Chapter Seventeen

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CHAPTER 17Consumption

®

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MACROECONOMICS, 7th. EditionN. Gregory Mankiw

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M.P.A., Harvard University Kennedy School of GovernmentM.B.A., Massachusetts Institute of Technology (MIT) Sloan School of

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The consumption function was central to Keynes’ theory of economicfluctuations 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 betweenzero and one. He claimed that the fundamental law is that out ofevery dollar of earned income, people will consume part of it and savethe 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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Consumptionspending byhouseholds

dependson

autonomousconsumption

marginalpropensity to

consume (MPC)

disposableincome

C = C + c Y, C > 0, 0 < c <1C = C + c Y, C > 0, 0 < c <1C

YC

C determines the intercept on the vertical axis. The slope of the consumption function is lower case c, the MPC.

C = C + c

C = C + c YY

C = C + c

C = C + c YY

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To understand the marginal propensity to consume (MPC), consider a shopping scenario. A person who loves to shop

probably has a large MPC, let’s 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.

To understand the marginal propensity to consume (MPC), consider a shopping scenario. A person who loves to shop

probably has a large MPC, let’s 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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C

Y

C

APC = C/Y = C/Y + cAPC = C/Y = C/Y + c

11

APC1

APC2

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 bycurrent income Y. Notice that theinterest rate is not included in this equation as a determinant of consumption.

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 bycurrent income Y. Notice that theinterest rate is not included in this equation as a determinant of consumption.

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 > 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

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During World War II, on the basis of Keynes’s consumption function,economists predicted that the economy would experience what theycalled secular stagnation—a 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 Keynes’s conjecturethat 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 incomewas stable over time, despite large increases in income; again, Keynes’sconjecture was called into question.This brings us to the puzzle…

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The failure of the secular-stagnation hypothesis and the findings ofKuznets both indicated that the average propensity to consume is fairlyconstant over time. This presented a puzzle: Why did Keynes’s 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?

The failure of the secular-stagnation hypothesis and the findings ofKuznets both indicated that the average propensity to consume is fairlyconstant over time. This presented a puzzle: Why did Keynes’s 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?

C

Y

Short-run consumption function (falling APC)

Long-run consumption function (constant APC)

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 income—this relationship is called the long-run consumption function.

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 income—this relationship is called the long-run consumption function.

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The economist Irving Fisher developed the model with which economists analyze how rational, forward-looking consumers make intertemporal choices—that 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.

The economist Irving Fisher developed the model with which economists analyze how rational, forward-looking consumers make intertemporal choices—that 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

NotationY1 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 < 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 (1+r ):

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The consumer’s intertemporal budget constraint

present value of lifetime consumption

present value of lifetime income

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Here is an interpretation of the consumer’s budget constraint:The consumer’s budget constraint implies that if the interest rate is zero, the budget constraint shows that totalconsumption in the two periods equals total income in the two periods. In the usual case in which theinterest rate is greater than zero, future consumption and future incomeare discounted by a factor of 1 + r. This discounting arises from theinterest earned on savings. Because the consumer earns interest oncurrent income that is saved, future income is worth less than currentincome. Also, because future consumption is paid for out of savingsthat have earned interest, future consumption costs less than currentconsumption. The factor 1/(1+r) 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.

Here is an interpretation of the consumer’s budget constraint:The consumer’s budget constraint implies that if the interest rate is zero, the budget constraint shows that totalconsumption in the two periods equals total income in the two periods. In the usual case in which theinterest rate is greater than zero, future consumption and future incomeare discounted by a factor of 1 + r. This discounting arises from theinterest earned on savings. Because the consumer earns interest oncurrent income that is saved, future income is worth less than currentincome. Also, because future consumption is paid for out of savingsthat have earned interest, future consumption costs less than currentconsumption. The factor 1/(1+r) 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 slope of the budget line equals -(1+r): to increase C1 by one unit, the consumer must sacrifice (1+r) units of C2.

Here are the combinations of first-period and second-period consumptionthe 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 thathis income in the first period and borrows to make up the difference.

Consumer’s (intertemporal) budget constraintshowing all combinations of C1 and C2 that are feasible. The slope equals –(1+r)

Consumer’s (intertemporal) budget constraintshowing all combinations of C1 and C2 that are feasible. The slope equals –(1+r)

Saving

BorrowingA

C

B

Horizontal intercept isY1 + Y2/(1+r)

Horizontal intercept isY1 + Y2/(1+r)

Vertical intercept is(1+r)Y1 + Y2

Vertical intercept is(1+r)Y1 + Y2

Y1

Y2

C1

C2

1

(1+r )

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The consumer’s 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.

The consumer’s 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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First-period consumption

Sec

ond-

peri

odco

nsum

ptio

n

W

Z

X

Y

IC1

IC2

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.

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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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.

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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Marginal rate of Marginal rate of substitutionsubstitution (MRS ): the amount of C2

consumer would be willing to substitute for one unit of C1.

Consumer preferences

C1

C2

IC1

The slope of an The slope of an indifference indifference curve at any curve at any point equals the point equals the MRSMRS at that point.at that point.1

MRS

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First-period consumption

Seco

nd-p

erio

dco

nsum

ptio

n O

IC1

IC2

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 curveequals the slope of the budget line. At the optimum, the indifference curve is tangent to the budget constraint. The slope of the indifferencecurve is the marginal rate of substitution MRS, and the slope of thebudget line is 1 + the real interest rate. At point O, MRS = 1 + r.

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 curveequals the slope of the budget line. At the optimum, the indifference curve is tangent to the budget constraint. The slope of the indifferencecurve is the marginal rate of substitution MRS, and the slope of thebudget line is 1 + the real interest rate. At point O, MRS = 1 + r.

IC3

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First-period consumption

Sec

ond-

peri

odco

nsum

ptio

nO

IC1

IC2

An increase in either first-period income or second-period incomeshifts the budget constraint outward. If consumption in period one andconsumption in period two are both normal goods - those that aredemanded 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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Economists decompose the impact of an increase in the real interestrate on consumption into two effects: - a substitution effect , the change in consumption that results from thechange in the relative price of consumption in the two periods;-an income effect , the change in consumption that results from themovement to a higher indifference curve.

Economists decompose the impact of an increase in the real interestrate on consumption into two effects: - a substitution effect , the change in consumption that results from thechange in the relative price of consumption in the two periods;-an income effect , the change in consumption that results from themovement to a higher indifference curve.

B

IC1

IC2

AY

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…….. !

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…….. !

New budgetconstraint

Old budget constraint

Y1

Y2

C1

C2

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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 conjectured that the interest rate matters for consumption only in theory.

In Fisher’s theory, the interest rate doesn’t affect current consumption if the income and substitution effects are of equal magnitude.

Keynes vs. Fisher about interest rate

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• In Fisher’s theory, the timing of income is less important because theconsumer 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 increasecurrent 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 exceedingcurrent income. A constraint on borrowing can therefore be expressedas C1 < Y1.

• In Fisher’s theory, the timing of income is less important because theconsumer 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 increasecurrent 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 exceedingcurrent income. A constraint on borrowing can therefore be expressedas C1 < Y1.

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The budget line with no borrowing constraints

Constraints on borrowing

C1

C2

Y1

Y2

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The borrowing constraint takes the form:

C1 Y1

Constraints on borrowing

C1

C2

Y1

Y2

The budget line with a borrowing constraint

The area under the blue line satisfies both budget and borrowing constraints

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The borrowing constraint is not binding if the consumer’s 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.

Consumer optimization when the borrowing constraint is not binding

C1

C2

Y1

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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.

Consumer optimization when the borrowing constraint is binding

C1

C2

Y1

D

E

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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(1+r), 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 l’elevata crescita del Giappone nel dopoguerra deriva dall’elevato 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 anni’90 è causata dall’elevato tasso di risparmio (basso consumo e bassa domanda aggregata).

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In the 1950s, Franco Modigliani, Albert Ando, and Richard Brumbergused Fisher’s model of consumer behavior to study the consumption function. One of their goals was to study the consumption puzzle. According to Fisher’s model, consumption depends on a person’s lifetime income. Modigliani emphasized that income varies systematically over people’slives and that saving allows consumers to move income from thosetimes 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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• due to Franco Modigliani (1950s)

• Fisher’s 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 consumer’s “life cycle,”and saving allows the consumer to achieve smooth consumption.

The Life-Cycle Hypothesis

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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 = 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

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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 = (W/Y ) +

• 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 person’s lifetime.

Saving

Dissaving

Retirement begins

End of life

Consumption

Income

€

Wealth

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In 1957, Milton Friedman proposed the permanent-income hypothesisto explain consumer behavior. Its essence is that current consumption isproportional to permanent income. Friedman’s permanent-income hypothesis complements Modigliani’s life-cycle hypothesis: both use Fisher’s 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 person’slifetime, the permanent-income hypothesis emphasizes that peopleexperience random and temporary changes in their incomes from yearto year.

Friedman suggested that we view current income Y as the sum of twocomponents, 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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• Consumers use saving & borrowing to smooth consumption in response to transitory changes in income Y T.

• The PIH consumption function:

C = Y P

where is the fraction of permanent income that people consume per year.

The Permanent Income Hypothesis

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The PIH can solve the consumption puzzle:• The PIH implies

APC = C/Y = Y 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.

The Permanent Income Hypothesis

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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 was first to derive the implications of rational expectationsfor consumption. He showed that if the permanent-income hypothesisis correct, and if consumers have rational expectations, then changesin consumption over time should be unpredictable. When changes in avariable are unpredictable, the variable is said to follow a random walk.According to Hall, the combination of the permanent-incomehypothesis and rational expectations implies that consumption followsa random walk.

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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.

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If consumers obey the PIH If consumers obey the PIH and have rational expectations, and have rational expectations,

then policy changes then policy changes will affect consumption will affect consumption

only if they are unanticipated. only if they are unanticipated.

Implication of the R-W Hypothesis

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Recently, economists have turned to psychology for further explanationsof consumer behavior. They have suggested that consumption decisionsare not made completely rationally. This new subfield infusingpsychology into economics is called behavioural economics. Harvard’sDavid 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 don’t save as much as a perfectly rational lifetime utility maximizer would save.

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Two Questions and Time Inconsistency1. 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 data:

APC does not fall as income rises

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Chapter summary2. Fisher’s 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. Modigliani’s 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 summary4. 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.

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.

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Chapter summary6. 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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Marginal propensity to consumeAverage propensity to consumeIntertemporal budget constraintDiscountingIndifference curvesMarginal rate of substitutionNormal goodIncome effect

Substitution effectBorrowing constraintLife-cycle hypothesisPrecautionary savingPermanent-income hypothesisPermanent incomeTransitory incomeRandom walk