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Chapter 18: Money Supply & Money DemandChapter 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
Quantity of Money
Interest Rate (%)
(M/P)s
80
5
10
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 + ERRR = 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 + RThe 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) = 2.3M = 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
Quantity of Money
Interest Rate (%)
(M/P)d
10
5
10080
M/P = L(Y, i)Y = incomei = interest rate
Money Market Equilibrium
Quantity of Money
Interest Rate (%)
(M/P)d
5
80
(M/P)s
Expansionary Monetary Policy
Quantity of Money
Interest Rate (%)
(M/P)d
5
80
(M1/P)s (M2/P)s
4
85
Portfolio Theory of Money Demand
(M/P)d = L(rs, rb, πe, W)M/P = real money balancesrs = expected real rate of return on stocks
rb = expected real rate of return on bonds
πe = expected rate of inflationW = 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 + FNThe annual number of trips that minimizes the total cost of bank trips is
N* = (iY/2F)1/2
Average transactionary money holding isMH = Y /2N* = (YF/2i)1/2
Optimal Conditions
Cost
Number of trip to bank, N
Foregone interest = iY/2N
Cost of bank trips = FN
Total cost of bank withdrawal
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 RateThe 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