Intermediate macroeconomics chapt18

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, interest-bearing
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