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