In: Economics
Consider an exchange economy with two agents, A, B, and two goods, x, y. A's endowment is x = 6, y = 4, and B's endowment is x = 4, y = 6.
(a) Suppose that A has utility function u(x, y) = x + y and B has utility function u(x, y) = xy. Find a competitive equilibrium allocation (CEA) and associated equilibrium prices. What difference would it make if A's endowment is x = 3, y = 1, and B's endowment is x = 7, y = 9? (Diagrammatic/geometric reasoning is sufficient.)
(b) A has utility function u(x, y) = x2 + y2 (for which the indifference curves which are “bowed out”); B’s utility function is min{x, y}. Find the contract curve for this economy. Is there a competitive equilibrium allocation (CEA) for some prices?