Suppose the price of good $x$ is $\$ 5$ and the price of good $y$ is $\$ 7$. Also, suppose $M U _ { x } = y$ and $M U _ { y } = x$. Which of the following baskets could be an interior optimum?
A) $x = 5 , y = 7$
B) $x = 4 , y = 6$
C) $x = 7 , y = 5$
D) $x = 6 , y = 4$

Question

Quizplus · Accepted Answer

For an interior optimum in consumer choice theory, the marginal rate of substitution (MRS), which is the ratio of the marginal utilities ($MU_x/MU_y$), must equal the ratio of the prices of the two goods ($P_x/P_y$). Given $MU_x = y$ and $MU_y = x$, the MRS is $y/x$. The price ratio is $5/7$. Only in option C, where $x = 7$ and $y = 5$, does the MRS ($5/7$) match the price ratio ($5/7$), indicating an interior optimum.

Suppose the Price of Good xxx Is $5\$ 5$5 And the Price of Good

Suppose the Price of Good $x$ Is $\$ 5$ And the Price of Good