Consider the following OLG economy with N individuals in each generation. Individuals are endowed with y units of the consumption good when young and nothing when old. Fiat money is supplied by the government. The initial old are endowed with M0 units of money. The growth rate of the money supply is z where Mt = z.Mt1 and z > 1. Newly printed money is used to finance government spending. Preferences are such that individuals would like to consume in both periods of life and young individuals also value government spending. That is, u(c1;t; c2;t+1; gt) = ln(c1;t +gt) + ln c2;t+1, where gt is the amount of government spending per young individual in real terms and gt < y. We focus on stationary allocations.

(a) Write down the first- and second-period budget constraints of a typical individual in period t.

(b) Combine the first- and second-period budget constraints to find the individual's lifetime budget constraint.

(c) Find the rate of return on money.

(d) Solve for the optimal choice of (c 1 ; c 2 ) in a stationary equilibrium. What is the level of government spending g consumed by the young?

(e) How does a change in z affect the optimal (c 1 ; c 2 ) and g ? Explain