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Chapter 10
A Monetary Intertemporal Model:
Money, Prices, and Monetary Policy
Topics in Macroeconomics 2
May 2010
Chapter 10 Topics
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What is money?
Monetary Intertemporal Model
Real and nominal interest rates
Neutrality of money
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10-2
What is Money?
• Medium of exchange
– Single coincidence of wants instead of double
– Credit: not always possible
• Store of value
• Unit of account
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10-3
Monetary Aggregates
• M0 liabilities of central bank outside banking
system (currency + deposits at central bank)
• M1=M0+chequing accounts deposits,
travellers checks,…
• M2=M1+savings deposits, small-denomin.
Time deposits and retail money market
mutual funds
• M3=M2+large denomin time deposits
• Useful indicators of econ. activity
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10-4
Real and Nominal Interest Rates and
Fisher Relation
Inflation rate:
Fisher relation:
Approximate Fisher relation:
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10-5
Monetary Intertemporal Model
• Type of cash-in-advance model.
• Representative consumer, representative
firm, and government.
• Consumers and firms require cash on hand to
purchase goods, or can expend resources to
use the services of banks to carry out
transactions.
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10-6
Representative Consumer
- Wakes up with
- Mc- units of cash/money (in ₤)
- Bc- units of bonds (in ₤) (which pay interest R-)
- Goes to Bank Machine
- Pays taxes
T (in real terms, i.e. in number of cons. goods)
PT (in nominal terms, i.e. P price of cons. goods)
- Buys Bonds Bc (in ₤) which will pay interest R next period
- Draws cash WDc (in ₤) where
WDc = Mc- + Bc- (1+R-) – PT – Bc
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10-7
Consumer (cont’d)
- Income during the period:
- Consumer earns wage income and dividend income, Y.
- He/she cannot access all of it at bank machine because
firm pays later during the period.
- Banking Services (e.g. debit/credit cards) :
- He/she knows in advance that he/she can access a real
amount X of his income using banking services.
- Therefore, PX is the nominal quantity of income that can
be spent on consumption during the period.
- Let H(X) be the real resource cost to use the transactions
services of the bank, paid at the end of the period.
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10-8
Consumer (cont’d)
Consumer’s cash-in-advance constraint, CIAC:
PC ≤ WDc + PX
PC ≤ Mc - + Bc- (1+R-) – PT – Bc + PX
Nominal consumption cannot exceed quantity of cash on
hand during the period.
Assuming R>0, no unnecessary cash held. Therefore,
PC = WDc + PX
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10-9
Consumer (cont’d)
Let H(X) be the real resource cost to use the
transactions services of the bank
H(X)
- increasing: more debit card
expenses => higher total cost
- convex: more debit card
expenses => higher aver. cost
increasing mg cost
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10-10
Consumer (cont’d)
Money balances held by the consumer at the
bank at the end of the day:
Mc = Mc - + Bc- (1+R-) + PY – PC – PT – Bc – PH(X)
Note: Use CIAC to substitute for PC
Mc = PY – PX – PH(X)
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10-11
Consumer: Choice of X
Marginal benefit and marginal cost of using more
banking services:
MBX = P(1+R)
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MCX = P(1+HX)
10-12
Consumer: Choice of X
Marginal benefit and marginal cost of using more
banking services:
MBX = P(1+R)
Hence,
MCX = P(1+HX)
HX = R
The marginal resource cost of one more unit of
banking services equals real interest rate.
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10-13
Consumer’s Optimal Choice of Banking
Services, X
Effect of an Increase in R on the
Consumer’s Optimal Choice of X
Effect of an Increase in R on the
Consumer’s Optimal Choice of X
The optimal choice of X is an increasing
function of the nominal interest rate, R:
X=J(R)
Representative Firm
- Begins every period with zero money balances
- Must buy investment goods, I, with money
- Conducts banking transactions at the
beginning of the period, making a withdrawal
of
WDf = Bf- (1+R-) – Bf
Notes: Bf<0 possible, no taxes
- Can spend PXf of PY to buy inv. goods using
banking services
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10-17
Firm (cont’d)
Firm’s cash-in-advance constraint, CIAC:
PI ≤ WDf + PXf
PI ≤ Bf- (1+R-) – Bf + PXf
Nominal investment cannot exceed quantity of cash on hand
during the period.
Assuming R>0, no unnecessary cash held. Therefore,
PI = WDf + PXf
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10-18
Firm (cont’d)
Total income in the form of wage and dividend
payments turned over to consumer through a
direct deposit is:
A = PY – PI – PH(Xf) + Bf- (1+R-) – Bf
Note: Use CIAC to substitute for PI
A = PY – PH(Xf) – PXf
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Note: missing P’s in book!!!
10-19
Firm: Choice of Xf
Marginal benefit and marginal cost (firm max.
money in cons. bank account):
MBXf = P(1+R)
Hence,
Consumer+Firm,
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MCX = P(1+HXf)
HXf = R
Xf = X
10-20
Government
Assume that single institution, government, does both:
- Fiscal policy as before (G and T)
- Monetary policy (issue money)
Government’s Budget constrain in the current period:
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10-21
Markets Clear
-
Current goods market: as in Ch. 9
Current labour narket: as in Ch. 9
Money market: new
Walras’ law => credit mkt clears
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10-22
Money Market
Income-Expenditure identity:
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10-23
Money Market
Income-Expenditure identity:
Substitute using CIAC
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10-24
Money Market
Income-Expenditure identity:
Substitute using CIAC
Using credit market clearing previous and current
period and money market clearing previous period…
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10-25
Money Market
In equilibrium, then:
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10-26
Money Market
In equilibrium, then:
Rewrite given the choice of banking services by
the consumer and the firm:
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10-27
Money Market
In equilibrium, then:
Rewrite given the choice of banking services by
the consumer and the firm:
For simplicity, define L(Y,R), incr.in Y, decr.in R:
=> money supply = money demand
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10-28
Nominal money demand function
Nominal money demand function:
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10-29
Nominal Money Demand and Fisher
Relation
Nominal money demand using the Fisher
relation:
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10-30
Nominal money and assuming the
inflation rate equals zero
Nominal money demand assuming the inflation
rate equals zero (harmless assumption for our
purposes here):
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10-31
The Nominal Money Demand Curve in the
Monetary Intertemporal Model
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10-32
The Effect of an Increase in Current Real Income
(decrease in Real IR) on the Nominal Money
Demand Curve
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10-33
The Current Money Market in the Monetary
Intertemporal Model
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10-34
The Complete Monetary
Intertemporal Model
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10-35
Monetary Policy
• Neutrality of Money: a level increase in Ms
• Shift in money demand: e.g. an increase H(X)
• Shift in output demand: e.g. increase in z’
• Shift in output supply: e.g. increase in z
• Money supply targeting.
• Nominal interest rate targeting.
• The Taylor rule.
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10-37
A Level Increase in the Money Supply in the
Current Period
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10-38
The Neutrality of Money
• In the monetary intertemporal model, a level
increase in the money supply increases the
price level and the nominal wage in
proportion to the money supply increase, but
has no effect on any real macroeconomic
variable.
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10-39
The Effects of a Level Increase in M—The
Neutrality of Money
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10-40
Increase in Total Factor Productivity
• If z increases, this increases money demand (Y
increases and r falls), which causes the price
level to fall.
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10-41
Short-Run Analysis of a Temporary Decrease in
Total Factor Productivity
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10-42
An Increase in the Cost of Banking
Services
The Effect of an Increase in the Cost of
Banking Services on the Choice of Banking
Services
Generates
A Shift in the Demand for Money
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10-45
A Shift in the Demand for Money
The price level falls unless the monetary authority
increases the money supply by the right amount.
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10-46
A Shift in the Output Demand
Curve
A Shift in the Output Supply Curve
Monetary Policy Rules
• Money supply targeting.
• Nominal interest rate targeting.
• The Taylor rule.