Question

Problem 2. Consider an overlapping generations model with money, where t = 1,2,3,.... So, every period t, a generation of two-period lived agents are born. Their preferences are . They are endowed with ey units of the consumption good, when young, and e° units of the consumption good, when old. Assume that e^y > e^o > 0. The consumption good is perishable The initial old also have a quantity M of intrinsically valueless fiat money. Trading takes place as described in class, i.e., old agents may purchase goods from young agents, using their money. Let st be the amount of savings, expressed in units of the good, which a young agent will save in period t, using money. There is no other store of ualue. Let π_t=P_t/P_t-1 be the inflation from period t-1 to t, where P is the price in units of money for one unit of the consumption good.

4. Find all stationary equilibria, where π_t ≡ π̅ is constant. Calculate them explicitly, when e^y=4 and e^o =1. Describe these equilibria.

Answer 1

If the inflation rate is higher than the rate of interest, consumption is more in the younger period, vice-versa.