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 ey > eo > 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 value. Let πt=Pt/Pt-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.

5. Find all equilibria, i.e. find all combination (P₁,π₂) of the initial price level P₁ and inflation rate π₂, resulting in an equilibrium, when ey=4 and eo =1 and M=1. What can you say about them? What happens to the inflation rates eventually, as t→∞? 

6. What happens to these equilibria, if the initial old would have had twice as much money instead?

Answer 1