Question

Suppose that MUY = 20, MUX = 15, PY = $5, and PX = $5. Which of the following statements is TRUE?

a. The consumer is receiving more marginal utility per dollar from good X than from good Y.
b. The consumer could increase utility by giving up 1units of good X for 1 unit of good Y.
c. The consumer is maximizing utility.
d. The consumer could increase utility by giving up 1 unit of good Y for 1 unit of good X.

Answer 1

The marginal utility per dollar for good Y is greater than that for good X, indicating that the consumer can increase utility by substituting good Y for good X on a one-to-one basis. Therefore, statement b is true.

Step-by-step explanation:

We can assess the consumer's utility maximization by calculating the marginal utility per dollar for each good. Marginal utility per dollar is calculated by dividing the marginal utility (MU) of a good by its price (P). For good X, the marginal utility per dollar is MUx/Px, and for good Y, it is MUy/Py.

In this case, MUx = 15, Px = $5, MUy = 20, and Py = $5. Thus, the marginal utility per dollar for X is 15/5 = 3, and for Y, it is 20/5 = 4. Given that the marginal utility per dollar of Y is higher than that of X, the consumer would gain more utility by consuming an additional unit of good Y rather than X, assuming they can be substituted on a one-to-one basis.

The correct answer to the question is therefore: b. The consumer could increase utility by giving up 1 unit of good X for 1 unit of good Y.