Chapter 9 A Two-Period Model: The

Consumption-Savings

Decision and Credit

Markets

Copyright © 2014 Pearson Education, Inc.

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Chapter 9 Topics

•  Consumer’s consumption/savings decision – responses of consumer to changes in income and interest rates.

•  Government budget deficits and the Ricardian Equivalence Theorem.

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Budget Constraints

The consumer’s current-period budget constraint:

tysc −=+

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Budget Constraints

The consumer’s future-period budget constraint:

srtyc )1(''' ++−=

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Simplify

Solve the future-period budget constraint for s:

rtycs

+

+−=1

'''

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Next,

•  Substitute in the current-period budget constraint obtaining lifetime budget constraint:

ty

rtycc −=

+

+−+1

'''

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Consumer’s Lifetime Budget Constraint

•  Substitute in the current-period budget constraint obtaining lifetime budget constraint:

r

tytyrcc

+

−+−=

++

1''

1'

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Consumer’s Lifetime Wealth

rtytywe

+

−+−=1

''

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Simplified Lifetime Budget Constraint

wercc =+

+1'

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Simplified Lifetime Budget Constraint: Slope-Intercept

)1()1(' rwecrc +++−=

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Figure 9.1 Consumer’s Lifetime Budget Constraint

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Figure 9.2 A Consumer’s Indifference Curves

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Optimization

•  Marginal condition that holds when the consumer is optimizing:

rMRS cc +=1',

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Figure 9.3 A Consumer Who Is a Lender

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Figure 9.4 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 9.5 The Effects of an Increase in Current Income for a Lender

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Observed Consumption-Smoothing 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 9.6 Percentage Deviations from Trend in Consumption of Durables and Real GDP

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Figure 9.7 Percentage Deviations from Trend in Consumption of Nondurables and Services and Real GDP

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An Increase in Future Income for the Consumer

•  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 9.8 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 9.9 Temporary Versus Permanent Increases in Income

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Figure 9.10 Stock Price Index and the Consumption of Nondurables and Services

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Figure 9.11 Scatter Plot: Consumption of Nondurables and Services vs. Stock Price Index

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Figure 9.12 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 9.13 An Increase in the Real Interest Rate for a Lender

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Figure 9.14 An Increase in the Real Interest Rate for a Borrower

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Effects of an Increase in the Real Interest Rate for a Lender

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Effects of an Increase in the Real Interest Rate for a Borrower

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Perfect Complements Example

•  With perfect complements, the ratio of future consumption to current consumption is constant.

•  The consumer’s budget constraint must hold.

acc ='

wercc =+

+1'

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Perfect Complements Example

•  With perfect complements we can solve explicitly for current and future consumption:

arrawec

arrwec

++

+=

++

+=

1)1('

1)1(

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Perfect Complements Example

⎥⎦

⎤⎢⎣

⎡++

−++−=

++

−++−=

artyrtyac

artyrtyc

1'')1)(('

1'')1)((

Substituting for lifetime wealth gives:

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Figure 9.15 Example with Perfect Complements Preferences

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Government Budget Constraints

The government’s current-period budget constraint:

BTG +=

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Government Budget Constraints

The government’s future-period budget constraint:

')1(' TBrG =++

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Government Budget Constraints

The government’s present-value budget constraint:

rTT

rGG

++=

++

1'

1'

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Credit Market Equilibrium Condition

•  Total private savings is equal to the quantity of government bonds issued in the current period.

BS p =

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Income-Expenditure Identity

•  Credit market equilibrium implies that the income-expenditure identity holds.

GCY +=

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Ricardian Equivalence

•  The Ricardian Equivalence Theorem is illustrated algebraically, numerically, and in two graphs.

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Ricardian Equivalence

•  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.

⎟⎠

⎞⎜⎝

⎛+

+=+

+r

GGNr

tt1'1

1'

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Ricardian Equivalence

•  Then, substitute in the consumer’s budget constraint – taxes do not matter in equilibrium for the consumer’s lifetime wealth, just the present value of government spending.

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Figure 9.16 Ricardian Equivalence with a Cut in Current Taxes for a Borrower

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Figure 9.17 Ricardian Equivalence and Credit Market Equilibrium

Figure 9.18 Perfect Substitutes, MRSl,C <1 + r.

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Figure 9.19 Perfect Substitutes, MRSl,C <1 + r.

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Figure 9.20 Competitive Equilibrium in the Example

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Figure 9.21 Total Government Surplus for the United States

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Figure 9.22 Total government Debt (federal, state, and local)

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