Question

Suppose apples come in two quality levels, low and high. At a store in the apple-growing region, the price of low-quality apples is $1 per pound, and the price of high-quality apples is $4 per pound. Johnny lives in the apple-growing region and buys eight pounds of each type. His marginal utility of apples is 3 utils for low-quality apples and 12 utils for high-quality apples.

a. Is Johnny maximizing his utility?
b. Suppose Johnny moves to an area outside the apple-growing region. Shipping the apples to his new area adds $2 to the price of a pound of apples, for both low- and high-quality apples. To simplify matters, assume Johnny's income increases by an amount large enough to fully offset the higher prices of apples. In other words, he can still afford the original bundle of eight pounds of each type of apples. If he continues to buy eight pounds of apples of each type, is he maximizing his utility? If not, how should he change his mix of high- and low-quality apples?
c. What are the implications for the mix of high- and low-quality apples in apple-growing areas and other regions? Where will most of the high-quality apples be sold?

Answer 1

a. Is Johnny maximizing his utility?

in order to determine if Johnny is maximizing his utility we must calculate the utils per dollar spent on apples:

• low = 3 / $1 = 3 utils per $
• high = 12 / $4 = 3 utils per $

since both types of apples yield the same utility per dollar spent, then Johnny is maximizing his utility.

b. Suppose Johnny moves to an area outside the apple-growing region. Shipping the apples to his new area adds $2 to the price of a pound of apples, for both low- and high-quality apples. To simplify matters, assume Johnny's income increases by an amount large enough to fully offset the higher prices of apples. In other words, he can still afford the original bundle of eight pounds of each type of apples. If he continues to buy eight pounds of apples of each type, is he maximizing his utility? If not, how should he change his mix of high- and low-quality apples?

• low = 3 / $3 = 1 util per $
• high = 12 / $6 = 2 utils per $

Johnny is no longer maximizing his utility since he should buy less-low quality apples and more high-quality apples

c. What are the implications for the mix of high- and low-quality apples in apple-growing areas and other regions? Where will most of the high-quality apples be sold?

Since distribution costs increase the price of apples equally regardless of their quality, low-quality apples will be consumer more in the areas surrounding apple-growing fields. On the other hand, high-quality apples will be sold in larger amounts in areas far away from apple-growing fields. Distribution costs are based on weight and volume, not quality. That is why it is more profitable to sell high-quality goods far away.