# Utility Maximization and Demand

UTILITY MAXIMIZATION AND DEMAND

L E A R N I N G O B J E C T I V E S

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1. Derive an individual demand curve from utility-maximizing adjustments to changes in price. 2. Derive the market demand curve from the demand curves of individuals. 3. Explain the substitution and income effects of a price change. 4. Explain the concepts of normal and inferior goods in terms of the income effect.

Choices that maximize utility—that is, choices that follow the marginal decision rule—generally produce downward-sloping demand curves. This section shows how an individual’s utility-maximizing choices can lead to a demand curve.

2.1 Deriving an Individual’s Demand Curve Suppose, for simplicity, that Mary Andrews consumes only apples, denoted by the letter A, and or- anges, denoted by the letter O. Apples cost \$2 per pound and oranges cost \$1 per pound, and her budget allows her to spend \$20 per month on the two goods. We assume that Ms. Andrews will adjust her consumption so that the utility-maximizing condition holds for the two goods: The ratio of mar- ginal utility to price is the same for apples and oranges. That is,

EQUATION 7.4 MUA

\$2 = MUO

\$1

Here MUA and MUO are the marginal utilities of apples and oranges, respectively. Her spending equals her budget of \$20 per month; suppose she buys 5 pounds of apples and 10 of oranges.

172 PRINCIPLES OF ECONOMICS VERSION 3.0

Now suppose that an unusually large harvest of apples lowers their price to \$1 per pound. The lower price of apples increases the marginal utility of each \$1 Ms. Andrews spends on apples, so that at her current level of consumption of apples and oranges

EQUATION 7.5 MUA

\$1 > MUO

\$1

Ms. Andrews will respond by purchasing more apples. As she does so, the marginal utility she re- ceives from apples will decline. If she regards apples and oranges as substitutes, she will also buy fewer oranges. That will cause the marginal utility of oranges to rise. She will continue to adjust her spending until the marginal utility per \$1 spent is equal for both goods:

EQUATION 7.6 MUA

\$1 = MUO

\$1

Suppose that at this new solution, she purchases 12 pounds of apples and 8 pounds of oranges. She is still spending all of her budget of \$20 on the two goods [(12 x \$1)+(8 x \$1)=\$20].

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