Ambrose has the utility function U(x₁, x₂)= 4x^1/2₁ + x₂.If Ambrose is initially consuming 25 units of nuts and 17 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 39 units of nuts? A)8 B)12 C)25 D)6 E)3

Question

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To find the answer, we need to determine the marginal rate of substitution (MRS) between nuts and berries. MRS = MU of nuts / MU of berries Taking the partial derivatives of the utility function with respect to nuts and berries, we get: MU of nuts = 2x^1/2₁ F1F1F1S1F1F1F10 4x²₂ F1F1F1S1 MU of berries = 4x^1/2₂ F1F1F1S1F1F1F10 x₁ Plugging in the initial consumption bundle of (25,17), we get: MU of nuts = 9.8 MU of berries = 6.5 Therefore, MRS = 1.5. This means that Ambrose is willing to give up 1.5 units of berries for each additional unit of nuts. To get an additional 39 units of nuts, he would be willing to give up: 39 * 1.5 = 58.5 units of berries. He cannot give up 58.5 units of berries, so he would give up the largest integer value less than or equal to 58.5, which is 12. Therefore, the answer is (B).

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

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