The Smith family is allocating its monthly household expenditure between only two goods, food and
Clothing. Suppose that the price of food is $12 per unit, and the price of clothing is $16 per unit and that the marginal utility that the family is receiving from its consumption of clothing is currently
200. What is the family's marginal utility from its consumption of food if it is maximizing its utility?

Question

Quizplus · Accepted Answer

To maximize utility, the family should allocate its expenditure between the two goods such that the ratio of their marginal utilities to their prices are equal. Given that the marginal utility per dollar of clothing is $\frac{200}{16}=12.5$, the family should choose to consume food such that its marginal utility per dollar is also equal to 12.5. We can find this by dividing the marginal utility of clothing by its price, and setting that equal to the marginal utility of food divided by its price:
$$\frac{MU_c}{P_c}=\frac{MU_f}{P_f}$$
$$\frac{200}{16}=\frac{MU_f}{12}$$
Solving for $MU_f$, we get $MU_f=150$. Therefore, the family's marginal utility from its consumption of food when it is maximizing its utility is 150.

The Smith Family Is Allocating Its Monthly Household Expenditure Between