III. OLG and money (25%) Time starts at t = 1 and lasts forever. At the start of period t, there are N, newly-born individuals; they are referred to as generation t. They live for two periods (i.e., they die at the end of period t + 1). A person is young in his first period (i.e., period t), and old in his second period (i.e., period t + 1). At the start of t = 1, along with generation 1, there are No people who live for only one period (i.e., they die at the end of period 1); they are referred to as the initial old. There is one good per period. The good is not storable. For simplicity, we assume that people from the same generation are all alike. Denote the (representative) generation-t person's endowment by (y;, y;+1), where y, is his endowment at young (i.e., period t) and y+1 is his endowment at old (i.e., period t+1). From consuming q at young and d at old, the generation-t's person's utility is Utch, CH1), where U, is strictly increasing in each of the two arguments. Also, denote the (representative) initial old's endowment at period 1 by of. From consuming ci, the initial old's utility is W(ci) at old, where W is strictly increasing. Money is a durable object which is intrinsically useless. At the start of period 0, the initial old holds, the M units of money. Let Me = 1, U.(d, CHA) = GG+1, and (y), yi+ 1) = (2,0.3), all t > 1. Let W(c) = cq, yi = 0.3, and M = 10. 1. Find the equilibrium condition that relates p with pi+1. 2. Solve the equilibrium price level in which the price is finite and constant over time. 3. Find the condition on pi so that the corresponding equilibrium has Pt+1 > pe all t 2 1. 4. Propose a policy that can eliminate the sort of equilibria in part 3. 5. Now suppose that the government taxes an agent 71 = 0.2 at young and 72 = 0.2 at old, that the government has a constant deficit G - T = 0.2 at each period, and that the government prints money to buy goods in the market to finance its deficit each period. What is the stock of money at period 3 if the economy is in an equilibrium with a constant inflation rate