Suppose A and B live in an exchange economy with two goods x1 and x2. A owns 50 of both goods, and B own 250 of both goods.
A's tastes are captured by the utility functionuA(x1,x2) = x2 + 50lnx1
and B's are captured by the utility functionuB(x1,x2) = x2 + 100lnx1.
a. Let the competitive equilibrium prices be p1 and p2 respectively. Derive both consumers demand functions for both goods.
b. Find the relationship between p1 and p2 in equilibrium. Does the relationship depend on the endowments (assume interior solutions)? How much of each good will each consumer choose?