0. Lecture 11
Consumption
This long chapter is a survey of the most prominent work on consumption since Keynes. After reviewing the Keynesian consumption function and its implications, the chapter presents Irving Fisher’s theory of intertemporal choice, the basis for much subsequent work on consumption. The chapter presents the Life-Cycle and Permanent Income Hypotheses, then discusses Hall’s Random Walk Hypothesis. Finally, there is a brief discussion of some very recent work by Laibson and others on psychology and economics, in particular how the pull of instant gratification can cause consumers to deviate from perfect rationality.

1. Keynes’s Conjectures 0 < MPC < 1
APC falls as income rises where APC = average propensity to consume = C/Y
Income is the main determinant of consumption.
The MPC was defined in chapter 3 and used in various chapters since.

2. The Keynesian Consumption Function
A consumption function with the properties Keynes conjectured: C Y
c = MPC
= slope of the consumption function c 1

3. The Keynesian Consumption Function
As income rises, the APC falls (consumers save a bigger fraction of their income). C Y
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 average propensity to consume at that point.
(Why? The slope equals the rise over the run. The rise from zero to that point equals the value of C at that point. The run from zero to that point equals the value of Y at that point. Hence, the rise over the run equals C/Y, or the APC.)
At higher values of Y, the APC (or the slope of the ray from the origin) is smaller. This is what Keynes conjectured: at higher values of income, people spend a smaller fraction of their income.
slope = APC

4. 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

5. 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, the APC did not fall, and C grew just as fast.
Simon Kuznets showed that C/Y was very stable in long time series data.

6. The Consumption Puzzle
Consumption function from long time series data (constant APC ) C Y
Consumption function from cross-sectional household data
(falling APC )

7. 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

8. Intertemporal Choice Most of macroeconomics is about changes over time
So far, have jus considered the decision of work versus leisure
Need to add choice of today versus tomorrow

9. Examples Some intertemporal choices: Borrowing and saving by consumers
Investment by firms
Human capital investment by students
Family decisions

10. Important Factors for Intertemporal Choice:
Preferences over time (patience)
Expected return on investment
Expected future economic conditions

11. 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 < 0 if the consumer borrows in period 1)

12. The Setup Utility function: Budget constraints:
Want to know how and depend on
(intertemporal preferences)
(economic conditions)
(return on investment)

13. Deriving the intertemporal budget constraint
Period 2 budget constraint:
Rearrange to put C terms on one side and Y terms on the other:
Explain the intuition/interpretation of the period 2 budget constraint. If students understand it, then everything else follows nicely.
Finally, divide through by (1+r ):

14. The intertemporal budget constraint
present value of lifetime consumption
present value of lifetime income
If your students are not familiar with the present value concept, it is explained in a very nice FYI box on p.439.

15. The intertemporal budget constraint
The budget constraint shows all combinations of C1 and C2 that just exhaust the consumer’s resources.
Saving
Consump = income in both periods
Borrowing Y1 Y2
The point (Y1, Y2) is always on the budget line because C1=Y1, C2=Y2 is always possible, regardless of the real interest rate or the existence of borrowing constraints.
To obtain the expression for the horizontal intercept, set C2=0 in the equation for the intertemporal budget constraint and solve for C1. Similarly, the expression for the vertical intercept is the value of C2 when C1=0. There is intuition for these expressions. Take the vertical intercept, for example. If the consumer sets C1=0, then he will be saving all of his first-period income. In the second period, he gets to consume this saving plus interest earned, (1+r)Y1, as well as his second-period income.
If the consumer chooses C1<Y1, then the consumer will be saving, so his C2 will exceed his Y2.
Conversely, if consumer chooses C1>Y1, then consumer is borrowing, so his second-period consumption will fall short of his second-period income (he must use some of the second-period income to repay the loan). C1

16. The intertemporal budget constraint
The slope of the budget line equals -(1+r ) 1
(1+r ) Y1 Y2
The slope of the budget line equals -(1+r):
To increase C1 by one unit, the consumer must sacrifice (1+r) units of C2. C1

17. Consumer preferences
Higher indifference curves represent higher levels of happiness.
An indifference curve shows all combinations of C1 and C2 that make the consumer equally happy. C1 C2
IC2
IC1

18. Consumer preferences C1 C2
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.
IC1 1
MRS

19. Optimization C1 C2
The optimal (C1,C2) is where the budget line just touches the highest indifference curve.
At the optimal point, MRS = 1+r O
All points along the budget line are affordable, including the two points where the orange indifference curve intersects the budget line. However, the consumer prefers (and can afford) point O to these points, because O is on a higher indifference curve.
At the optimal point, the slope of the indifference curve (MRS) equals the slope of the budget line (1+r).

20. How C responds to changes in Y
An increase in Y1 or Y2 shifts the budget line outward. C1 C2
Results: Provided they are both normal goods, C1 and C2 both increase,
…regardless of whether the income increase occurs in period 1 or period 2.

21. 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.

22. How C responds to changes in r
An increase in r pivots the budget line around the point (Y1,Y2 ). A A B
As depicted here, C1 falls and C2 rises.
However, it could turn out differently… Y1 Y2

23. 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.
Note: 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.
After you have shown and explained this slide, it would be useful to pause for a moment and ask your students (perhaps working in pairs) to do the analysis of an increase in the interest rate on the consumption choices of a borrower. 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.

24. Constraints on borrowing
In Fisher’s theory, the timing of income is irrelevant because the 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

25. Constraints on borrowing
The budget line with no borrowing constraints Y2 Y1

26. Constraints on borrowing
The borrowing constraint takes the form: C1  Y1 C1 C2
The budget line with a borrowing constraint Y2
Similar to Figure 16-8 on p. 445. Y1

27. Consumer optimization when the borrowing constraint is not binding
The borrowing constraint is not binding if the consumer’s optimal C1 is less than Y1.
(Figure 16-9, panel (a), on p.446)
In this case, the consumer optimally was not going to borrow, so his inability to borrow has no impact on his choices. Y1

28. 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. E
(Figure 16-9, panel (b), on p.446)
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 do is at point E.
If you have a few minutes of classtime 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.
In the text, pages contain a case study on the high Japanese saving rate that relates to the material on borrowing constraints just covered. D Y1

29. Mathematical Solution
Substitute constraints into utility function:
Setting derivative wrt. s to zero:

30. Outcome MRS = Interest rate Same as before – Simple Model:
Choice between leisure and labor
MRS(l,C) = Relative price (l, C)
Intertemporal model:
Choice between today and tomorrow
MRS = Relative price

31. The Present-Value Budget Constraint
Present value of x dollars tomorrow:
Amount needed to be saved today to have x dollars tomorrow
Solving period-2 constraint for s:

32. The Present-Value Budget Constraint
Plugging the result into the period-1 constraint:
PV(total consumption)=PV(total income)

33. Outcome MRS = Relative price
Pure income effect (increase in either or ) will increase both and
Implies that s increases when rises
Implies that s falls when rises
Only present value of income matters, distribution irrelevant for consumption

34. Example: Log Utility
FOC for and

35. Computing Consumption
Example I:
Example II:

36. Conclusions
Model predicts strong consumption smoothing: timing of income does not matter
Result relies on perfect capital market
Even so, evidence for consumption smoothing is strong

37. Consumption Smoothing in Practice
Life-cycle consumption: borrow early in life, then save for retirement

38. Informal Capital Markets
Default risk prevents some people from borrowing
Society often finds ways around that problem:
Transfers from parents and relatives
Gift giving and neighborhood help
Social insurance

39. 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.

40. 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 initial wealth could be zero, or could be a gift from parents to help the consumer get started on her own.

41. 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

42. 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, wealth does not vary as much as income, 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.

43. Implications of the Life-Cycle Hypothesis$
The LCH implies that saving varies systematically over a person’s lifetime.
Wealth
Income
Saving
Consumption
Dissaving
Retirement begins
End of life

44. 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)
The middle of page 452 gives two hypothetical examples that help students understand the concepts of permanent and transitory income.

45. The Permanent Income Hypothesis
Consumers use saving & borrowing to smooth consumption in response to transitory changes in income.
The PIH consumption function:
C = aY P
where a is the fraction of permanent income that people consume per year.

46. 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 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.

47. PIH vs. LCH
In both, 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.

48. 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.

49. 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.

50. 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.
This result is important because many policies affect the economy by influencing consumption and saving. For example, a tax cut to stimulate aggregate demand only works if consumers respond to the tax cut by increasing spending. The R-W Hypothesis implies that consumption will respond only if consumers had not anticipated the tax cut.
This result also implies that consumption will respond immediately to news about future changes in income. Students connect with the following example: Suppose a student is job-hunting in her senior year for a job that will begin after graduation. If the student secures a job with a higher salary than she had expected, she is likely to start spending more now in anticipation of the higher-than-expected permanent income.

51. 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.

52. 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.

53. 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 question 1, the pull of instant gratification may induce him to change his mind.
The text discusses time inconsistency in this context. Time inconsistency was introduced and defined in chapter 14.

54. Summing up
Keynes suggested that consumption depends primarily on current income.
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.

55. 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

56. Chapter summary 2. 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.

57. 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.
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.

58. 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.