{Cagan Model and PPP): We have the following Cagan equation: m: p: = ?]I'E:[Pt+1 Pt]: (1) where m: E IH(M), 325 E En(H), H: price level at period t, and ME: money supply at t. a) (10 marks) Find an expression of p; in terms of a sequence of money supply (m,m+1 ,, ,,), assuming a no-bubble condition. -2- b} [10 marks} Households are now at period t=0. The money supply stays constant at W}: = M from t:2 on. That is, Bums : M for s )3 1. The money supply at t:0 and t:1 are, respectively, %?}M and mi? . What is the price level at tz T In other words, what is pg ? c} [20 marks} The money supply m, is expected to stay constant at m, = M from t=0 on. At period 1, a government unexpectedly increase the money supply, 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 generate 100% ination rate from period 0 to 1, (i) how much money will it supply? (ii) how much is the amount of senoriage in log? d} [15 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? ZfA-l-gt (2) For country B, the money supply over time is given by m? = \"HEB + ,Ugt (3) (a) Let ,LLA : 2% and p3 = 4%. What is the ination rate for each country between period 0 and 1? (you need to show your work to get points) [5points). (b) Suppose that the relative PPP holds between the two countries even in the shortrun. How much will the country B's currency against the country A's currency depreciate or appreciate between the period 0 and 1? (10 points)