Consider a 2-period overlapping generations economy with an initial population No = 500. Each generation is n = 1.5 times larger than the previous one. Each individual is endowed with y = 100 units of the consumption good when young, and nothing when old. The only way to acquire consumption in old age is by exchanging part of the endowment when young for fiat 1 of 2 money. The initial old are endowed with Mo = 20,000 units of fiat money. The money stock grows at rate z = 1.01 every period. Newly created fiat money in every period t is distributed as a lump-sum transfer to old individuals worth a units of the consumption good. Assume stationary allocations of consumption throughout the exercise. (a) (5 points) Write down total sources and total uses of goods in this economy in period t and find the per-capita feasible set that a central planner faces in this economy. (b) (5 points) Turning to the monetary equilibrium, write down equations that represent the constraints on first- and second-period consumption for a typical person born in period t. Combine these constraints into a lifetime budget constraint. (Hint: Make sure to consider all sources of funds for the old.) (c) (5 points) Find the equation representing the equality of supply and demand in the mar- ket for money (money market clearing) in an arbitrary period t. Starting from this equation, derive the real rate of return to fiat money, 04+1 (d) (10 points) Assume that a = 0.8. Use a graph that combines the feasible set, the lifetime budget constraint, and arbitrarily drawn indifference curves to argue whether or not the monetary equilibrium attains the Golden Rule in this economy. Clearly label all axes and other relevant elements in the graph. Explain in your own words. Ut