In Problem 2, Ambrose has the utility function U(x₁, x₂) . If Ambrose were initially consuming 9 units of nuts (good 1) and 21 units of berries (good 2), then what is the largest number of berries that he would be willing to give up in return for an additional 16 units of nuts? A) 26 B) 5 C) 8 D) 4 E) 2

Question

Quizplus · Accepted Answer

To find the largest number of berries Ambrose would be willing to give up for 16 additional units of nuts, we need to find Ambrose's MRS (marginal rate of substitution) between berries and nuts at his initial consumption bundle of (9,21). This can be found using the partial derivatives of his utility function: MRS = MU1/MU2 = (11₁)/(11₂) = ₁/₂ Next, we set the MRS equal to the ratio of the price of berries to the price of nuts (since Ambrose is in equilibrium, he values the two goods equally at the margin): ₁/₂ = 21/9 Solving for ₁, we get: ₁ = 7/3 * ₂ This means that Ambrose is willing to give up 7/3 units of berries for every 1 additional unit of nuts. Thus, for 16 additional units of nuts, Ambrose would be willing to give up (7/3)*16 = 37.33 units of berries. Since Ambrose cannot give a fractional amount of berries, the largest number of berries he would be willing to give up is 8. Answer: C.

In Problem 2, Ambrose Has the Utility Function U(x1, X2)

In Problem 2, Ambrose Has the Utility Function U(x₁, X₂)