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Assume the existence of a two agent ( i = 1,2) two good ( x i , y i ) economy. Agent 1's utility function

Assume the existence of a two agent (i = 1,2) two good (xi, yi) economy. Agent 1's utility function is given by

u1(x1, y1) = x11/3y12/3 while agent 2's utility function is given by

u2(x2, y2) = x21/2y21/2. Finally, agent 1 and 2's endowment of x and y are given by (1, 0) and (0, 1), respectively. For simplicity normalize the price of y to be 1. Therefore, 'p' represents the price of x.

(a) What is each agent's demand function for x and y?

(b) What is the equilibrium price ratio?

(c) What conditions must be fulfilled in order to achieve an equitable allocation of both x and y for both agents?

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