Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 10 A Monetary Intertemporal Model: Money, Prices, and Monetary Policy.

Chapter 10

A Monetary Intertemporal Model: Money, Prices, and Monetary Policy

Chapter 10 Topics

• What is money?

• Monetary Intertemporal Model

• Real and nominal interest rates

• Neutrality of money

• Monetary policy: targets and rules

What is Money?

• Medium of exchange

• Store of value

• Unit of account

Table 10.1 Monetary Aggregates, July 2006 (in $Billions)

Equation 10.1

Inflation rate:

Equation 10.2

Fisher relation:

Equation 10.3

Approximate Fisher relation:

Figure 10.1 Real and Nominal Interest Rates, 1934-2006

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.

Timing of Events – Morning Session

• In the morning, consumers have money and bond balances, M-

c and B-c , carried forward

from last period.

• Pay taxes T in real terms.

• Buy bonds Bc.

• Withdraw the remaining money, WDc.

Equation 10.4

Consumer’s currency withdrawal at the beginning of the day:

Timing of Events – Afternoon Session

• In the afternoon, the bank ATM machine is closed. No way to withdraw money any more. This makes the services of bank the only option.

• Receive wage income and dividend income.• Choose a real amount X of the total real income to pay for

consumption purchase. So PX is the nominal quantity of income spent on consumption via services of bank.

• Services of bank are costly, H(X) in real terms. • Total expenditure of consumption purchase is a sum of PX and

WDc. That is, PC = PX + WDc .

Equation 10.5

Consumer’s cash-in-advance constraint:

Timing of Events – Evening Session

• In the evening, carry forward what remains after all purchases are made and all income is received during the day.

Equation 10.6

Money balances held by the consumer at the bank at the end of the day:

PY: income and dividend income.

Figure 10.2 The Cost of Banking Services

Equation 10.7

The marginal benefit for the consumer of using more banking services:

Equation 10.8

Consumer’s end-of-day money holdings:

Equation 10.9

Marginal cost for the consumer of using more banking services:

Equation 10.10

Determine the optimal choice of X:

Equation 10.11

Optimal choice of X, simplified:

Figure 10.3 The Consumer’s Optimal Choice of Banking Services

Figure 10.4 The Effect of an Increase in R on the Consumer’s Optimal Choice of Banking Services

Equation 10.12

The optimal choice of X is an increasing function of the nominal interest rate, R:

Representative Firm - Morning

• Begin with zero money balance (transfer to workers as wage and dividend income last period).

• Buy bond in the morning session.

• Withdraw the remaining money to pay for investment purchases.

Equation 10.13

Firm’s currency withdrawal at the beginning of the day:

Firm’s Behavior - Afternoon

• Use an amount Xf of the total real revenue Y to pay for investment purchase via services of bank, which incurs real costs H (Xf).

• The total nominal purchase of investment goods, PI, is a sum of WDf + PXf .

Equation 10.14

Firms’ cash-in-advance constraint:

Firm’s Behavior - Evening

• Transfer what remains after all purchases are made.

Equation 10.15

Direct deposit made by the firm to the consumer’s bank:

Equation 10.16

Simplified direct deposit to the consumer:

A = PY – PXf – H (Xf )

Choice of Banking Services

• Like what happens to consumers, the optimal amount of banking service is determined by marginal costs = marginal benefits.

• The firms and consumers choose the same quantity of banking service.

Government

• Responsible for fiscal and monetary policy.

• Purchase G goods.

• Pay nominal interest and principal on government bond outstanding from last period.

• Finance G and payments by taxes, issuing new government bonds, and printing money.

Equation 10.17

Government budget constraint:

Competitive Equilibrium

• Consider only three markets: for current goods, for current labor, and money market.

• Focus on money market equilibrium.

Equation 10.18

Income-Expenditure identity:

Equation 10.19

Substitute using cash-in-advance constraints and government budget constraint:

Equation 10.20

Credit market clears in previous period:

Equation 10.21

Current credit market clears:

Equation 10.22

Money market clears in previous period:

Equation 10.23

In equilibrium, then:

Equation 10.24

Rewrite given the choice of banking services by the consumer and the firm:

Equation 10.25

“Money demand” relationship:

Equation 10.26

Nominal money demand function:

Equation 10.27

Nominal money demand using the Fisher relation:

Equation 10.28

Nominal money demand assuming the inflation rate equals zero (harmless assumption for our purposes here):

Equation 10.29

Money supply equals money demand:

Figure 10.5 The Nominal Money Demand Curve in the Monetary Intertemporal Model

Figure 10.6 The Effect of an Increase in Current Real Income on the Nominal Money Demand Curve

Figure 10.7 The Current Money Market in the Monetary Intertemporal Model

Figure 10.8 The Complete Monetary Intertemporal Model

Figure 10.9 A Level Increase in the Money Supply in the Current Period

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.

Figure 10.10 The Effects of a Level Increase in M—The Neutrality of Money

Increase in Total Factor Productivity

• If z increases, this increases money demand (Y increases and r falls), which causes the price level to fall.

Figure 10.11 Short-Run Analysis of a Temporary Decrease in Total Factor Productivity

Figure 10.14 An Increase in the Cost of Banking Services

Figure 10.15 The Effect of an Increase in the Cost of Banking Services on the Choice of Banking Services

Figure 10.16 A Shift in the Demand for Money

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 10 A Monetary Intertemporal Model: Money, Prices, and Monetary Policy.

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monetary policy slide

cost of banking services

total real income

remaining money

money balances

day money holdings

services of banks

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