3. Consider an economy with a constant population of N = 100. Each person is endowed with y = 20 units of the consumption good when young and nothing when old. 1 (a) What is the equation for the feasible set of this economy? Portray the feasible set on a graph. With arbitrarily drawn indifference curves, illustrate the stationary combination of cand e that maximizes the utility of future generations. (b) Now look at a monetary equilibrium. Write down equations that represent the constraints on first- and second-period consumption for a typical person. Combine these constraints into a lifetime budget constraint. (c) Suppose the initial old are endowed with a total of M = 400 units of fiat money. What condition represents the clearing of the money market in an arbitrary period + ? Use this condition to find the real return of fiat money. For the remaining parts of this exercise, suppose preferences are given by [18]2+ (a) What is the value of money in period /, ? What is the price of the consumption good ? (e) If the rate of population growth increased, what would happen to the rate of return of fiat money, the real demand for fiat money, the value of a unit of fiat money in the initial period, and the utility of the initial old? Explain your answers. (1) Suppose instead that the initial old were endowed with a total of 800 units of fiat money. How do your answers to part (d) change? Are the initial old better off with more units of fiat money