Consider an overlapping generations model in which individuals live for two periods. Assume that the population grows at rate n > 1 per period. Each individual is endowed with y units of the single consumption good when young, and nothing when old. The consumption good is non-storable. The valued stock of fiat money, evolves each period according to, Mt = zMt1, where z > 1. In each period t, the government uses the receipts from the newly printed money to: make lump-sum transfers at to every old individual, and to finance government purchases of g per old individual. (a) (10 marks) Write down the feasibility constraint that a central planner would face. (b) (6 marks) Write down the government budget constraint. (c) (12 marks) Write down an individual's first and second period budget constraints. Derive the individual's lifetime budget constraint. Solve for a stationary monetary equilibrium and draw it on a graph. With the help of a graph show whether the stationary monetary equilibrium obeys the golden rule. Explain why or why not. (d) (7 marks) Assume now that the government, maintains a constant money supply (z = 1), and instead provides for the subsidies to the old and g by imposing a lump-sum tax of on every young individual. However, tax collection is costly, i.e., for every unit collected from the young 1/4 is lost. Does this policy maximize the welfare of future generations? Briefly explain.