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CHAPTER 16 Consumption
Topic 13:
Consumption(chapter 16) (revised 11/19/03)
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CHAPTER 16 Consumption slide 1
Chapter overview
This chapter surveys the most prominent workon consumption:
John Maynard Keynes: consumption andcurrent income
Irving Fisher and Intertemporal Choice Franco Modigliani: the Life-Cycle Hypothesis
Milton Friedman: the Permanent IncomeHypothesis
Robert Hall: the Random-Walk Hypothesis
David Laibson: the pull of instant gratification
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CHAPTER 16 Consumption slide 2
Keyness Conjectures
1. 2.
whereAPC
= average propensity to consume= C/Y
3.
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CHAPTER 16 Consumption slide 3
The Keynesian Consumption Function
A consumption function with theproperties Keynes conjectured:C
Y
1
c
C C cY
C
c= MPC
= slope of theconsumptionfunction
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CHAPTER 16 Consumption slide 4
The Keynesian Consumption Function
C
Y
C C cY
slope =APC
As income rises, the APC falls (consumerssave a bigger fraction of their income).
_____________APC
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CHAPTER 16 Consumption slide 5
Early Empirical Successes:Results from Early Studies
Households with higher incomes:
MPC> 0
MPC< 1
APC as YVery strong correlation between income and
consumption
income seemed to be the maindeterminant of consumption
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CHAPTER 16 Consumption slide 6
Problems for theKeynesian Consumption Function
Based on the Keynesian consumption function,economists predicted that__________
_________________________________.
This prediction did not come true:As incomes grew, the APC did not fall,
and C grew just as fast.
Simon Kuznets showed that C/Y wasvery stable in long time series data.
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CHAPTER 16 Consumption slide 7
The Consumption Puzzle
C
Y
Consumption functionfrom long time seriesdata (constantAPC)
Consumption functionfrom cross-sectionalhousehold data
(fallingAPC)
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CHAPTER 16 Consumption slide 8
Irving Fisher and Intertemporal Choice
The basis for much subsequent work onconsumption.
Assumes consumer is forward-looking andchooses consumption for the present andfuture to maximize lifetime satisfaction.
Consumers choices are subject to an___________________________,
a measure of the total resources availablefor present and future consumption
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CHAPTER 16 Consumption slide 9
The basic two-period model
Period 1: the present
Period 2: the future
Notation
Y1 is income in period 1Y2 is income in period 2
C1 is consumption in period 1
C2
is consumption in period 2
S= Y1-C1 is ______________
(S< 0 if the consumer borrows in period 1)
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CHAPTER 16 Consumption slide 10
Deriving theintertemporal budget constraint
Period 2 budget constraint:
2 2 (1 )C Y r S
_______________
Rearrange to put C terms on one sideand Y terms on the other:
1 2 2 1(1 ) (1 )r C C Y r Y
Finally, divide through by (1+r):
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CHAPTER 16 Consumption slide 11
The intertemporal budget constraint
2 21 1
1 1
C YC Y
r r
present value of
______________
present value of
_____________
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CHAPTER 16 Consumption slide 12
The budgetconstraintshows all
combinationsofC1 and C2that justexhaust the
consumersresources.
The intertemporal budget constraint
C1
C2
_____________
__________
Y1
Y2_______
_____
Consump =
income inboth periods
2 21 1
1 1C YC Yr r
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CHAPTER 16 Consumption slide 13
The slope ofthe budgetline equals
_________)
The intertemporal budget constraint
C1
C2
Y1
Y2
2 21 1
1 1C YC Yr r
1(1+r)
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CHAPTER 16 Consumption slide 14
An______________showsall combinationsofC1 and C2 that
make theconsumer__________________________.
Consumer preferences
C1
C2
IC1
IC2
Higherindifferencecurvesrepresent
higher levelsof happiness.
Y
ZX
W
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CHAPTER 16 Consumption slide 15
Marginal rate of
substitution (MRS):
the amount ofC2consumer would be
________________
_________________.
Consumer preferences
C1
C2
IC1
The slope ofan indifferencecurve at anypoint equals
the MRSat that point.1
MRS
So the MRS is the (negative) of the
___________________________.
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CHAPTER 16 Consumption slide 16
The optimal (C1,C2)
is where the budget
line just touches the
highest indifference
curve.
Optimization
C1
C2
O
At the
optimal point,
__________
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CHAPTER 16 Consumption slide 17
An increase in Y1 orY2shifts the budget line
outward.
How C responds to changes inY
C1
C2Results:
Provided they are
both normal goods,
C1 and C2 bothincrease,
_____________
______________
____________________________.
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CHAPTER 16 Consumption slide 18
Temporary v. permanent
Temporary rise inincome: Y1 alonePermanent rise in income:Y1 and Y2 equally
S
Y2
Save part of income:
So ________________.
1 1
11
'
'
CC
YYC moves with Y:
So _________________.
1 1
11
'
'
CC
YY
C2=
C1
C2 C2=
=C1
=C1
C2=
=
C1
Y1
Y2
Y1Y1
Y2
Y1
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CHAPTER 16 Consumption slide 19
Keynes vs. Fisher
Keynes:current consumption depends only oncurrent income
Fisher:current consumption depends only on
________________________________;the timing of income is irrelevant
because the consumer can borrow or lendbetween periods.
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CHAPTER 16 Consumption slide 20
A
An increase in rpivots the budget
line around the
point (Y1,Y2).
How C responds to changes inr
C1
C2
Y1
Y2
A
B
As depicted here,
______________.
However, it could
turn out differently
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CHAPTER 16 Consumption slide 21
How C responds to changes inr
___________If consumer is a saver, the rise in r makes himbetter off, which tends to increase consumptionin both periods.
____________The rise in r increases the opportunity cost ofcurrent consumption, which tends to reduce C1and increase C2.
Both effects C2.
Whether C1 rises or falls depends on therelative size of the income & substitutioneffects.
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CHAPTER 16 Consumption slide 22
Constraints on borrowing
In Fishers theory, the timing of income is irrelevantbecause the consumer can borrow and lend acrossperiods.
Example: If consumer learns that her future income
will increase, she can spread the extra consumptionover both periods by borrowing in the current period.
However, if consumer faces_______________(aka liquidity constraints), then she may not be able
to increase current consumptionand her consumption may behave as in the Keynesiantheory even though she is rational & forward-looking
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CHAPTER 16 Consumption slide 23
The borrowingconstraint takesthe form:
______
Constraints on borrowing
C1
C2
Y1
Y2
The budget
line with aborrowingconstraint
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CHAPTER 16 Consumption slide 24
The borrowingconstraint is not
binding if theconsumersoptimal C1
___________.
Consumer optimization when theborrowing constraint is not binding
C1
C2
Y1
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CHAPTER 16 Consumption slide 25
The optimalchoice is atpoint D.
But since theconsumercannot borrow,the best he cando is point E.
Consumer optimization when theborrowing constraint is binding
C1
C2
Y1
D
E
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CHAPTER 16 Consumption slide 26
So underborrowingconstraints,currentconsumption
__________
__________
__________.
Suppose increase in income in period 1
C1
C2
E
The rise inincome to Y1shifts the budgetconstraint right.C1rises with Y1.
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CHAPTER 16 Consumption slide 27
due to Franco Modigliani (1950s) Fishers model says that consumption
depends on lifetime income, and people tryto achieve smooth consumption.
The LCH says that _________
__________ over the phases of theconsumers life cycle,
and saving allows the consumer to achievesmooth consumption.
The Life-Cycle Hypothesis
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CHAPTER 16 Consumption slide 28
The Life-Cycle Hypothesis
The basic model:W=
Y=
(assumed constant)
R= number of years until retirement
T= lifetime in years
Assumptions:
zero real interest rate (for simplicity)
consumption-smoothing is optimal
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CHAPTER 16 Consumption slide 29
The Life-Cycle Hypothesis
Lifetime resources = To achieve smooth consumption, consumer
divides her resources equally over time:
C= _____________ , or
C = aW+bYwhere
a = (1/T) is the marginal propensity toconsume out of wealthb = (R/T) is the marginal propensity toconsume out of income
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CHAPTER 16 Consumption slide 30
Implications of the Life-Cycle Hypothesis
The Life-Cycle Hypothesis can solve theconsumption puzzle:
TheAPC implied by the life-cycleconsumption function is
C/Y= _____________Across households, wealth does not vary as
much as income, so high income households_______________________ than low income
households.
Over time, aggregate wealth and incomegrow together, causing APC __________.
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CHAPTER 16 Consumption slide 31
Implications of the Life-Cycle Hypothesis
The LCHimplies thatsaving variessystematicallyover apersonslifetime. Saving
Dissaving
Retirementbegins
Endof life
Consumption
Income
$
Wealth
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CHAPTER 16 Consumption slide 32
Numerical Example
Suppose you start working at age 20, workuntil age 65, and expert to earn $50,000each year, and you expect to live to 80.
Lifetime income =
Spread over 60 years, so
C =
So need to save $12,500 per year.
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CHAPTER 16 Consumption slide 33
Example continued
Suppose you win a lottery which gives you $1000today.
Will spread it out over all T years, so consumptionrises by only $1000/T = $16.70 this year.
So temporary rise in income has a _____
____________.
But if lottery gives you $1000 every year for the Tyears, consumption rises by ________
_________ this year.
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CHAPTER 16 Consumption slide 34
The Permanent Income Hypothesis
due to Milton Friedman (1957) The PIH views current income Y as the sum
of two components:
_______________YP(average income, which people expect topersist into the future)
_______________YT
(temporary deviations from averageincome)
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CHAPTER 16 Consumption slide 35
Consumers use saving & borrowing tosmooth consumption in response totransitory changes in income.
The PIH consumption function:
C =
where a is the fraction of permanentincome that people consume per year.
The Permanent Income Hypothesis
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CHAPTER 16 Consumption slide 36
The PIH can solve the consumption puzzle: The PIH implies
APC= C/Y =
To the extent that high income households
have higher transitory income than lowincome households, the APC will be _____
_________________ income households.
Over the long run, income variation is duemainly if not solely to variation in permanentincome, which implies a __________.
The Permanent Income Hypothesis
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CHAPTER 16 Consumption slide 37
PIH vs. LCH
In both, people try to achieve smoothconsumption in the face of changing currentincome.
In the LCH, current income changes
systematically as people move through theirlife cycle.
In the PIH, current income is subject torandom, transitory fluctuations.
Both hypotheses can explain the consumptionpuzzle.
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CHAPTER 16 Consumption slide 38
The Random-Walk Hypothesis
due to Robert Hall (1978)
based on Fishers model & PIH, in whichforward-looking consumers base consumptionon expected future income
Hall adds the assumption ofrationalexpectations, that people use all availableinformation to forecast future variables like
income.
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CHAPTER 16 Consumption slide 39
The Random-Walk Hypothesis
If PIH is correct and consumers have rationalexpectations, then consumption should follow arandom walk: ________________________
_____________________.
A change in income or wealth that wasanticipated has already been factored intoexpected permanent income, so it will notchange consumption.
Only unanticipated changes in income or wealththat alter expected permanent income willchange consumption.
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CHAPTER 16 Consumption slide 40
If consumers obey the PIH
and have rational expectations,
then policy changeswill affect consumption
only if _________________.
Implication of the R-W Hypothesis
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CHAPTER 16 Consumption slide 41
The Psychology of Instant Gratification
Theories from Fisher to Hall assumes thatconsumers are rational and act to maximizelifetime utility.
recent studies by David Laibson and others
consider the psychology of consumers.
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CHAPTER 16 Consumption slide 42
The Psychology of Instant Gratification
Consumers consider themselves to beimperfect decision-makers.
E.g., in one survey, 76% said they werenot saving enough for retirement.
Laibson: The pull of instant gratificationexplains why people dont save as much as aperfectly rational lifetime utility maximizer
would save.
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CHAPTER 16 Consumption slide 43
Two Questions and Time Inconsistency
1. Would you prefer(A) a candy today, or(B) two candies tomorrow?
2. Would you prefer(A) a candy in 100 days, or(B) two candies in 101 days?
In studies, most people answered A to question 1,and B to question 2.
A person confronted with question 2 may choose B.100 days later, when he is confronted with question1, the pull of instant gratification may induce him tochange his mind.
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Summing up
Recall simple Keynesian consumption function:
where only current income (Y) mattered.
Research shows other things should be included: expected future income (permt income model)
wealth (life cycle model)
interest rates (Fisher model)
but current income should still be present (dueto borrowing constraints)
Modern policy analysis models allow for all this.
C C cY
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