Demand for real money balances

cr+1 B. M M Problem 4. (10 points) Consider an economy whose money supply M is determined by the households’ cash-deposit ratio cr, banks’ reserve-deposit ratio it, and the monetary base B: M cr + rr Moreover, the price level P in this economy is determined by the equilibrium condition for the real money balances: P – L(i,Y), where L is the demand for real money balances as a function of the interest rate i and the real output Y. Assume further that Y L6,Y) = Vi i=r + ET, r= 2, E = 2, Y =Y, cr = 0.1, rr = 0.1. where En is the expected inflation rate in percentages. –

(a) Suppose that the central bank wants the annual) inflation rate over the next year to be 2 percent.

How much should the central bank let the monetary base B grow over this period relative to the current level?

(b) Suppose that the stock market crashes and the banks in this economy become extremely cautious. As a result, they raise their reserve-deposit ratio to rr = 0.2. The central bank still wants the inflation rate over the next year to be 2 percent.

How much should the central bank let the monetary base B grow over this period relative to the current level?

(c) In addition to the banks’ change in the reserve-deposit ratio to rr = 0.2, households also respond by raising their cash-deposit ratio to cr = 0.2 and adjusting their expected inflation to En = 1 percent. The central bank still wants the inflation rate over the next year to be 2 percent.

How much should the central bank let the monetary base B grow over this period relative to the current level?