Imagine an OLG economy where people face a lump sum tax of ~ goods when old and a rate of expansion of the fiat money supply of > > 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 / people 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. 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 > > 1 to the values when = = 1. 7. From now on, assume that U (cut, cant ) = log(cut) + log (cart). Find the equilibrium allocations for first period consumption, second period consumption and real money holdings. 8. Find an expression for g in equilibrium