Ambrose has the utility function U(x₁, x₂)= 4x^1/2₁ + x₂.If Ambrose is initially consuming 64 units of nuts and 10 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 17 units of nuts? A)9 B)19 C)4 D)2 E)1

Question

Quizplus · Accepted Answer

We need to find the marginal rate of substitution (MRS) between nuts and berries, which is given by the partial derivative of the utility function with respect to berries divided by the partial derivative of the utility function with respect to nuts. MRS = (∂U/∂x₂) / (∂U/∂x₁) = (1x1/2x(10-0)^(-1/2)) / (4x1/2x(64-0)^(-1/2)) = 1/8 This means that Ambrose is willing to give up 1 unit of berries in exchange for 8 additional units of nuts. In order to get 17 additional units of nuts, he would be willing to give up: = 17/8 ≈ 2 Therefore, the largest number of berries that he would be willing to give up is 2. The correct answer choice is C.

Ambrose Has the Utility Function U(x1, X2)= 4x1/21 + X2

Ambrose Has the Utility Function U(x₁, X₂)= 4x^1/2₁ + X₂