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Macroeconomics III Assignment 2 - The Cagan Model Submit your assignment using Virtual Campus. You can perform this assignment in a group of maximum 3 people. 1. Assume that the supply of money (in logarithms) is equal to mt – P4 and the demand for money (in logarithms) depends solely on expected inflation (T&+1 =p&#1 – pł) and is equal to: m+ – P+ = -3 (pé+1 – pt). - = Suppose that at time t = 0,1 and 2, the nominal money stock (in logarithms) is equal to 100 (i.e., mo = mı = m2 = 100) and the price index (in logarithms) is equal to 100 time t = 0 and 1 (i.e., Po = P1 = 100). At t = 1, the central bank announces that the nominal money stock will increase at t = 3 to m3 = 150 and remain at that level forever. (a) Use demand and supply of money to derive price level pt for any time t as a function of the nominal money stock mt and expected price level in the next period p+1 (b) Suppose that agents' have adaptive expectations of the following form: 1 3 pe = 4Pt-1+ Calculate the price level at time t = 2,3,4, and 5: P2, P3, P4, P5. (c) Calculate the price levels P2, P3, P4, and p3 assuming that agents have rational expectations and imposing "no bubble" condition. Explain why your answer differs from (b). (d) Graphically show the change pt from t = 0 to t= 5 with adaptive expectations and rational expectations.