Imagine an OLG economy where people face a lump-sum tax ofgoods when

old and a rate of expansion of the fiat money supply of z > 1. The tax and

the expansion of the fiat money stock are used to finance government purchases

of g goods per young person in every period. There are N people in every

generation.

1. Find the individual's budget constraints when young and when old. Combine

them to find the lifetime budget constraint. Plot this last constraint.

2. Find the government's budget constraint.

3. Find the real return on money. Plug it to the lifetime budget constraint.

4. Graph together the per-capita resource constraint and the lifetime budget

constraint. Indicate where is the competitive equilibrium and the allocation

that the planner would have chosen on the graph.

5. Do the same as in point 4 but now assume that z = 1.

6. Compare the real balances of fiat money on the graphs when z > 1 to the

values when z = 1.

7. From now on, assume that U (c1t; c2t+1) = log(c1t) + log (c2t+1). Find

the equilibrium allocations for first period consumption, second period

consumption and real money holdings.

8. Find an expression for g in equilibrium.