Question

Problem . Apu receives utility from consuming X and Y. The price of good X is S2 and the price of good Y is S6. Apu's income is S12 (a) Graph Apu's budget constraint (b) If Apu's utility function is U(X, Y)-X+4Y, how much X and Ywill he buy? (e) How will your answer change if U(X, )-X + 3Y?

Answer 1

U(X, Y) = X + 3Y MU_x = partial differential U(X, Y)/partial differential X = 1 MU_y = partial differential U(X, Y)/partial differential Y = 3 MU_x/MU_y = P_n/P_y = 1/3 So, any quantity of good X and Y can be consumed. \r\n Budget Constraint XP_n + YP_y = Income 2X + 6Y = 12 To graph the budget constraint Put X = 0 = > Y = 12/6 = 2 Put Y = 0 = > X = 12/2 = 6 U(X, Y) = X + 4Y Marginal utility of X (MU_x) = partial differential U(X, Y)/partial differential X = 1 Marginal Utility of Y(MU_y) = partial differential U(X, Y)/partial differential Y = 4 At optimal condition, MU_x/MU_y = P_n/P_y = > 1/4 < 2/6 So, only good y will be consumed Y = 12/2 = 2 = > X = 0 Y = 2