. 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)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.