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Transcript of Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 10 A Monetary Intertemporal...
![Page 1: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 10 A Monetary Intertemporal Model: Money, Prices, and Monetary Policy.](https://reader036.fdocuments.us/reader036/viewer/2022062312/551c0304550346a84f8b4d08/html5/thumbnails/1.jpg)
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 10
A Monetary Intertemporal Model: Money, Prices, and Monetary Policy
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Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-2
Chapter 10 Topics
• What is money?
• Monetary Intertemporal Model
• Real and nominal interest rates
• Neutrality of money
• Monetary policy: targets and rules
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What is Money?
• Medium of exchange
• Store of value
• Unit of account
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Table 10.1 Monetary Aggregates, July 2006 (in $Billions)
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Equation 10.1
Inflation rate:
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Equation 10.2
Fisher relation:
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Equation 10.3
Approximate Fisher relation:
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Figure 10.1 Real and Nominal Interest Rates, 1934-2006
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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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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.
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Equation 10.4
Consumer’s currency withdrawal at the beginning of the day:
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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 .
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Equation 10.5
Consumer’s cash-in-advance constraint:
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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.
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Equation 10.6
Money balances held by the consumer at the bank at the end of the day:
PY: income and dividend income.
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Figure 10.2 The Cost of Banking Services
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Equation 10.7
The marginal benefit for the consumer of using more banking services:
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Equation 10.8
Consumer’s end-of-day money holdings:
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Equation 10.9
Marginal cost for the consumer of using more banking services:
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Equation 10.10
Determine the optimal choice of X:
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Equation 10.11
Optimal choice of X, simplified:
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Figure 10.3 The Consumer’s Optimal Choice of Banking Services
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Figure 10.4 The Effect of an Increase in R on the Consumer’s Optimal Choice of Banking Services
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Equation 10.12
The optimal choice of X is an increasing function of the nominal interest rate, R:
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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.
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Equation 10.13
Firm’s currency withdrawal at the beginning of the day:
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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 .
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Equation 10.14
Firms’ cash-in-advance constraint:
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Firm’s Behavior - Evening
• Transfer what remains after all purchases are made.
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Equation 10.15
Direct deposit made by the firm to the consumer’s bank:
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Equation 10.16
Simplified direct deposit to the consumer:
A = PY – PXf – H (Xf )
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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.
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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.
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Equation 10.17
Government budget constraint:
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Competitive Equilibrium
• Consider only three markets: for current goods, for current labor, and money market.
• Focus on money market equilibrium.
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Equation 10.18
Income-Expenditure identity:
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Equation 10.19
Substitute using cash-in-advance constraints and government budget constraint:
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Equation 10.20
Credit market clears in previous period:
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Equation 10.21
Current credit market clears:
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Equation 10.22
Money market clears in previous period:
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Equation 10.23
In equilibrium, then:
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Equation 10.24
Rewrite given the choice of banking services by the consumer and the firm:
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Equation 10.25
“Money demand” relationship:
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Equation 10.26
Nominal money demand function:
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Equation 10.27
Nominal money demand using the Fisher relation:
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Equation 10.28
Nominal money demand assuming the inflation rate equals zero (harmless assumption for our purposes here):
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Equation 10.29
Money supply equals money demand:
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Figure 10.5 The Nominal Money Demand Curve in the Monetary Intertemporal Model
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Figure 10.6 The Effect of an Increase in Current Real Income on the Nominal Money Demand Curve
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Figure 10.7 The Current Money Market in the Monetary Intertemporal Model
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Figure 10.8 The Complete Monetary Intertemporal Model
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Figure 10.9 A Level Increase in the Money Supply in the Current Period
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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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Figure 10.10 The Effects of a Level Increase in M—The Neutrality of Money
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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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Figure 10.11 Short-Run Analysis of a Temporary Decrease in Total Factor Productivity
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Figure 10.14 An Increase in the Cost of Banking Services
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Figure 10.15 The Effect of an Increase in the Cost of Banking Services on the Choice of Banking Services
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Figure 10.16 A Shift in the Demand for Money