Problem 1. There are two consumers, A and B, and two periods. A has a monetary endowment of mA = (mA , mA ) = (2, 4) in the two periods, and B has a monetary endowment of mB = (mB , mB ) = (4, 2) 1 2 1 2 in the two periods. Both consumers consume a consumption good in period 1, x1 , and period 2, x2 and have identical preferences, represented by the utility function, u(x1 , x2 ) = x1 x2 . The two consumers can borrow and lend money to one another, at interest rate, r ≥ 0. (a) Draw the Edgeworth Box and identify all Pareto efficient allocations. (b) Identify all allocations which are at least as good as the initial endowment for both consumers. (c) Determine the competitive equilibrium interest rate, r. (d) Redo parts (a)-(c) with mB = (4, 3).
Problem 2. There are two goods, x1 and x2 , and two consumers, A and B. For each of the following economies, determine the competitive equilibrium prices and allocations. (a) uA (xA , xA ) = xA + xA , uB (xB , xB ) = min{xB , xB }, wA = (1, 2), wB = (3, 2). 1 2 1 2 1 2 1 2 (b) uA (xA , xA ) = xA + xA , uB (xB , xB ) = xB xB , wA = (0, 2), wB = (2, 1). 1 2 1 2 1 2 1 2 (c) uA (xA , xA ) = min{xA , xA }, uB (xB , xB ) = xB , wA = (2, 2), wB = (1, 1). 1 2 1 2 1 2 1 (d) uA (xA , xA ) = xA , uA (xB , xB ) = xB , wA = (1, 1), wB = (1, 1). 1 2 1 1 2 2
