4. (15 points) Consider an exchange economy with two representative consumers (1 and 2) and two goods (A and B). The preference of both consumers are given asu1(x1A,x1B) =x1/2x1/2,

1A1Bu2(x2A,x2B) =x2Ax2B. The initial endowments for consumer 1 isw1= (w1A,w1B) = (10,3)

1/2 1/2

and the initial endowments for consumer 2 isw2= (w2A,w2B) = (6,7).

Suppose there is a market and the two consumers are both price-takers. They meet in the market and trade with each other. Suppose the price for good A is normalized to be always 1,pA1.

(a) (5 points) Suppose the initial endowment is highlighted as point E in the following Edgeworth box. Highlight (1) the Pareto efficient set , and (2) the possible trading outcomes based on voluntary transaction no matter what is the market mechanism

(economic core).

(b) (3 points) Given PA = 1 and PB (to be solved). Write down the budget constraint for each consumer.

(c) (7 points) Solve for the general equilibrium price PB? What is the consumption for each consumer?