Question 3 (25 points) Consider au economy with a constant population of N = 2, 000. Individuals are endowed with y = 50 units of the consumption good when young and nothing when old. All seigniorage revenue is used to finance government expenditures. There are no subsidies and no taxes other than seigniorage. Suppose that preferences are such that each individual wishes to hold real balances of fiat money worth _uv_ goods. 1+ (a) (10 points) Write down the budget constraints in the first and second period of an in- dividual's life. Determine consumption when young and when old as a function of Vt Show that the lifetime budget constraint is satisfied. (b) (10 points) Use the equality of supply and demand in the money market to determine the real rate of return to fiat money. Using this, determine the total real balances of fiat money in a stationary equilibrium as a function of the rate of fiat money creation z. (c) (5 points) Use your answer in part (b) to find total seigniorage revenue as a function of z.