Suppose M_1 is given by currency plus deposits: M_1 = C + D, and the base is giv

Question

Suppose M_1 is given by currency plus deposits: M_1 = C + D, and the base is given by currency plus reserves: B = C + R. Recall that the base and the money supply are connected by the multiplier, m, such that B * m = M1. Suppose further that banks must keep a fraction, rr, of their deposits on hand R = rr * D, and the public holds a fraction, k, of their deposits as cash so C = k * D. Solve for the multiplier in terms of just r and k. 2. Refer to the above. Recessions historically have been (and sometimes still are) accompanied by runs on banks. What complications are presented for monetary policy in this situation? What happens if the central bank does nothing?

Explanation / Answer

Q1. Money supply is connected to Multiplier in following fashion -

B * m = M1

m = M1/B             ... (1)

M1 = C + D

B = C + R

Putting value of B amd M1 is equation 1

m = (C + D)/(C + R) .... (2)

C = k*D

R = r*D

Putting value of C and R in equation 2

m = (k*D + D)/(k*D + r*D)

m = D(k + 1)/D(k + r)

m = (k+1)/(k+r)

The Multiplier in terms of just r and k is m = (k+1)/(k+r).

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