Xavier and Yvette are the only two persons on a desert island.There are only two goods, nuts and berries.Xavier's utility function is U(N_x, B_x)= N_xB_x.Yvette's utility function is U(N_y, B_y)=2N_y + B_y.Xavier is endowed with 5 units of berries and 13 units of nuts.Yvette is endowed with 6 units of berries and 8 units of nuts.In a competitive equilibrium for this economy, how many units of berries does Xavier consume? A)13.50 B)18.50 C)15.50 D)31 E)None of the above.

Question

Quizplus · Accepted Answer

To find the competitive equilibrium, we need to solve for the prices of nuts and berries. Let the price of berries be P and the price of nuts be 1. Then we have the following optimization problems for Xavier and Yvette: Max U(N_x, B_x) subject to P(N_x) + 1(B_x) ≤ 13 and P(B_x) + 1(N_x) ≤ 5 Max U(N_y, B_y) subject to P(N_y) + 1(B_y) ≤ 8 and P(B_y) + 1(N_y) ≤ 6 Solving these problems, we get: N_x = 7, B_x = 6.5, P = 2/13, N_y = 2.5, B_y = 6, P = 2/8 Therefore, Xavier consumes 6.5 units of berries.

Xavier and Yvette Are the Only Two Persons on a Desert