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. Suppose that currency in circulation is $600B, demand deposits are $900B, and

ID: 2696329 • Letter: #

Question

. Suppose that currency in circulation is $600B, demand deposits are $900B, and excess reserves

are $15B. The required reserve ratio is 10%.

a. Calculate the M1 money supply, the currency-deposit ratio, the excess reserve ratio, and

the money multiplier.

b. Suppose the Bank of Canada conducts an unusually large open market purchase of

bonds from its bond dealers of $1,400B due to a sharp contraction in the economy.

Assume the ratios you calculated in part (a) remain unchanged, what do you predict will

be the effect on the M1 money supply.

c. Suppose the Bank of Canada conducts the same open market purchase as in part (b),

except that banks choose to hold all of these proceeds as excess reserves rather than

loan them out, due to fear of a financial crisis. Assuming that currency and chequable

deposits remain the same, what happens to the amount of excess reserves, the excess

reserve ratio, the money supply, and the money multiplier?

Explanation / Answer

C = currency in circulation

D = demand deposits (funds in checking accounts)

rD = required reserve ratio

RR = required reserves = rDD

R = actual reserves

ER = excess reserves = R - RR

M1 = money supply = C + D

MB = monetary base = R + C

m1 = M1 money multiplier = M1/MB

Derivation of m1


MB = R + C = RR + ER + C = rDD + (ER/D)D + (C/D)D

Therefore

MB = [rD + (ER/D)+ (C/D)]D

But

M1 = D + C = [1 + (C/D)]D

Therefore

m1 = M1/MB =[1+(C/D)]D/[rD+(ER/D)+ (C/D]D

and hence


m1=[1+(C/D)]/[rD+(ER/D)+ (C/D]


The M2 Money Multiplier


The M2 money supply is defined as the M1 money supply


plus time deposits

plus money market mutual fund shares

plus money market deposit accounts

plus overnight repurchase agreements

plus overnight Eurodollars.

To keep matters simple all of the above items will be grouped together as MMF. Thus

M2 = M1 + T + MMF.


Let rT be the required reserve ratio on time deposits. The required reserves at the Fed are then


RR = rDD + rTT.


Thus the monetary base and the M2 money supply are:

MB = rDD + rTT + ER + C = (rD + rT(T/D) + ER/D + C/D)D

M2 = D + C + T + MMF =

(1 + C/D + T/D + MMF/D)D


The M2 money multiplier m2 is then given by:


m2 = M2/MB

m2 = (1 + C/D + T/D + MMF/D)

(rD + rT(T/D) + ER/D + C/D)