Assume the existence of a two agent (i = 1,2) two good (x_i, y_i) economy. Agent 1's utility function is given by u₁(x₁, y₁) = x₁^1/3y₁^2/3 while agent 2's utility function is given by u₂(x₂, y₂) = x₂^1/2y₂^1/2. 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?