Consider an overlapping generations economy in which capital pays a 25 percent net rate of return. The population of a generation grows by 10 percent each period. In the initial period (period 1), there are 100 people and a preexisting fiat money stock of M₀ = $1 million. Because of a political impasse, government expenditures exceed (nonseigniorage) tax revenues by 50 goods per young person in every period. Each young person wishes to hold real money balances worth 200 goods regardless of the rate of inflation.
a. Use the government budget constraint to find the rate of fiat money creation that is required to finance the excess of government expenditures over taxes. Find also the fiat money stock and the price level in periods 1 and 2.
b. Suppose that, in the initial period, the monetary authority hesitates to print new money, forcing the government to issue debt at the market rate of interest. In the second period, the monetary authority relents, printing enough new money to pay off the debt as well as to pay for the second period’s excess of government expenditures over taxes. Find the fiat money stock in period 2 and compare it with your answers in part a. Explain the difference.
c. Suppose that, in the initial period, you anticipate the actions of the monetary authority described in part b. What rate of inflation do you expect? If (contrary to our assumption) anticipated inflation discourages the use of fiat money, why will the price level rise in period 1 even though no fiat money is printed?