Q. Exercise 2 Consider the following overlapping generations model with private debt. Consumers are heterogeneous with respect to their preferences. The lenders' utility function is uL(c1,t , c2,t+1 ) = ln(c1,t ) + ln(c2,t+1 ). The borrowers' utility function is uB (c1,t ,c2,t+1 ) = ln(c1,t ) + 0.5ln(c2,t+1 ). All consumers are endowed with y1 = y2 = 1. There are equal numbers of lenders also borrowers in each generation. Assume the population of each generation is Nt = 1. Let lt also bt denote the individual quantities of lending also borrowing also rt denote the gross real interest rate on loans. There are no assets other than private loans.

(a) Write down the budget constraints when young also when old also the lifetime budget constraint for both types of consumers. Write down the market clearing conditions.

(b) Solve for the stationary competitive equilibrium (r, (cL 1, cL2 ), (cB1 , cB2 ), b, l).

(c) Now Assume to we introduce ?at money into this economy. The money stock Mt grows at the rate z > 1. Find the value of ?at money vt.