In The Republic Of Pecunia 1100 Individuals Are Born In Period

In the Republic of Pecunia 1100 individuals are born in period t. The population grows according to Nt = 1.1Nt−1. Each citizen in Pecunia is endowed with y1 = 15 units of the consumption good when young, and y2 = 5.5 units when old. Preferences are such that individuals will always want to consume more than their endowment when old. The fiat money stock in period t amounts to 2500. The Pecunian government is increasing the stock of fiat money in circulation by 5 percent each period (z = 1.05). The additional units of money printed every period are used to purchase Gt units of the consumption good for government consumption which is wasteful from the perspective of the Pecunian citizens. Assume stationarity throughout the exercise.

(a) (5 points) Define total uses and total sources of goods in this economy in period t and derive the (per-capita) feasible set. Use gt = Gt Nt−1 . (b) (5 points) Now look at the monetary equilibrium. Combine the constraints on first- and second-period consumption for a typical person into a lifetime budget constraint. Hint: Make sure to consider all available endowments. (c) (5 points) Derive the real rate of return of fiat money. Plug into the lifetime budget constraint. (d) (5 points) Now assume that the government raises lump-sum taxes τ from young individuals to finance its government consumption Gt and does not print new fiat money (z = 1). Show how this policy affects the life-time budget constraint of an individual born in t both directly and indirectly through changes in the rate of return to fiat money.