Suppose a consumer buys two goods, $x$ and $y$, and has income of $\$ 30$. Initially $P _ { x } = 3$ and $P _ { y } =$ 3 and the consumer chooses basket $A$ with $x = 5$ and $y = 5$. The prices change to $P _ { x } = 4$ and $P _ { y } = 2$ and the consumer chooses basket $B$ with $x = 1$ and $y = 13$.
A) These choices are consistent with utility maximization.
B) These choices are not consistent with utility maximization.
C) With this information it is not possible to determine if these choices are consistent with utility maximization.
D) Basket $B$ must be strictly preferred to basket $A$.

Question

Quizplus · Accepted Answer

To determine if these choices are consistent with utility maximization, we must compare the marginal utilities per dollar spent on each good before and after the price change.

Initial marginal utilities per dollar spent:
MUx/Px = 1/3
MUy/Py = 1/3

Final marginal utilities per dollar spent:
MUx/Px = 1/4
MUy/Py = 2/3

Since the marginal utility per dollar spent on both goods increased after the price change, the consumer would choose a bundle with more of both goods. This is confirmed by the fact that basket B has more of both goods compared to basket A.

Therefore, these choices are consistent with utility maximization. However, we cannot determine if B is strictly preferred to A without knowing the consumer's utility function. In order to determine if these choices are consistent with utility maximization, we need to compare the consumer's marginal rate of substitution (MRS) to the ratio of the prices of the two goods in each basket.

For basket A, MRS = MUx/MUy = 3/3 = 1, and the price ratio is Px/Py = 3/3 = 1. So, the consumer is choosing a combination of goods where the marginal utility per dollar spent on each good is equal, which is a necessary condition for utility maximization.

For basket B, MRS = MUx/MUy = 4/2 = 2, and the price ratio is Px/Py = 4/2 = 2. So, the consumer is choosing a combination of goods where the marginal utility per dollar spent on each good is also equal, and the MRS is twice as high as the price ratio, which means the consumer is willing to trade two units of y for one unit of x.

Since both baskets satisfy the necessary condition for utility maximization, we can conclude that these choices are consistent with utility maximization. We cannot determine if basket B is strictly preferred to basket A, because we do not know the consumer's utility function or preferences.

Suppose a Consumer Buys Two Goods xxx And yyy , and Has Income Of

Suppose a Consumer Buys Two Goods $x$ And $y$ , and Has Income Of