We have the following Cagan equation: mt - pt = -1Et[Pt+1 Pt], where m = ln(Mt), pt = ln (Pt), Pt: price level at period t, and M: money supply at t. (1) a) (10 marks) Find an expression of p, in terms of a sequence of money supply (m,mt+1 ), assuming a no-bubble condition. = M b) (10 marks) Households are now at period t=0. The money supply stays constant at m from t 2 on. That is, Eoms = M for s> 1. The money supply at t=0 and t=1 are, respectively, nM and nM. What is the price level at t=0? In other words, what is po ? M from t=0 on. At c) (20 marks) The money supply mt is expected to stay constant at m = period 1, a government unexpectedly increase the money supply for seigniorage, and once it has increased the money supply at period 1, the money supply will stay constant at the level from period 1 onward. If the government wants to have a seigniorage amounting to b in real terms, by how much does the government increase its money supply? it is assumed that b < 1, and you don't have to convert m, to Mt. That is, just solve for the answer in the logged term. d) (20 marks) Now assume that there are two countries A and B, and the Cagan equation holds for both countries. For country A, the money supply over time is given by m = mA + HAt For country B, the money supply over time is given by m = mB+ Bt (a) Let A = 2% and = B 0 and 1? (you need to show your work to get points). (3) 4%. What is the inflation rate for each country between period (b) Suppose that the relative PPP holds between the two countries. How much will the country B's currency depreciate or appreciate over the next 5 years?