Consumption

In this chapter, you will learn…

an introduction to the most prominent work on
consumption, including:
• John Maynard Keynes: consumption and current income
• Irving Fisher: intertemporal choice
• Franco Modigliani: the life-cycle hypothesis
• Milton Friedman: the permanent income hypothesis
• Robert Hall: the random-walk hypothesis
• David Laibson: the pull of instant gratification
Keynes’s conjectures
1. 0 < MPC < 1
2. Average propensity to consume (APC)
falls as income rises.
(APC = C/Y )
3. Income is the main determinant of
consumption.
The Keynesian consumption function

C = C + cY

c c = MPC
= slope of the
1
consumption
C function

Y
The Keynesian consumption function
As income rises, consumers save a bigger
C fraction of their income, so APC falls.

C = C + cY

C C
APC = = + c
Y Y
slope = APC
Y
Early empirical successes:
Results from early studies
• Households with higher incomes:
• consume more,  MPC > 0
• save more,  MPC < 1
• save a larger fraction of their income,
 APC  as Y 
• Very strong correlation between income and consumption:
 income seemed to be the main
determinant of consumption
Problems for the
Keynesian consumption function

• Based on the Keynesian consumption function, economists predicted

that C would grow more slowly than Y over time.
• This prediction did not come true:
• As incomes grew, APC did not fall,
and C grew at the same rate as income.
• Simon Kuznets showed that C/Y was
very stable in long time series data.
The Consumption Puzzle
Consumption function
C from long time series
data (constant APC )

Consumption function
from cross-sectional
household data
(falling APC )

Y
Irving Fisher and Intertemporal Choice

• The basis for much subsequent work on consumption.

• Assumes consumer is forward-looking and chooses consumption for
the present and future to maximize lifetime satisfaction.
• Consumer’s choices are subject to an intertemporal budget
constraint,
a measure of the total resources available for present and future
consumption.
The basic two-period model
• Period 1: the present
• Period 2: the future
• Notation
Y1, Y2 = income in period 1, 2
C1, C2 = consumption in period 1, 2
S = Y1 − C1 = saving in period 1
(S < 0 if the consumer borrows in period 1)
Deriving the intertemporal
budget constraint
• Period 2 budget constraint:
C 2 = Y 2 + (1 + r ) S
= Y 2 + (1 + r ) (Y1 − C 1 )

▪ Rearrange terms:
(1 + r ) C 1 + C 2 = Y 2 + (1 + r )Y1

▪ Divide through by (1+r ) to get…

The intertemporal budget constraint

C2 Y2
C1 + = Y1 +
1+r 1+r

present value of lifetime present value of

consumption lifetime income
The intertemporal budget constraint
C2 C2 Y2
C1 + = Y1 +
1+r 1+r

(1 + r )Y1 +Y 2
Consump =
Saving income in
The budget
both periods
constraint shows all
combinations Y2
of C1 and C2 that Borrowing
just exhaust the
consumer’s
resources. C1
Y1
Y1 +Y 2 (1 + r )
The intertemporal budget constraint
C2 C2 Y2
C1 + = Y1 +
1+r 1+r
The slope of
the budget
line equals
1
−(1+r )
(1+r )

Y2

C1
Y1
Consumer preferences
Higher
C2
An indifference indifference
curve shows curves
all combinations of represent
C1 and C2 higher levels
that make the of happiness.
consumer
equally happy. IC2

IC1
C1
Consumer preferences
C2 The slope of an
Marginal rate of indifference
substitution (MRS ): curve at any
the amount of C2 point equals the
the consumer MRS
would be willing to 1 at that point.
substitute for MRS
one unit of C1.

IC1
C1
Optimization
C2
The optimal (C1,C2) is
At the optimal point,
where the
MRS = 1+r
budget line
just touches
the highest
indifference curve. O

C1
How C responds to changes in Y
C2 An increase
Results: in Y1 or Y2
Provided they are both shifts the
normal goods, C1 and C2 budget line
both increase, outward.

…regardless of
whether the income
increase occurs in
period 1 or period 2.
C1
Keynes vs. Fisher

• Keynes:
Current consumption depends only on
current income.
• Fisher:
Current consumption depends only on
the present value of lifetime income.
The timing of income is irrelevant
because the consumer can borrow or lend between periods.
How C responds to changes in r
C2
An increase in r
As depicted here, pivots the budget
C1 falls and C2 rises. line around the
However, it could turn point (Y1,Y2 ).
out differently… B

A
Y2

Y1 C1
How C responds to changes in r
• income effect: If consumer is a saver,
the rise in r makes him better off, which tends to
increase consumption in both periods.
• substitution effect: The rise in r increases
the opportunity cost of current consumption,
which tends to reduce C1 and increase C2.
• Both effects  C2.
Whether C1 rises or falls depends on the relative size of
the income & substitution effects.
Constraints on borrowing
• In Fisher’s theory, the timing of income is irrelevant:
Consumer can borrow and lend across periods.
• Example: If consumer learns that her future income will
increase, she can spread the extra consumption over both
periods by borrowing in the current period.
• However, if consumer faces borrowing constraints (aka
“liquidity constraints”), then she may not be able to
increase current consumption
…and her consumption may behave as in the Keynesian
theory even though she is rational & forward-looking.
Constraints on borrowing
C2
The budget
line with no
borrowing
constraints

Y2

Y1 C1
Constraints on borrowing
C2
The borrowing
constraint takes
the form:
The budget
C1  Y1 line with a
borrowing
Y2 constraint

Y1 C1
Consumer optimization when the borrowing constraint is not
binding
C2
The borrowing
constraint is not
binding if the
consumer’s
optimal C1
is less than Y1.

Y1 C1
Consumer optimization when the borrowing constraint is binding
C2
The optimal
choice is at point
D.
But since the
consumer cannot
borrow, the best
he can do is point E
E.
D

Y1 C1
The Life-Cycle Hypothesis

• due to Franco Modigliani (1950s)

• Fisher’s model says that consumption depends on lifetime income,
and people try to achieve smooth consumption.
• The LCH says that income varies systematically over the phases of the
consumer’s “life cycle,”
and saving allows the consumer to achieve smooth consumption.
The Life-Cycle Hypothesis
• The basic model:
W = initial wealth
Y = annual income until retirement (assumed
constant)
R = number of years until retirement
T = lifetime in years
• Assumptions:
• zero real interest rate (for simplicity)
• consumption-smoothing is optimal
The Life-Cycle Hypothesis
• Lifetime resources = W + RY
• To achieve smooth consumption,
consumer divides her resources equally over time:
C = (W + RY )/T , or
C =  W + Y
where
 = (1/T ) is the marginal propensity to
consume out of wealth
 = (R/T ) is the marginal propensity to consume out of income
Implications of the Life-Cycle Hypothesis
The LCH can solve the consumption puzzle:
• The life-cycle consumption function implies
APC = C/Y = (W/Y ) + 
• Across households, income varies more than wealth, so
high-income households should have a lower APC than low-
income households.
• Over time, aggregate wealth and income grow together,
causing APC to remain stable.
Implications of the Life-Cycle Hypothesis
$

The LCH
implies that Wealth
saving varies
systematically
over a person’s Income
lifetime.
Saving

Consumption Dissaving

Retirement End
begins of life
The Permanent Income Hypothesis
• due to Milton Friedman (1957)
• Y = YP + YT
where
Y = current income
YP = permanent income
average income, which people expect to persist into
the future
YT = transitory income
temporary deviations from average income
The Permanent Income Hypothesis

• Consumers use saving & borrowing to smooth consumption in

response to transitory changes in income.
• The PIH consumption function:
C = YP
where  is the fraction of permanent income that people consume
per year.
 The Permanent Income Hypothesis
The PIH can solve the consumption puzzle:
• The PIH implies
APC = C / Y =  Y P/ Y
• If high-income households have higher transitory income
than low-income households,
APC is lower in high-income households.
• Over the long run, income variation is due mainly (if not
solely) to variation in permanent income, which implies a
stable APC.
PIH vs. LCH
• Both: people try to smooth their consumption
in the face of changing current income.
• LCH: current income changes systematically
as people move through their life cycle.
• PIH: current income is subject to random, transitory
fluctuations.
• Both can explain the consumption puzzle.
The Random-Walk Hypothesis

• due to Robert Hall (1978)

• based on Fisher’s model & PIH,
in which forward-looking consumers base consumption on expected
future income
• Hall adds the assumption of
rational expectations,
that people use all available information
to forecast future variables like income.
The Random-Walk Hypothesis
• If PIH is correct and consumers have rational
expectations, then consumption should follow a
random walk: changes in consumption should
be unpredictable.
• A change in income or wealth that was anticipated has
already been factored into expected permanent
income,
so it will not change consumption.
• Only unanticipated changes in income or wealth that
alter expected permanent income
will change consumption.
Implication of the R-W Hypothesis

If consumers obey the PIH

and have rational expectations, then
policy changes
will affect consumption
only if they are unanticipated.
The Psychology of Instant Gratification

• Theories from Fisher to Hall assume that consumers are rational and
act to maximize lifetime utility.
• Recent studies by David Laibson and others consider the psychology
of consumers.
The Psychology of Instant Gratification

• Consumers consider themselves to be imperfect decision-makers.

• In one survey, 76% said they were not saving enough for retirement.
• Laibson: The “pull of instant gratification” explains why people don’t
save as much as a perfectly rational lifetime utility maximizer would
save.
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 1 and (B) to 2.
A person confronted with question 2 may choose (B).
But in 100 days, when confronted with question 1,
the pull of instant gratification may induce her to change her
answer to (A).
Summing up
• Keynes: consumption depends primarily on current
income.
• Recent work: consumption also depends on
• expected future income
• wealth
• interest rates
• Economists disagree over the relative importance of
these factors, borrowing constraints,
and psychological factors.
Chapter Summary
1. Keynesian consumption theory
• Keynes’ conjectures
• MPC is between 0 and 1
• APC falls as income rises
• current income is the main determinant of current consumption
• Empirical studies
• in household data & short time series: confirmation of Keynes’
conjectures
• in long-time series data:
APC does not fall as income rises

CHAPTER 16 Consumption slide 43

Chapter Summary
2. Fisher’s theory of intertemporal choice
• Consumer chooses current & future consumption to
maximize lifetime satisfaction of subject to an intertemporal
budget constraint.
• Current consumption depends on lifetime income, not
current income, provided consumer can borrow & save.

CHAPTER 16 Consumption slide 44

Chapter Summary
3. Modigliani’s life-cycle hypothesis
• Income varies systematically over a lifetime.
• Consumers use saving & borrowing to smooth
consumption.
• Consumption depends on income & wealth.

CHAPTER 16 Consumption slide 45

Chapter Summary
4. Friedman’s permanent-income hypothesis
• Consumption depends mainly on permanent income.
• Consumers use saving & borrowing to smooth consumption
in the face of transitory fluctuations in income.

CHAPTER 16 Consumption slide 46

Chapter Summary
5. Hall’s random-walk hypothesis
• Combines PIH with rational expectations.
• Main result: changes in consumption are unpredictable,
occur only in response to unanticipated changes in
expected permanent income.

CHAPTER 16 Consumption slide 47

Chapter Summary
6. Laibson and the pull of instant gratification
• Uses psychology to understand consumer behavior.
• The desire for instant gratification causes people to save
less than they rationally know they should.

CHAPTER 16 Consumption slide 48