Chapter 18: Money Supply
& Money Demand
Federal Reserve System, FED
The central bank of the U.S.
Independent decision making unit with regional
banks
In charge of money supply management and
economic stabilization
Money Supply
M=C+D
C = Currency: coins & bills (25%)
D = Demand Deposits: checking account
deposits (75%)
Money Supply Line
The quantity of money in circulation is controlled
by the central bank in real value
Interest Rate (%)
(M/P)s
10
5
80
Quantity of Money
Fractional Banking System
Banks are required by law to hold a percentage of all
deposits with the FED to be able to return the deposits:
– R = reserves: deposits
– RR = required reserves: reserves held by the FED
– rr = reserve-deposit ratio: percentage determined by the FED
(rr = R/D)
– ER = excess reserves: reserves used by banks to lend or
investment
Fractional Banking System
R = RR + ER
RR = rr R
ER = (1 – rr)R
Banks’ lending and investing ER will create money
through a multiplier effect
A Model of Money Supply
The monetary base (B) is money held by the
public in currency and by banks as reserves R
B=C+R
The currency-deposit ratio (cr) is the amount of
currency people hold as a fraction of their demand
deposits
cr = C / D
A Model of Money Supply
Divide M = C + D by B = C + R:
M/B = (C + D) / (C + R)
Divide the numerator and denominator by D:
M/B = (C/D + 1) / (C/D + R/D)
M/B = (cr + 1) / (cr + rr)
M = [(cr + 1) / (cr + rr)]B = m  B
Define money multiplier m = (cr + 1) / (cr + rr),so far any
$1 increase in the monetary base, money supply
increases by $m.
A Model of Money Supply
Example: B = $500 billion, cr = 0.6 and rr = 0.1:
m=(0.6 + 1) / (0.6 +0.1) = 2.3
M = 2.3(500) = $1,150 billion
Change in Money Supply
The money supply is proportional to the monetary base.
So, an increase in B increases M m-fold.
The lower the reserve-deposit ratio, the more loans banks
make and the higher is the money multiplier
The lower the currency deposit ratio, the fewer dollars of
the monetary base the public holds as currency and the
lower is the money multiplier
Tools of Monetary Policy
Reserve-deposit ratio: ratio of cash reserves to
deposits that banks are required to maintain
By lowering the ratio, banks will have more
reserves to lend and invest, increasing the money
supply
Tools of Monetary Policy
Discount rate: rate of interest the FED charges on
loans to banks
By lowering the rate, banks encourage borrowing
from the FED and lending to the public, increasing
the money supply
Tools of Monetary Policy
Open Market Operations: FED’s purchases and
sales of government bonds
By purchasing bonds and paying the sellers, the
FED increases the money supply
Expansionary Monetary Policy
Increase the money supply by any one or
combination of the above tools
Reduce the interest rate to encourage investment
Increase employment & income
Money Demand
The amount of money demanded for transaction
and speculative purposes depends: personal
income and interest rate
At any level of personal income, quantity
demanded of money is a negative function of
interest rate; (M/P)d = L(i, Y)
Money Demand Line
M/P = L(Y, i)
Y = income
i = interest rate
Interest Rate (%)
10
5
(M/P)d
80
100
Quantity of Money
Money Market Equilibrium
Interest Rate (%)
(M/P)s
5
(M/P)d
80
Quantity of Money
Expansionary Monetary Policy
Interest Rate (%)
(M1/P)s
(M2/P)s
5
4
(M/P)d
80 85
Quantity of Money
Portfolio Theory of Money Demand
(M/P)d = L(rs, rb, πe, W)
M/P = real money balances
rs = expected real rate of return on stocks
rb = expected real rate of return on bonds
πe = expected rate of inflation
W = real wealth
(M/P)d is positively related to W and negatively
affected by rs, rb, πe
The Baumol-Tobin Model
Define
– Y = transactionary money an individual holds in bank
– N = annual number of trips to bank an individual
makes to withdraw money
– F = cost of a trip to the bank
– i = nominal interest rate
Optimal Conditions
Total cost of money withdrawal = Foregone
interest + Cost of trips
TC = iY/2N + FN
The annual number of trips that minimizes the
total cost of bank trips is
N* = (iY/2F)1/2
Average transactionary money holding is
MH = Y /2N* = (YF/2i)1/2
Optimal Conditions
Cost
Total cost of bank withdrawal
Cost of bank trips = FN
Foregone interest = iY/2N
N*
Number of trip to bank, N
Speculative Demand for Money
Money individuals hold for investment in the
financial market
Near money consists of non-monetary, interestbearing assets such as stocks and bonds
The Federal Funds Rate
The short-term interest rate at which banks make loans to
each other
The FED uses this rate as the basis for its interest rate
policy
Taylor’s rule for the determination of the nominal federal
funds rate:
Inflation rate + 2 + 0.5(Inflation rate + 2) – 0.5(GDP gap)
Actual vs. Taylor’s Rule