more on pizza and less on burritos.

4.4 Constrained Consumer Choice (2 of 4)

There are two ways to reach an optimal bundle, interior and corner solutions.

Interior Solutions

An interior solution occurs when the optimal bundle has positive quantities of both goods and lies between the ends of the budget line.

In Figure 4.8, bundle e with 30 pizzas and 10 burritos per

semester is on indifference curve

It is an optimum interior

solution.

Corner Solutions

A corner solution occurs when the optimal bundle is at one end of the budget line, where the budget line forms a corner with one of the axes.

In Figure 4.9, bundle e with 0 pizzas and 25 burritos per semester

is on indifference curve

It is an optimum corner solution.

Figure 4.8 Consumer Maximization, Interior Solution

Figure 4.9 Consumer Maximization, Corner Solution

4.4 Constrained Consumer Choice (3 of 4)

Promotions

Managers induce consumers to buy more units with promotions. The two most used are buy one, get one free (B O G O) and buy one, get the second at a half price.

Buy One, Get One Free (B O G O)

The B O G O promotion creates a kink in the budget line and its acceptance depends on the shape of the indifference curves.

In Figure 4.10, with the B O G O promotion “buy 3 nights, get the 4th free” the new

budget line is

for both Angela and Betty.

In panel a, without the promotion, Angela’s indifference curve

is tangent to

at point x, so she chooses to spend two nights at the resort. With the B O G O

promotion, her indifference curve

cuts the new budget line

There’s a higher

indifference curve,

that touches

at point y, where she chooses to stay four

nights.

In panel b, without the promotion, Betty chooses to stay two nights at x where her

indifference curve

does not cut the new budget line

no higher indifference curve can touch

so Betty stays only two nights, at x,

and does not take advantage of the B O G O promotion.

Figure 4.10 B O G O Promotions

4.4 Constrained Consumer Choice (4 of 4)

Managerial Implication: Designing Promotions

When deciding whether to use a B O G O promotion, a manager should compare the benefit to the cost.

For example, offering such a promotion is more likely to raise the hotel’s profit if it has excess capacity, so that the cost of providing a room for an extra night’s stay is very low.

To design an effective promotion, a manager should use experiments to learn about customers’ preferences.

For example, a manager could offer each promotion for a short period and keep track of how many customers respond to each promotion, how many nights they choose to stay, and by how much the promotion increases the firm’s profit.

4.5 Deriving Demand Curves

We use consumer theory to show how much the quantity demanded of a good falls as its price rises.

An individual chooses an optimal bundle of goods by picking the point on the highest indifference curve that touches the budget line.

In panel a of Figure 4.11 , e1 is the highest indifference curve that touches

A change in price causes the budget line to rotate, so that the consumer chooses a new optimal bundle.

In panel a of Figure 4.11, a price change from £2 to £1 makes the budget line to

rotate from

The new optimal bundle is e2.

By varying one price and holding other prices and income constant, we determine how the quantity demanded changes as the price changes, which is the information we need to draw the demand curve.

In panel b of Figure 4.11, E1, E2, and E3 are the points of the demand curve derived from price changes, budget lines, and indifference curves in panel a.

Figure 4.11 Deriving an Individual’s Demand Curve

4.6 Behavioral Economics (1 of 3)

So far, we have assumed that consumers are rational, maximizing individuals.

Behavioral economics adds insights from psychology and empirical research on human cognitive and emotional biases to the rational economic model to better predict economic decision making.

We discuss three applications of behavioral economics: tests of transitivity, endowment effects, and salience.

Tests of Transitivity

It is appropriate to assume that adults exhibit transitivity for most economic decisions. But, it is not appropriate for children or when novel goods are introduced.

Some argue that children need some form of protection because they lack of transitivity to maximize their well-being.

4.6 Behavioral Economics (2 of 3)

Endowment Effects

People place a higher value on a good if they own it than they do if they are considering buying it.

One implication of the endowment effect is that consumer’s behavior may differ depending on how a choice is posed.

However, the common belief (common confusion) is that people respond the same way to equivalent questions.

Salience

People are more likely to consider information if it is presented in a way that grabs their attention or if it takes relatively little thought or calculation to understand.

If tax requires calculations, buyers may just ignored it because of costly calculations (bounded rationality).

4.6 Behavioral Economics (3 of 3)

Managerial Implication: Simplifying Consumer Choices

Today’s consumers often feel overwhelmed by choices, for instance, hundreds of channels in Cable T V subscriptions. Because consumers have bounded rationality, most dislike considering all the possibilities and making decisions. At the end, many consumers do not buy these services just to avoid this problem.

Good managers can make decision making easier for consumers. They may offer default bundles so consumers don’t have to make difficult decisions.

For example, Cable T V companies package groups of channels by content, sports, or movie packages. Rather than thinking through each option, the customer can make a much easier decision, such as “I like sports” or “I like movies,” and is more likely to make a purchase.

Managerial Solution

Paying Employees to Relocate

How can a manager use consumer theory to optimally compensate employees who are transferred to other cities?

Solution

Managers collect information about the cost of living in various cities. They know that it is more expensive to buy the same bundle of goods in one city than another and that relative prices differ across cities.

Typical relocation: Alex’s firm wants to transfer him from Seattle to London, where he will face different prices and cost of living. Alex spends his money on housing and entertainment and gets a bundle s that maximizes his satisfaction in Seattle. The firm offers him enough money to buy bundle s in London.

Alex may be better off: entertainment is relatively cheaper in London, but Alex is paid enough to buy bundle s. So, he can substitute housing with entertainment and reach a higher indifference curve.

The firm may offer him less income: There is a lower budget constraint that can put Alex in London at the same indifference curve as in Seattle with less income than the previous solution.

Figure 4.2 Impossible Indifference Curves

Table 4.1 Allocations of a $50 Budget Between Burritos and Pizza

Bundle	Burritos, $2 each	Pizza, $1 each
a	25	0
b	20	10
c	10	30
d	0	50

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