8. (6 marks) Consider the following OLG economy withNindividuals in each gen- eration. Individuals are endowed withyunits of the consumption good when young and nothing when old. Fiat money is supplied by the government. The initial old are endowed withM0units of money. The growth rate of the money supply iszwhereMt=zMt1andz >1. Newly printed money is used to nance government spending. Preferences are such that individuals would like to consume in both periods of life andyoung individuals also value government spending. That is,u(c1;t; c2;t+1; gt) = ln(c1;t+gt) + lnc2;t+1, wheregtis the amount of government spending per young individual in real terms andgt< y. We focus on stationary allocations.

(a) Write down the first- and second-period budget constraints of a typical individual in periodt. (1 mark)

(b) Combine the first- and second-period budget constraints to find the individuals lifetime budget constraint. (1 mark)

(c) Find the rate of return on money. (1 mark)

(d) Solve for the optimal choice of (c1; c2) in a stationary equilibrium. What is the level of government spendinggconsumed by the young? (2 marks)

(e) How does a change inzaect the optimal(c1;c2)andg? Explain.