Imagine an OLG economy where people face a lump-sum tax ofgoods when old and a rate of expansion of the fiat money supply ofz >1. The tax and the expansion of the fiat money stock are used to finance government purchases ofggoods per young person in every period. There areNpeople in every generation.

1. Find the individual's budget constraints when young and when old. Com- bine 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 alloca- tion that the planner would have chosen on the graph.
5. Dothesameasinpoint4butnowassumethatz=1. 1

1. Compare the real balances of fiat money on the graphs whenz >1to the values whenz= 1.
2. From now on, assume thatU(c1t, c2t+1) = log(c1t) + log (c2t+1). Find the equilibrium allocations for first period consumption, second period consumption and real money holdings.
3. Find an expression forgin equilibrium.