Questions: Suppose a consumer spends all his income. His marginal utility per dollar on X is 4 and marginal utility per dollar on Y is 2. We know that a. Utility can be increased by increasing the consumption of X and decreasing the consumption of Y. b. utility can be increased by decreasing the consumption of X and increasing the consumption of Y. c. the price of Y must be eight times the price of X. d. utility is maximized. e. the price of Y must be one-third the price of X.

Suppose a consumer spends all his income. His marginal utility per dollar on X is 4 and marginal utility per dollar on Y is 2. We know that

a. Utility can be increased by increasing the consumption of X and decreasing the consumption of Y.
b. utility can be increased by decreasing the consumption of X and increasing the consumption of Y.
c. the price of Y must be eight times the price of X.
d. utility is maximized.
e. the price of Y must be one-third the price of X.

Transcript text: Suppose a consumer spends all his income. His marginal utility per dollar on $X$ is 4 and marginal utility per dollar on Y is 2 . We know that a. Utility can be increased by increasing the consumption of $X$ and decreasing the consumption of $Y$. b. utility can be increased by decreasing the consumption of $X$ and increasing the consumption of $Y$. c. the price of Y must be eight times the price of X : d. utility is maximized. e. the price of $Y$ must be one-third the price of $X$.

Solution

The answer is the first one (a): Utility can be increased by increasing the consumption of $X$ and decreasing the consumption of $Y$.

Explanation for each option:

a. Utility can be increased by increasing the consumption of $X$ and decreasing the consumption of $Y$.

This option is correct. The marginal utility per dollar spent on $X$ is higher (4) than that on $Y$ (2). This means that for each dollar spent, $X$ provides more utility than $Y$. Therefore, reallocating spending from $Y$ to $X$ will increase total utility.

b. Utility can be increased by decreasing the consumption of $X$ and increasing the consumption of $Y$.

This option is incorrect. Since the marginal utility per dollar for $X$ is higher than for $Y$, decreasing $X$ and increasing $Y$ would decrease total utility.

c. The price of $Y$ must be eight times the price of $X$.

This option is incorrect. The marginal utility per dollar is not directly related to the price ratio in this context. The statement does not follow from the given information.

d. Utility is maximized.

This option is incorrect. Utility is maximized when the marginal utility per dollar is equal for all goods. Since the marginal utility per dollar for $X$ is greater than for $Y$, utility is not maximized.

e. The price of $Y$ must be one-third the price of $X$.