5. (15 points) Consider the OLG framework we discussed in class. Now assume that the utility function of people in the economy is log (1.1) + log (02.2+1). Assume that people face a lump- sum tax of goods when old and a rate of expansion of the fiat money supply of 2 > 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. Focus on the Stationary Monetary Equilibrium in the following analysis. (a) (5 points) Find the real demand for money (g = vm) as a function of z and 7. (b) (5 points) Find the government budget constraint in a stationary equilibrium. Solve it for 7 as a function of z. (c) (5 points) Solve the seigniorage and write it as a function of 2. Graph seigniorage as a function of z. 5. (15 points) Consider the OLG framework we discussed in class. Now assume that the utility function of people in the economy is log (1.1) + log (02.2+1). Assume that people face a lump- sum tax of goods when old and a rate of expansion of the fiat money supply of 2 > 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. Focus on the Stationary Monetary Equilibrium in the following analysis. (a) (5 points) Find the real demand for money (g = vm) as a function of z and 7. (b) (5 points) Find the government budget constraint in a stationary equilibrium. Solve it for 7 as a function of z. (c) (5 points) Solve the seigniorage and write it as a function of 2. Graph seigniorage as a function of z