Chapter 8

Report
Chapter 8
A Two-Period
Model: The
Consumption–
Savings Decision
and Credit Markets
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Chapter 8 Topics
• Consumer’s consumption/savings decision –
responses of consumer to changes in income and
interest rates.
• Government budget deficits and the Ricardian
Equivalence Theorem.
• Social Security.
• Credit market imperfections.
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Equation 8.1
The consumer’s current-period budget constraint:
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Equation 8.2
The consumer’s future-period budget constraint:
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Equation 8.3
Solve the future-period budget constraint for s:
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Equation 8.4
Substitute in the current-period budget constraint
obtaining lifetime budget constraint:
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Equation 8.5
Consumer’s lifetime wealth:
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Equation 8.6
Simplified lifetime budget constraint for the
consumer:
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Equation 8.7
Lifetime budget constraint in slope-intercept form:
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Figure 8.1 Consumer’s Lifetime
Budget Constraint
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Figure 8.2 A Consumer’s
Indifference Curves
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Table 8.1 Sara’s Desire for
Consumption Smoothing
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Equation 8.8
Marginal condition that holds when the consumer
is optimizing:
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Figure 8.3 A Consumer Who Is a
Lender
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Figure 8.4 A Consumer Who Is a
Borrower
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An Increase in Current Income
for the Consumer
• Current and future consumption increase.
• Saving increases.
• The consumer acts to smooth consumption over
time.
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Figure 8.5 The Effects of an Increase
in Current Income for a Lender
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Equation 8.9
Decomposing the change in saving for the
consumer:
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Observed ConsumptionSmoothing Behavior
• Aggregate consumption of non-durables and
services is smooth relative to aggregate income,
but the consumption of durables is more volatile
than income.
• This is because durables consumption is
economically more like investment than
consumption.
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Figure 8.6 Percentage Deviations
from Trend in GDP and Consumption,
1947–2006
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An Increase in Future Income
for the Consumer
• Current and future consumption increase.
• Saving decreases.
• Again, these results are explained by the
consumer’s motive to smooth consumption over
time.
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Figure 8.7 An Increase in Future
Income
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Temporary and Permanent
Increases in Income
• As a permanent increase in income will have a
larger effect on lifetime wealth than a temporary
increase, there will be a larger effect on current
consumption.
• A consumer will tend to save most of a purely
temporary income increase.
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Figure 8.8 Temporary Versus Permanent
Increases in Income
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Figure 8.9 Stock Prices and
Consumption of Nondurables and
Services, 1985–2006
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Figure 8.10 Scatter Plot of Percentage Deviations from
Trend in Consumption of Nondurables and Services
Versus Percentage Deviations from Trend in a Stock
Price Index
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Figure 8.11 An Increase in the
Real Interest Rate
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An Increase in the Market Real
Interest Rate
An increase in the market real interest rate
decreases the relative price of future
consumption goods in terms of current
consumption goods – this has income and
substitution effects for the consumer.
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Figure 8.12 An Increase in the
Real Interest Rate for a Lender
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Figure 8.13 An Increase in the
Real Interest Rate for a Borrower
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Table 8.2 Effects of an Increase in
the Real Interest Rate for a Lender
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Table 8.3 Effects of an Increase in
the Real Interest Rate for a Borrower
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Figure 8.14 Example with Perfect
Complements Preferences
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Equation 8.10
With perfect complements, the ratio of future
consumption to current consumption is constant.
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Equation 8.11
The consumer’s lifetime budget constraint must
also hold.
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Equation 8.12
The consumer’s lifetime wealth:
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Equation 8.13
With perfect complements we can solve explicitly
for current consumption:
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Equation 8.14
We can also solve explicitly for future
consumption:
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Equation 8.15
Substituting for lifetime wealth gives:
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Equation 8.16
After substituting for lifetime wealth:
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Equation 8.17
The government’s current-period budget
constraint:
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Equation 8.18
The government’s future-period budget constraint:
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Equation 8.19
The government’s present-value budget
constraint:
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Equation 8.20: Credit Market
Equilibrium Condition
Total private savings is equal to the quantity of
government bonds issued in the current period.
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Equation 8.21
Credit market equilibrium implies that the incomeexpenditure identity holds.
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Ricardian Equivalence
The Ricardian Equivalence Theorem is illustrated
algebraically, numerically, and in two graphs.
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Equation 8.22
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Equation 8.23
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Equation 8.24
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Equation 8.25
Key equation: The consumer’s lifetime tax burden
is equal to the consumer’s share of the present
value of government spending – the timing of
taxation does not matter for the consumer.
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Equation 8.26
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Figure 8.15 Ricardian Equivalence
with a Cut in Current Taxes for a
Borrower
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Figure 8.16 Ricardian Equivalence
and Credit Market Equilibrium
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Pay-as-you-go Social Security
• Taxes on the working population pay for social
security transfers to the retired each period.
• Suppose two generations alive at each date,
young and old.
• The young pay social security taxes t, the old
receive social security benefits b.
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Equation 8.27
The population grows according to the following
equation. Each period, there are N’ young and N
old alive.
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Equation 8.28
Total social security benefits must equal total taxes
on the young.
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Equation 8.29
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Figure 8.17 Pay-As-You-Go Social
Security for Consumers Who Are Old in
Period T
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Figure 8.18 Pay-As-You-Go Social
Security for Consumers Born in Period
T and Later
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Pay-as-you-go Social Security
• Pay-as-you-go is beneficial only if the
population growth rate exceeds the real interest
rate.
• The interpretation is that the population growth
rate is the implied rate of return for an individual
from the social security system, so social
security is only worthwhile if the return exceeds
what could be obtained in private credit markets.
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Fully Funded Social Security
Essentially a mandated savings program where
assets are acquired by the young, with these
assets sold in retirement.
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Figure 8.19 Fully Funded Social
Security When Mandated Retirement
Saving Is Binding
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Credit Market Imperfections
• Assume that lenders can lend at a lower interest
rate than the one faced by borrowers.
• The government borrows and lends at the
interest rate that lenders face.
• This implies that Ricardian equivalence does not
hold, in general.
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Equation 8.30
Lifetime budget constraint for a lender:
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Equation 8.31
Lifetime budget constraint for a borrower:
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Figure 8.20 A Consumer Facing
Different Lending and Borrowing Rates
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Figure 8.21 Effects of a Tax Cut for a
Consumer with Different Borrowing and
Lending Rates
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Effects of a Tax Cut with Credit
Market Imperfections
• Suppose a consumer initially is credit
constrained – that is he or she saves zero.
• For such a consumer, the entire tax cut will be
spent on current consumption.
• This is very different from the case with no
credit market imperfections, where the consumer
will save the entire tax cut to pay higher future
taxes.
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Figure 8.22 Real Consumption of
Durables, 1991–1993
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Figure 8.23 Real Consumption of
Nondurables, 1991–1993
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Figure 8.24 Real Consumption of
Services, 1991–1993
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