Joseph's utility function is given by U_J = x_A+ 2x_B_,where x_A denotes his consumption of apples and x_B his consumption of bananas. Clara's utility function is given by U_C = 3x_A + 2x_B. Joseph and Clara shop at the same grocery store. A) When we observe that Joseph leaves the store with some bananas, then we can deduce that Clara also buys some bananas. B) There exist prices of apples and bananas such that both consumers buy strictly positive amounts of both goods. C) When we observe that Joseph leaves the store with some apples and some bananas, then we can deduce that Clara also buys some apples and some bananas. D) When we observe that Joseph leaves the store with some apples, then we can deduce that Clara also buys some apples. E) Apples and bananas are perfect complements for Joseph.

Question

Quizplus · Accepted Answer

From Joseph's utility function, we can see that he has a positive marginal utility for bananas, i.e., consuming more bananas will increase his utility. Therefore, if Joseph leaves the store with some bananas, it is likely that he has reached a point where the marginal utility from bananas is equal to the price of bananas, and he is maximizing his utility by buying some bananas. Since Clara's utility function does not involve any interaction between the goods, we cannot deduce anything about her consumption solely from Joseph's choice of bananas.

Option A is not necessarily true since Clara may have already had bananas or may prefer a different combination of goods. Option B is also not necessarily true since it depends on the relative prices of the goods and the shapes of the indifference curves. Option C is not true either as Joseph could have bought some bananas and apples in different proportions than Clara, based on their marginal utilities and prices. Finally, option E is not true since the utility function does not exhibit a fixed proportion relationship between apples and bananas.

Joseph's Utility Function Is Given by UJ = XA

Joseph's Utility Function Is Given by U_J = X_A