Problem: Assume that in a certain economy the LM curve is given by Y = 2000r - 2000 + 2 (M/P), and the IS curve is given by Y = 8000 - 2000r + v, where v is a shock that is equal to 200 half of the time and –200 half of the time. The price level is fixed at P=1 for simplicity. The natural output level is 4000. The government wants to keep output as close to 4000 as possible and does not care about anything else. Consider the following two policy rules:
(i) Set the money supply M=1000 and keep it there;
(ii) Manipulate M from day to day to keep the interest rate constant at 2%.
(a) Under rule (i), what will Y be when v=200? What will Y be when v=-200?
(b) Under rule (ii), what will Y be when v=200? What will Y be when v=-200?
(c) Which rule will keep output close to 4000?