Consumption

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CHAPTER 17 Consumption
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John Maynard Keynes and the Consumption Function

• The consumption function was central to Keynes
  theory of economic
• fluctuations presented in The General Theory in
  1936.
• Keynes conjectured that the marginal propensity
  to consume the amount consumed out of an
  additional dollar of income is between
• zero and one. He claimed that the fundamental law
  is that out of
• every dollar of earned income, people will
  consume part of it and save
• the rest.
• Keynes also proposed the average propensity to
  consume, the ratio of consumption to income falls
  as income rises.
• Keynes also held that income is the primary
  determinant of consumption and that the interest
  rate does not have an important role.

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The Consumption Function
C C c Y, C gt 0, 0 lt c lt1
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The Marginal Propensity to Consume
To understand the marginal propensity to consume
(MPC), consider a shopping scenario. A person who
loves to shop probably has a large MPC, lets say
(.99). This means that for every extra dollar he
or she earns after tax deductions, he or she
spends .99 of it. The MPC measures the
sensitivity of the change in one variable,
consumption, with respect to a change in the
other variable, income.
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The Average Propensity to Consume
The C function exhibits three properties that
Keynes conjectured. (1) the marginal propensity
to consume c is between zero and one. (2) the
average propensity to consume falls as income
rises. (3) consumption is determined by current
income Y. Notice that the interest rate is not
included in this equation as a determinant of
consumption.
C
APC1
C
APC2
1
1
Y
What Keynes conjectured at higher values of
income, people spend a smaller fraction of their
income. So, as Y rises, the average propensity to
consume C/Y falls. Pick a point on the
consumption function that point represents a
particular combination of consumption and income.
Now draw a ray from the origin to that point. The
slope of that ray equals the APC at that point.
At higher values of Y, the APC (slope of the ray)
is smaller.
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Early Empirical Successes Results from Early
Studies

• Households with higher incomes
• consume more
• ? MPC gt 0
• save more
• ? MPC lt 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

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Secular Stagnation, Simon Kuznets, and the
Consumption Puzzle
During World War II, on the basis of Keyness
consumption function, economists predicted that
the economy would experience what they called
secular stagnationa long depression of infinite
duration unless the government used fiscal
policy to stimulate aggregate demand. It turned
out that the end of the war did not throw the
United States into another depression, but it
did suggest that Keyness conjecture that the
average propensity to consume would fall as
income rose appeared not to hold. Simon Kuznets
constructed new aggregate data on consumption and
investment dating back to 1869. His work would
later earn him a Nobel Prize. Kuznets discovered
that the ratio of consumption to income was
stable over time, despite large increases in
income again, Keyness conjecture was called
into question. This brings us to the puzzle
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Consumption Puzzle
The failure of the secular-stagnation hypothesis
and the findings of Kuznets both indicated that
the average propensity to consume is
fairly constant over time. This presented a
puzzle Why did Keyness conjectures hold up well
in the studies of household data (cross-sections)
and in the studies of short time-series, but fail
when long-time series were examined?
Studies of household data and short time-series
found a relationship between consumption and
income similar to the one Keynes conjectured
this is called the short-run consumption
function. But, studies using long time-series
found that the APC did not vary systematically
with incomethis relationship is called the
long-run consumption function.
C
Long-run consumption function (constant APC)
Short-run consumption function (falling APC)
Y
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Irving Fisher and Intertemporal Choice
The economist Irving Fisher developed the model
with which economists analyze how rational,
forward-looking consumers make intertemporal
choicesthat is, choices involving different
periods of time to maximize lifetime
satisfaction. The model illuminates the
constraints consumers face, the preferences they
have, and how these constraints and preferences
together determine their choices about
consumption and saving. When consumers are
deciding how much to consume today versus how
much to consume in the future, they face an
intertemporal budget constraint, which measures
the total resources available for consumption
today and in the future.
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The basic two-period model

• Period 1 the present
• Period 2 the future
• Notation
• Y1 is income in period 1
• Y2 is income in period 2
• C1 is consumption in period 1
• C2 is consumption in period 2
• S Y1 - C1 is saving in period 1
• (S lt 0 if the consumer borrows in period 1)

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Deriving the intertemporal budget constraint

• Period 2 budget constraint

• Rearrange

• Finally, divide by (1r )

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The consumers intertemporal budget constraint
present value of lifetime consumption
present value of lifetime income
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Here is an interpretation of the consumers
budget constraint The consumers budget
constraint implies that if the interest rate is
zero, the budget constraint shows that
total consumption in the two periods equals total
income in the two periods. In the usual case in
which the interest rate is greater than zero,
future consumption and future income are
discounted by a factor of 1 r. This discounting
arises from the interest earned on savings.
Because the consumer earns interest on current
income that is saved, future income is worth less
than current income. Also, because future
consumption is paid for out of savings that have
earned interest, future consumption costs less
than current consumption. The factor 1/(1r) is
the price of second-period consumption measured
in terms of first-period consumption it is the
amount of first-period consumption that the
consumer must forgo to obtain 1 unit of
second-period consumption.
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The Consumer's Budget Constraint
Here are the combinations of first-period and
second-period consumption the consumer can
choose. If he chooses a point between A and B, he
consumes less than his income in the first
period and saves the rest for the second period.
If he chooses between A and C, he consumes more
that his income in the first period and borrows
to make up the difference.
Consumers (intertemporal) budget
constraint showing all combinations of C1 and C2
that are feasible. The slope equals (1r)
C2
B
Saving
Vertical intercept is (1r)Y1 Y2
A
Borrowing
Horizontal intercept is Y1 Y2/(1r)
Y2
C
The slope of the budget line equals -(1r) to
increase C1 by one unit, the consumer must
sacrifice (1r) units of C2.
Y1
C1
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Consumer Preferences
The consumers preferences regarding consumption
in the two periods can be represented by
indifference curves. An indifference curve shows
the combination of first-period and second-period
consumption, C1 and C2, that makes the consumer
equally happy.
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Consumer Preferences
Second-period consumption
Z
Y
IC2
X
IC1
W
First-period consumption
Higher indifferences curves such as IC2 are
preferred to lower ones such as IC1. The consumer
is equally happy at points W, X, and Y, but
prefers point Z to all the others. Point Z is on
a higher indifference curve and is therefore not
equally preferred to W, X, and Y.
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Consumer Preferences
The slope at any point on the indifference curve
shows how much second-period consumption the
consumer requires in order to be compensated for
a 1-unit reduction in first-period consumption.
This slope is the marginal rate of substitution
between first-period consumption and
second-period consumption. It tells us the rate
at which the consumer is willing to substitute
second-period consumption for first-period
consumption.
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Consumer preferences
The slope of an indifference curve at any point
equals the MRS at that point.

• Marginal rate of substitution (MRS ) the amount
  of C2 consumer would be willing to substitute for
  one unit of C1.

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Optimization
O
Second-period consumption
IC3
IC2
IC1
First-period consumption
The consumer achieves his highest (or optimal)
level of satisfaction by choosing the point on
the budget constraint that is on the highest
indifference curve. Here the slope of the
indifference curve equals the slope of the budget
line. At the optimum, the indifference curve is
tangent to the budget constraint. The slope of
the indifference curve is the marginal rate of
substitution MRS, and the slope of the budget
line is 1 the real interest rate. At point O,
MRS 1 r.
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How Changes in Income Affect Consumption
Second-period consumption
IC2
O
IC1
First-period consumption
An increase in either first-period income or
second-period income shifts the budget constraint
outward. If consumption in period one
and consumption in period two are both normal
goods - those that are demanded more as income
rises, this increase in income raises
consumption in both periods.
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Keynes vs. Fisher about income

• 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.

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How Changes in the Real Interest Rate Affect
Consumption

• Economists decompose the impact of an increase in
  the real interest
• rate on consumption into two effects
• - a substitution effect , the change in
  consumption that results from the
• change in the relative price of consumption in
  the two periods
• an income effect , the change in consumption that
  results from the
• movement to a higher indifference curve.

Suppose the consumer is a saver (his choice is
point A). An increase in r (increase in the
slope) rotates the budget constraint around the
point C, where C is (Y1, Y2). As depicted here,
the saver goes from A to B, reducing first-period
consumption and raising second-period
consumption. But for a saver it could turn out
differently.. !
C2
New budget constraint
B
Old budget constraint
A
Y
IC2
Y2
IC1
Y1
C1
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How C responds to changes in r

• substitution effectThe rise in r increases the
  opportunity cost of current consumption, which
  tends to reduce C1 and increase C2.
• income effectIf the consumer is a saver, the
  rise in r makes him better off, which tends to
  increase consumption in both periods.
• Both effects ? ?C2.
• But whether C1 rises or falls depends on the
  relative size of the income substitution
  effects.

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• An answer/exercise for you do the analysis of an
  increase in the interest rate on the consumption
  choices of a borrower..
• Hint in that case, the income effect tends to
  reduce both current and future consumption,
  because the interest rate hike makes the borrower
  worse off. The substitution effect still tends to
  increase future consumption while reducing
  current consumption. In the end, current
  consumption falls unambiguously future
  consumption falls if the income effect dominates
  the substitution effect, and rises if the reverse
  occurs.

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Keynes vs. Fisher about interest rate

• Keynes conjectured that the interest rate
  matters for consumption only in theory.
• In Fishers theory, the interest rate doesnt
  affect current consumption if the income and
  substitution effects are of equal magnitude.

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Constraints on Borrowing

• In Fishers theory, the timing of income is less
  important because the
• consumer can borrow and lend across periods.
• Example If a 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
• (or 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
• The inability to borrow prevents current
  consumption from exceeding
• current income. A constraint on borrowing can
  therefore be expressed
• as C1 lt Y1.

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Constraints on borrowing

• The budget line with no borrowing constraints

Y2
Y1
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Constraints on borrowing

• The borrowing constraint takes the form
• C1 ? Y1

Y2
Y1
The area under the blue line satisfies both
budget and borrowing constraints
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Consumer optimization when the borrowing
constraint is not binding

• The borrowing constraint is not binding if the
  consumers optimal C1 is less than Y1.
• In this case, the consumer would not have
  borrowed anyway, so his inability to borrow has
  no impact on consumption choices.

Y1
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Consumer optimization when the borrowing
constraint is binding

• The optimal choice is at point D. But since the
  consumer cannot borrow, the best he can do is
  point E.
• In this case, the consumer would like to borrow
  to achieve his optimal consumption at point D. If
  he faces a borrowing constraint, though, then the
  best he can achieve is the consumption plan of
  point E.

E
D
Y1
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• If you have a few minutes of class time
  available, have your students do the following
  experiment
• (This is especially useful if you have recently
  covered Chapter 15 on Government Debt)
• Suppose Y1 is increased by 1000 while Y2 is
  reduced by 1000(1r), so that the present value
  of lifetime income is unchanged. Determine the
  impact on C1
• - when consumer does not face a binding
  borrowing constraint - when consumer does face a
  binding borrowing constraint
• Then relate the results to the discussion of
  Ricardian Equivalence from Chapter 15.
• Note that the intertemporal redistribution of
  income in this exercise could be achieved by a
  debt-financed tax cut in period 1, followed by a
  tax increase in period 2 that is just sufficient
  to retire the debt.
• The text contains a case study on the high
  Japanese saving rate that relates to the material
  on borrowing constraints just covered.

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Europa Austria,Belgio,Danimarca, Finlandia,
Francia, Germania, Grecia,Irlanda, Italia,
Norvegia, Olanda,Portogallo, UK,Spagna,Svezia,
Svizzera. (OECD, IMF,Eurostat).
Per alcuni lelevata crescita del Giappone nel
dopoguerra deriva dallelevato tasso di risparmio
(nel modello di crescita di Solow vedremo che il
risparmio determina il livello di reddito di
stato stazionario). Per altri la lunga recessione
degli anni90 è causata dallelevato tasso di
risparmio (basso consumo e bassa domanda
aggregata).
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Franco Modigliani and the Life-Cycle Hypothesis
In the 1950s, Franco Modigliani, Albert Ando,
and Richard Brumberg used Fishers model of
consumer behavior to study the consumption
function. One of their goals was to study the
consumption puzzle. According to Fishers model,
consumption depends on a persons lifetime
income. Modigliani emphasized that income varies
systematically over peoples lives and that
saving allows consumers to move income from
those times in life when income is high to those
times when income is low. This interpretation of
consumer behavior formed the basis of his
life-cycle hypothesis.
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The Life-Cycle Hypothesis

• due to Franco Modigliani (1950s)
• Fishers model says that consumption depends on
  lifetime income, and people try to achieve a
  smooth consumption pattern.
• The LCH says that income varies systematically
  over the phases of the consumers life cycle,
• and saving allows the consumer to achieve smooth
  consumption.

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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

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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 aW bY
• where
• a (1/T ) is the marginal propensity to consume
  out of wealth
• b (R/T ) is the marginal propensity to consume
  out of income

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Implications of the Life-Cycle Hypothesis

• The Life-Cycle Hypothesis can solve the
  consumption puzzle
• The APC implied by the life-cycle consumption
  function is C/Y a(W/Y ) b
• Across households or in the short-run, wealth
  does not vary as much as income, so high income
  households should have a lower APC than low
  income households ? similar to Keynes
• Over time, aggregate wealth and income grow
  together, causing APC to remain stable ? Simon
  Kuznets puzzle solved.

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Implications of the Life-Cycle Hypothesis

• The LCH implies that saving varies systematically
  over a persons lifetime.

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Milton Friedman and the Permanent-Income
Hypothesis
In 1957, Milton Friedman proposed the
permanent-income hypothesis to explain consumer
behavior. Its essence is that current consumption
is proportional to permanent income. Friedmans
permanent-income hypothesis complements
Modiglianis life-cycle hypothesis both use
Fishers theory of the consumer to argue that
consumption should not depend on current income
alone. But unlike the life-cycle hypothesis,
which emphasizes that income follows a regular
pattern over a persons lifetime, the
permanent-income hypothesis emphasizes that
people experience random and temporary changes in
their incomes from year to year. Friedman
suggested that we view current income Y as the
sum of two components, permanent income YP and
transitory income YT.
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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
• permanent income Y P (average income, which
  people expect to persist into the future)
• transitory income Y T(temporary deviations from
  average income)

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The Permanent Income Hypothesis

• Consumers use saving borrowing to smooth
  consumption in response to transitory changes in
  income Y T.
• The PIH consumption function
• C aY P
• where a is the fraction of permanent income
  that people consume per year.

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The Permanent Income Hypothesis

• The PIH can solve the consumption puzzle
• The PIH implies APC C/Y aY P/Y
• To the extent that high income households have on
  average a higher transitory income than low
  income households, the APC will be 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. ? policy changes
  will affect consumption only if they are
  permanent.

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PIH vs. LCH

• In both cases, people try to achieve smooth
  consumption in the face of changing current
  income.
• In the LCH, current income changes systematically
  as people move through their life cycle.
• In the PIH, current income is subject to random,
  transitory fluctuations.
• Both hypotheses can explain the consumption
  puzzle.

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Robert Hall and the Random-Walk Hypothesis
Robert Hall was first to derive the implications
of rational expectations for consumption. He
showed that if the permanent-income hypothesis is
correct, and if consumers have rational
expectations, then changes in consumption over
time should be unpredictable. When changes in
a variable are unpredictable, the variable is
said to follow a random walk. According to Hall,
the combination of the permanent-income hypothesis
and rational expectations implies that
consumption follows a random walk.
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The Random-Walk Hypothesis

• due to Robert Hall (1978)
• based on Fishers 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.

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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.

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David Laibson and the Pull of Instant
Gratification
Recently, economists have turned to psychology
for further explanations of consumer behavior.
They have suggested that consumption
decisions are not made completely rationally.
This new subfield infusing psychology into
economics is called behavioural economics.
Harvards David Laibson notes that many consumers
judge themselves to be Imperfect decisionmakers.
Consumers preferences may be time- inconsistent
they may alter their decisions simply because
time passes.
Pull of Instant Gratification
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The Psychology of Instant Gratification

• Theories from Fisher to Hall assumes that
  consumers are rational and act to maximize
  lifetime 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 be imperfect
  decision-makers.
• e.g., in one survey, 76 said they were not
  saving enough for retirement.
• Laibson The pull of instant gratification
  explains why people dont save as much as a
  perfectly rational lifetime utility maximizer
  would save.

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Two Questions and Time Inconsistency

• 1. Would you prefer (A) a chocolate bar today,
  or (B) two chocolate bars tomorrow?
• 2. Would you prefer (A) a chocolate bar in 100
  days, or (B) two chocolate bars 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
  question 1, the pull of instant gratification may
  induce him to change his mind and to select A. ?
  People are more patient in the long-run than in
  the short-run. Time inconsistency.

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Summing up

• Keynes suggested that consumption depends
  primarily on current income.
• More recent work suggests instead that
  consumption depends on
• current income
• expected future income
• wealth
• interest rates
• Economists disagree over the relative importance
  of these factors and of borrowing constraints and
  psychological factors.

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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 dataAPC does not fall as
  income rises

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Chapter summary

• 2. Fishers theory of intertemporal choice
• Consumer chooses current future consumption to
  maximize lifetime satisfaction subject to an
  intertemporal budget constraint.
• Current consumption depends on lifetime income,
  not current income, provided consumer can borrow
  save.
• 3. Modiglianis Life-Cycle Hypothesis
• Income varies systematically over a lifetime.
• Consumers use saving borrowing to smooth
  consumption.
• Consumption depends on income wealth.

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Chapter summary

• 4. Friedmans Permanent-Income Hypothesis
• Consumption depends mainly on permanent income.
• Consumers use saving borrowing to smooth
  consumption in the face of transitory
  fluctuations in income.
• 5. Halls 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.

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Chapter summary

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

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Key Concepts of Chapter 17
Marginal propensity to consume Average propensity
to consume Intertemporal budget
constraint Discounting Indifference
curves Marginal rate of substitution Normal
good Income effect
Substitution effect Borrowing constraint Life-cycl
e hypothesis Precautionary saving Permanent-income
hypothesis Permanent income Transitory
income Random walk