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 $x = 7$ and $y = 3$. The prices change to $P _ { x } = 4$ and $P _ { y } = 2$ and the consumer chooses basket $B$ with $x = 5$ and $y = 5$.
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 preferred to basket A.

Question

Quizplus · Accepted Answer

Since the consumer chooses a higher quantity of good $x$ when its price increases and a higher quantity of good $y$ when its price decreases, the choices are consistent with the law of demand. Moreover, basket B gives the consumer more utility as both goods are consumed in equal amounts, hence this choice is possible with utility maximization. Therefore, the answer is A. To determine if the consumer is maximizing utility, we need to compare the marginal utilities per dollar spent on each good between the two baskets.

For basket A:

MUx/Px = 1/3 
MUy/Py = 1/3

For basket B:

MUx/Px = 1/4 
MUy/Py = 1/2

Since the consumer chose basket B over A, it must be the case that the marginal utility per dollar spent on both goods was higher in basket B. Therefore, the consumer is maximizing utility and choice A is correct.

Choice D cannot be determined based on the information given as we do not know the consumer's preferences and cannot conclude that basket B is preferred to basket A.

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