Suppose Alex and Brianna are consumers in a pure exchange economy, with two goods, thneeds1 and zaboomafoos2 . Alex has 2 units of thneeds and 4 units of zaboomafoos. Brianna has 8 units of thneeds and 6 units of zaboomafoos. Alex and Brianna have identical preferences given by the utility function U(xi) = (x 1 i) 1/2(x 2 i) 1/2 for i = A;B (Alex and Brianna).

a) Suppose the price of zaboomafoos, p2, is normalized to 1. In a perfectly competitive market, solve for the equilibrium price of thneeds, p1 and the optimal allocation of consumption for both consumers Alex and Brianna.

b) Calculate the utility for Alex and Brianna at the initial endowment allocation and the optimal allocation of consumption. Are Alex and Brianna made better off at the optimal allocation of consumption?

c) Show in the Edgeworth box the initial allocation of endowment W, the optimal allocation of consumption M, the price line, and Alex and Brianna's indifference curves which go through the optimal allocation of consumption.

d) Is there another allocation of endowment which can achieve the general equilibrium solved in question (b)? If so, what is it?