Question

Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $200 and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function is Uſa, k) = 3a + 5k. That is, his constant marginal utility for apples is 3 and his constant marginal utility for kumquats is 5. What bundle of apples and kumquats should Andy purchase to maximize his utility? Why? Andy should maximize his utility buy purchasing apples (lbs.) and kumquats (lbs.). (Enter your responses rounded to the nearest whole number.)

Answer 1

To maximize his utility, Andy should purchase 0 pounds of apples and 50 pounds of kumquats.

Step-by-step explanation:

In order to find Andy's utility-maximizing choice, we need to compare the marginal utility per dollar spent on each good. To do this, we calculate the marginal utility per dollar for apples and kumquats. For apples, we divide the marginal utility of apples (3) by the price of apples ($2) to get 1.5. For kumquats, we divide the marginal utility of kumquats (5) by the price of kumquats ($4) to get 1.25. Since the marginal utility per dollar is higher for apples, Andy should allocate more of his income to purchasing apples.

Let's calculate how many pounds of apples Andy should purchase:

Andy's income is $200 and the price of apples is $2 per pound. Therefore, he can purchase up to 100 pounds of apples (200 / 2). Using the marginal utility per dollar calculation, we can allocate the optimal amount of pounds of apples:

For every additional pound of apples, Andy's marginal utility decreases by 1.5. To find the optimal amount of apples, we need to set the marginal utility per pound equal to the marginal utility per dollar (1.5):

1.5 = 3 / (2 + a)

1.5(2 + a) = 3

3 + 1.5a = 3

1.5a = 0

a = 0

Therefore, Andy should purchase 0 pounds of apples. Since he can purchase up to 100 pounds of apples and his optimal choice is 0 pounds, he should allocate the rest of his income ($200) to purchasing kumquats. Let's calculate how many pounds of kumquats he can purchase:

Andy's income is $200 and the price of kumquats is $4 per pound. Therefore, he can purchase up to 50 pounds of kumquats (200 / 4).

So, Andy should purchase 0 pounds of apples and 50 pounds of kumquats to maximize his utility.