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 pt and the demand for money (in logarithms) depends solely on expected ination (1r;5 +1 2 pf +1 pi) and is equal to: mt '19: = '3 (pfH 'Pt) - Suppose that at time t = 0, 1 and 2, the nominal money stock (in logarithms) is equal to 100 (Le, m0 = m1 = m2 = 100) and the price index (in logarithms) is equal to 100 at time t = 0 and 1 (Le, p0 2 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 303 +1. (b) Suppose that agents' have adaptive expectations of the following form: a 3 1 Pt = apt1 'l' apt2- Calculate the price level at time t = 2, 3, 4, and 5: 392,193, 114, p5