Assume That in a Certain Economy the LM Curve Is $Y$

Assume that in a certain economy the LM curve is given by Y = 2,000r - 2,000 + 2(M/P), and the IS curve is given by Y = 8,000 - 2,000r + u, where u is a shock that is equal to +200 half the time and -200 half the time. The price level (P) is fixed at 1.0. The natural rate of output is 4,000. The government wants to keep output as close as possible to 4,000 and does not care about anything else. Consider the following two policy rules: i. Set the money supply M equal to 1,000 and keep it there. ii. Manipulate M from day to day to keep the interest rate constant at 2 percent.

a. Under rule i, what will $Y$ be when $u = + 200$ ? What will $Y$ be under rule i when $u = - 200$ ?
b. Under rule ii, what will $Y$ be when $u = + 200$ ? What will $Y$ be under rule ii, when $u = - 200$ ?
c. Which rule will keep output closer to 4,000 ?