0. 17
Consumption
This long chapter is a survey of the most prominent work on consumption since Keynes. It is particularly useful to students who expect to continue with graduate studies in economics.
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. This section of the chapter uses indifference curves and budget constraints. The chapter and this PowerPoint presentation do not require or assume that students know these tools. But if they do not, then this section of the chapter is the most difficult.
The chapter then presents the Life-Cycle and Permanent Income Hypotheses, and 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.
Note: if you are covering or have covered Chapter 16 on government debt, please note that you can better explain Ricardian Equivalence (a topic from Chapter 16) using the Fisher model presented in this chapter. Just show students that a debt-financed tax cut is a movement along the budget constraint, not an outward shift of the constraint, and it should be clear that the optimal bundle of current and future consumption is not affected.
U P D A T E

1. This chapter presents:
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 (not covered)
David Laibson: the pull of instant gratification(not covered) 1

2. Keynesian consumption function 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 MPC was defined in chapter 3 and used in various chapters since.

3. The Keynesian consumption function
c = MPC
= slope of the consumption function c 1
Interpretations of C-bar:
autonomous consumption: the portion of consumption that does not depend on income
the value of consumption if income were zero.
a shift parameter

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

5. Early empirical successes: Cross section and short time series 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

6. 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.

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

8. 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.

9. The basic two-period model
Representative consumer lives for two periods
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)
For now we assume no taxes, T = 0
Note: There is no saving in period 2. Period 2 is the final period, and there are no bequests, so saving in period 2 would only reduce lifetime consumption and therefore lifetime utility/satisfaction.

10. Deriving the intertemporal budget constraint
Period 2 budget constraint:
Rearrange terms:
Divide through by (1+r ) to get…

11. 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.502.

12. The intertemporal budget constraint
Saving
Consump = income in both periods
The budget constraint shows all combinations of C1 and C2 that just exhaust the consumer’s resources.
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).

13. 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

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

15. Optimization C1 C2
The optimal (C1,C2) is where the budget line just touches the highest indifference curve.
Consumers maximize satisfaction over time
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).

16. How C responds to changes in Y
An increase in Y1 or Y2 shifts the budget line outward.
Temporary increase in Income Y2
ΔY1

17. How C responds to changes in Y
An increase in Y1 or Y2 shifts the budget line outward.
Permanent increase in Income
ΔY2
ΔY1

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

19. 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.
If you covered Ricardian Equivalence in Chapter 16, you might wish to revisit it briefly at or around this point in the presentation.
Draw the intertemporal budget constraint. Pick a point on it to represent (Y1–T1, Y2–T2).
Now suppose the government gives each consumer a one-unit tax cut. Disposable income in period 1 rises by 1.
Assume the government is not changing G1 or G2, and, just to keep things simple, assume that the government’s budget was balanced prior to the tax cut.
Then, cutting taxes by one unit in period 1 requires that the government borrow one unit in period 1, which it must repay with interest in period 2. In order to retire this debt in period 2, the government must raise period-2 taxes by (1+r).
Thus, disposable income rises by 1 in period 1 and falls by (1+r) in period 2.
Notice that the present value of the fall in period-2 income is exactly equal to the rise in period 1 income. Thus, consumer is not any better off.
What’s happened here is that the government has altered the timing of taxes (shifting some of the burden from the present to the future), but has not altered the present value of lifetime taxes. Therefore, the budget constraint does not shift out. Rather, the income point simply moves along the line toward the southeast (one unit to the right, and 1+r units downward).
The combination (C1, C2) that was optimal before will still be feasible and optimal.

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

21. 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.

22. 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.

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

24. Constraints on borrowing
The borrowing constraint takes the form:
C1  Y1
The budget line with a borrowing constraint Y2
Similar to Figure 17-8 on p. 508. Y1

25. 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 17-9, panel (a), on p.509)
In this case, the consumer optimally was not going to borrow, so his inability to borrow has no impact on his choices. Y1

26. 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 17-9, panel (b), on p.509)
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 class time available, have your students do the following experiment:
(This is especially useful if you have recently covered Chapter 16 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 16.
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. D Y1

27. 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.

28. 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.

29. Implications of the Life-Cycle Hypothesis$
Wealth
The LCH implies that saving varies systematically over a person’s lifetime.
Income
Saving
Figure 17-12, p.513.
Consumption
Dissaving
Retirement begins
End of life

30. 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

31. Implications of the Life-Cycle Hypothesis
The LCH can solve the consumption puzzle:
The life-cycle consumption function implies APC = C/Y = a(W/Y ) + b
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. .

32. The Permanent Income Hypothesis
due to Milton Friedman (1957)
Y = Y P + Y T
where
Y = current income
Y P = permanent income average income, which people expect to persist into the future. Expected income from both human and non-human wealth.
Y T = transitory income temporary deviations from average income
The middle of page 514 gives two hypothetical examples that help students understand the concepts of permanent and transitory income.

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

34. The Permanent Income Hypothesis
The PIH can solve the consumption puzzle:
The PIH implies APC = C / Y = a Y P/ Y = a (1- Y T/ 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. Y = Y P => APC = a.

35. 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.
Policy Implication: Changes in current income have a strong effect on current consumption ONLY if they affect expected lifetime income.
In Q2 1975, a one-time tax rebate of $8 billion was paid out to taxpayers to stimulate AD.
The rebate had little effect

36. 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.

37. 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 37

38. 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. 38

39. 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. 39

40. 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. 40