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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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Keyness Conjectures

1. 2.

whereAPC

= average propensity to consume= C/Y

3.

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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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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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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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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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The Consumption Puzzle

C

Y

Consumption functionfrom long time seriesdata (constantAPC)

Consumption functionfrom cross-sectionalhousehold data

(fallingAPC)

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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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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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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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The intertemporal budget constraint

2 21 1

1 1

C YC Y

r r

present value of

______________

present value of

_____________

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The budgetconstraintshows all

combinationsofC1 and C2that justexhaust the

consumersresources.


C1

C2

_____________

__________

Y1

Y2_______

_____

Consump =

income inboth periods

2 21 1

1 1C YC Yr r

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The slope ofthe budgetline equals

_________)


C1

C2

Y1

Y2

2 21 1

1 1C YC Yr r

1(1+r)

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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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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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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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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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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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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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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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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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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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The borrowingconstraint takesthe form:

______

Constraints on borrowing

C1

C2

Y1

Y2

The budget

line with aborrowingconstraint

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The borrowingconstraint is not

binding if theconsumersoptimal C1

___________.

Consumer optimization when theborrowing constraint is not binding

C1

C2

Y1

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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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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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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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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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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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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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Implications of the Life-Cycle Hypothesis

The LCHimplies thatsaving variessystematicallyover apersonslifetime. Saving

Dissaving

Retirementbegins

Endof life

Consumption

Income

$

Wealth

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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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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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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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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.


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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 __________.


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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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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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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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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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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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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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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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