Question

1. 30 points total] Consider the economy characterized with the following equations Y a-b(R- T), b> 0 IS relation Phillips TtTt-1 +vY+ o, v > 0 curve The economy has been in the long-run equilibrium up to period 0. In period 1, however, a one-time inflation shock o > 0 hits the economy. In other words, o > 0 in period 1 but o 0 in all other periods. (a) [10 points] The monetary policy rule (MPR) is given as follows. R=rm (T- ), m> 0 Describe the dynamics of (Yt, Tt, Rt in response to the shock. Provide intuitions. (b) [10 points] Consider an alternative MPR: Rt =r+n, n > 0 I Comment on this MPR and resulting AD curve. Describe the dynamics of (Yt, Tt, R in response to the shock Provide intuitions. (c) 10 points] Let's consider still another MPR as follows. Te= Again, answer the questions given in (b) for this MPR.

Answer 1

a) Due to an inflation shock in period 1, o>0.

$\prod$t is higher than normal, for which the MPR R_t rises. R_t-r rises. -(R_t-r) falls.

This leads to rise in Y_t falls.

b)due to inflationary shock, o>0, the level of inflation at period 1, $\prod$t rises ( from Phillips curve equation).

From the MPR equation: as R_t-r= nY_t remains constant as Y_t remains constant. therefore Y_t the IS curve equation remains constant.

c)