Suppose the economy consists of two individuals, Ariel and Brad, who consume two goods, and , with the following preferences and initial endowments.

U_A (x, y) = x_A. y_A

_A = (4, 2)

U_B (x, y) = x_B. y_B

_B = (2, 3)

a.In an Edgeworth Box label the initial endowment, draw an indifference curve through the initial endowment for each individual, and shade the region of allocations that would be a Pareto improvement to the initial endowment.

b.Derive an equation to describe the set of Pareto-optimal allocations, and draw it in the Edgeworth Box.

c.Define the competitive equilibrium allocation [(x_A, y_A), (X_B, y_B)] and price ratio P_X/P_Y. (Remember that without loss of generality, you may set P₁ 1.)

d.Find a set of transfers, and , where _A + = 0, such that the competitive equilibrium becomes [(1, 1), (5, 4)].