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Problem 4 [based on CFH exercise 3-4}. Let the number of young people born in each period be constant at N. There is a constant stock of fiat money M. Each young person born in period t is endowed with y, units of the consumption good and nothing when old. Suppose the en- dowment grows over time if; = {no-1 for o 3:- 1. For simplicity, assume that in each period if, people desire to hold real moneyr balances equal to one-half of their endowment, so that't!,rr.'r, : H.515\". a) (5 points} Write down the budget constraints an agent born in period t faces when young and old. Combining these constraints, write the agent's lifetime budget constraint. b) (5 points} Write down the condition that represents the clearing of the money market in an arbitrar}r period 4'. Use this condition to find the real return of fiat money in a monetary equilibrium, 4\". , \"to. c) (5 points) Derive the Quantity Theoryr of Money equation for this economy. Explain in words how it depends on the rate of endowment growth n. d) (5 points} Suppose a new technology arrives in which n increases. Explain in words the effect on an agent's optimal consumption path (rm. r-3_,.,., )