9
A Chapter Real
Intertemporal
Model with
Investment
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Chapter 9 Topics
Construct a real intertemporal model that will serve as a
basis for studying money and business cycles in
Chapters 10-12.
Understand the investment decision of the firm.
Show how macroeconomic shocks affect the economy.
Focus on the implications of future expectations for
current macroeconomic performance, and the
difference between temporary and permanent shocks.
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Real Intertemporal Model
Current and future periods.
Representative Consumer
consumption/savings decision
Representative Firm hires labor and invests in
current period, hires labor in future
Government spends and taxes in present and
future, and borrows on the credit market.
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Equation 9.1
Consumers current-period budget constraint:
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Equation 9.2
Consumers future-period budget constraint:
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Equation 9.3
Consumers lifetime budget constraint:
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Equation 9.4
Consumers current-period marginal condition:
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Equation 9.5
Consumers future-period marginal condition:
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Equation 9.6
Consumers intertemporal marginal condition:
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Consumers Current Labor
Supply Behavior
Current labor supplied increases with the real
wage (substitution effects are assumed to
dominate income effects).
Labor supply increases with an increase in the
real interest rate, through an intertemporal
substitution effect.
An increase in lifetime wealth (e.g. taxes fall)
reduces labor supply.
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Figure 9.1 The Representative
Consumers Current Labor Supply
Curve
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Figure 9.2 An Increase in the Real
Interest Rate Shifts the Current Labor
Supply Curve to the Right
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Figure 9.3 Effects of an Increase
in Lifetime Wealth
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Equation 9.7
Firms current-period production function:
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Equation 9.8
Firms future-period production function:
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Equation 9.9
Evolution of the firms capital stock:
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Equation 9.10
Firms current-period profits:
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Equation 9.11
Firms future-period profits:
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Equation 9.12
The firm maximizes the present value of profits,
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The Firms Labor Demand
As in Chapter 4, the firms labor demand schedule
is the marginal product of labor for the firm,
which is downward sloping.
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Figure 9.4 The Demand Curve for Current
Labor Is the Representative Firms Marginal
Product of Labor Schedule
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Figure 9.5 The Current Demand Curve for Labor
Shifts Due to Changes in Current Total Factor
Productivity z and in the Current Capital Stock K
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The Representative Firms
Investment Decision
The firm invests to the point where the marginal
benefit from investment equals the marginal
cost.
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Equation 9.13
The marginal cost of investment is 1, as the firm
gives up one unit of current profits for each unit
it invests, so:
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Equation 9.14
The marginal benefit of investment is the marginal
product of future capital plus the quantity of
capital that will be left in the future after
depreciation, all discounted back to the present:
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9-25
Equation 9.15
The firms optimal investment rule, obtained by
equating the marginal benefit and marginal cost
of investment:
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Equation 9.16
Simplified optimal investment rule:
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Figure 9.6 Optimal Investment
Schedule for the Representative Firm
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Figure 9.7 The Optimal Investment Schedule Shifts to
the Right if Current Capital Decreases or Future Total
Factor Productivity Is Expected to Increase
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Table 9.1 Data for Christines
Orchard
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Equation 9.17
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Figure 9.8 The Relative Price
of Housing
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Figure 9.9 Residential Construction as
a Percentage of GDP
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Equation 9.18
The governments present-value budget constraint:
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Figure 9.10 Determination of Equilibrium
in the Labor Market Given the Real
Interest Rate r
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Figure 9.11 Construction of
the Output Supply Curve
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Figure 9.12 An Increase in Current or
Future Government Spending Shifts
the Ys Curve
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Figure 9.13 An Increase in Current
Total Factor Productivity Shifts the Ys
Curve
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Equation 9.19
Total demand for output equals demand for
consumption goods plus demand for investment
goods, plus demand for goods from government:
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Equation 9.20
Determining the total effect on the change in
demand of an exogenous change in expenditure
on goods.
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Equation 9.21
The multiplier.
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Figure 9.14 The Output
Demand Curve
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Figure 9.15 A Shift in the
Output Demand Curve
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Figure 9.16 The Complete
Real Intertemporal Model
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Experiments Using the Real
Intertemporal Model
G increases temporarily.
G increases permanently.
K decreases.
z increases.
z increases.
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Temporary Increase in
Government Purchases
Output increases, real interest rate increases, real
wage falls, consumption and investment
decrease, employment rises.
Government spending crowds out both
consumption and investment.
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Figure 9.17 A Temporary Increase in
Government Purchases
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Permanent Increase in
Government Purchases
Output increases by the amount of the increase
in government spending.
No change in the real interest rate, investment
and consumption unchanged, real wage falls,
employment rises.
No crowding out of C and I, but leisure falls for
the consumer.
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Figure 9.19 Natural Log of
Real Investment, 19292005
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Figure 9.18 A Permanent Increase in
Government Expenditures
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A Decrease in the Current
Capital Stock
This could arise due to a war or natural disaster.
Output may rise or fall, depending on how large
the output demand effect is relative to the output
supply effect.
The real interest rate rises, the real wage falls,
employment may rise or fall.
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Figure 9.20 The Equilibrium Effects of a
Decrease in the Current Capital Stock
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Current Total Factor
Productivity Increases
Real interest rate falls, consumption and
investment rise, employment rises, real wage
rises.
Productivity shocks are a potential explanation
for business cycles see Chapter 11.
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Figure 9.21 The Equilibrium Effects of an
Increase in Current Total Factor
Productivity
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Total Factor Productivity
Expected to Increase in Future
Output demand curve shifts right.
Real interest rate rises, investment increases,
consumption may rise or fall, employment rises,
real wage falls, output rises.
Important in explaining investment boom in the
1990s.
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Figure 9.22 The Equilibrium Effects of
an Increase in Future Total Factor
Productivity
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Figure 9.23 Percentage Deviations
From Trend in GDP and Investment,
19902006
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Figure 9.24 Investment as a
Percentage of GDP, 19902006
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Figure 9.25 S and P 500
Stock Price Index, 19902005
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