CHAPTER 10: Decision-Makers: The Household Sector
FOCUS OF THE CHAPTER
This chapter describes how a household makes its consumption and saving decisions,
according to existing theories or models of household consumption and saving behaviour.
The intertemporal choice model, the life cycle theory of consumption, and the
permanent income hypothesis are discussed. The influence of fiscal policy on
consumption and saving decisions is also discussed using the Ricardian equivalence
theorem.
Learning Objectives:
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Define savings
Determine the principal elements of the consumption-savings decision
Identify the main features of an intertemporal model of consumption behaviour
Analyze the impact of interest rates, income, and other institutional constraints on
consumption behaviour
Distinguish between short-run and long-run consumption behaviour and describe the
importance of the difference between the two
Determine why consumption spending is not volatile
Describe both the permanent income hypothesis and the life cycle hypothesis and
what they tell us about consumers’ lifetime spending-saving habits
Understand the potential connection between government spending, taxes and
consumption or savings behaviour
SECTION SUMMARIES
Intertemporal Savings Behaviour
Consider a simple model of intertemporal choice, where the household is assumed to
have a life of two periods (present and future) and zero initial wealth. Also assume that
present and future income levels (y1 and y2 respectively) are known with certainty;
preferences of the household and the real rate of interest (ρ) are given. The household
does not wish to bequeath any wealth to the next generation. The objective of the
household is to maximize utility (U). The household’s problem is to determine the utilitymaximizing combination of present and future consumption levels (c1* and c2* ,
respectively), subject to its lifetime budget constraint.
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i.e.,
Maximize
Subject to
U = u(c1, c 2 )
c1 + ( c 2/1+ ρ) = y1 + ( y 2/1+ ρ)
Note that the right (left) hand side of the budget constraint gives the present value of
income (consumption). In the present period, the household can choose to consume less
(more) than the present period income y1 and become a saver (borrower), or just to
consume an equal amount to y1. The choice of the household can be illustrated with a
Fisher diagram (also called an intertemporal choice diagram).
The present consumption (c1) and future consumption (c2 ) levels are given by
horizontal and vertical axes respectively. The budget constraint is given by line AB,
which passes through the endowment point. The household preferences are given by the
indifference curves. The optimal choice (utility maximizing combination of c1 and c2) lies
on the budget line at a point where the slope of the budget line is equal to the slope of an
indifference curve. The slope of the budget line is equal to -(1+ ρ). The slope of an
indifference curve is the rate of time preference (or the marginal rate of intertemporal
substitution). If the optimal present consumption c1* is smaller (larger) than y1, the
difference between y1 and c1* is the saving (borrowing).
The Determinants of Intertemporal Savings Behaviour
The effects of the changes in real interest rate (ρ), present and future period income levels
(y1 and y2), and a liquidity constraint on the optimal choice of the household are discussed
in this section.
Effect of an Interest Rate Change: An increase in the real interest rate increases the
slope of the budget constraint. As a result, the budget constraint rotates clockwise, still
passing through the endowment point. If the household is a saver, the new budget
constraint would be tangent to a higher level indifference curve. If the household is a
borrower (dissaver), the new budget constraint would be tangent to a lower level
indifference curve. In general, in cases of both the saver and the borrower, the increase in
the real rate of interest leads to lower current consumption and higher future consumption
levels. The final outcome depends not only on the slope and position of the budget
constraint but also on the shape of the indifference curves (or the preferences). Therefore,
an increase in the real interest rate can lead to different outcomes depending on the
preferences of the household.
Effect of an Income Change: An increase in the level of income in period one (present
period) expands the household’s set of consumption possibilities. As a result the budget
constraint shifts upward/rightward. The slope of the new budget constraint is the same as
the original one, since the real rate of interest is the same (i.e., the new budget constraint
is parallel to the original budget constraint). The tangency of the new budget constraint
and an indifference curve occurs at a point on a higher level indifference curve. The
results, in general, are increases in both present and future consumption levels.
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Effect of a Liquidity Constraint: Liquidity constraint is a situation where the household
does not have enough liquidity (because income is low) to consume as much as desired in
the present period (period one) and cannot borrow, even though the future income level is
expected to be higher. The budget constraint for such a household is kinked at the
endowment point. Such a household is likely to be constrained to choose the endowment
point (i.e., the household’s present and future consumption levels will be equal to the
income levels of the respective periods).
Life Cycle Explanations of Consumption Behaviour
The intertemporal choice model discussed in the previous section showed that the real
interest rate, level of income, individual’s (household’s) rate of time preference, and
situations such as the liquidity constraint are important determinants of optimal
consumption choice. In addition, the age of the household (individual) and the nature of
changes in income (whether temporary or permanent) over the lifetime also influence
consumption choice.
In the 1930s, John Maynard Keynes introduced the idea of the consumption
function. According to him, the consumption level for a given period depends on the
disposable income (after-tax income) level of that period. This idea is known as the
current income hypothesis. The change in consumption due to a one-unit change (say
one dollar) in disposable income is called the marginal propensity to consume (MPC).
MPC is measured by dividing the change in consumption (Δc) by the change in
disposable income (Δy) (i.e., MPC = Δc/Δy). Several empirical findings show that: a)
MPC is greater in the long run than in the short run; b) consumption spending evolves
more smoothly than income over time; c) temporary changes in income appear to have a
relatively small influence on consumption; and d) changes in income and consumption
seem to move together over long periods of time. The Keynesian consumption function
(current income hypothesis) does not satisfactorily explain these empirical findings.
The Life Cycle Pattern of Consumption: A Stylized Sketch
The relative smoothness of consumption over time suggests either that consumption
behaviour is influenced by whether the changes in income are expected to be temporary
or permanent, or that households attempt to smooth their consumption spending over
their lifetime, even though their incomes vary considerably over their lifetime.
Over a typical life cycle, individuals (households) accumulate wealth during
much of their working life, and dissave (take on debts or spend savings) during the early
and latter stages of the life cycle.
The Permanent Income Hypothesis: According to the permanent income hypothesis
proposed by Milton Friedman, consumption depends largely on permanent income
(average income over one's lifetime). Permanent income is stable; therefore, consumption
spending is also stable. Actual income (y) is the sum of permanent income (yP) and
transitory income (yT). The marginal propensity to consume out of permanent income
(long-run MPC) is high; therefore, changes in permanent income lead to significant
changes in consumption. The marginal propensity to consume out of transitory income
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(short-run MPC) is low; therefore, changes in transitory income do not lead to significant
changes in consumption.
The Life Cycle Theory of Consumption: According to the life cycle theory, proposed by
Franco Modigliani, consumption spending depends on the age of the household
(individual). Consumption (c) is determined by the levels of labour income (y) and assets
(a) of the household. The life cycle consumption function is given by:
c = k0y + k1a
where k0 and k1 are marginal propensities to consume out of income and assets,
respectively. In this theory, marginal propensities (k0 and k1) depend on the age of the
household. In the early stages of life, k0 is relatively high and k1 is relatively low. In the
later stages of life, k0 is relatively low and k1 is relatively high.
The Role of Government and Taxes
Many governments have followed the Keynesian policy prescription of cutting taxes and
increasing government spending to increase the level of consumption. The validity of
these Keynesian policy prescriptions has been brought into question by the Ricardian
equivalence theorem coined by Robert Barro. According to this theorem, a temporary tax
cut financed by government borrowing (bonds) will not change the permanent income of
the household, and, therefore, the current level of consumption is not significantly
affected. Nevertheless, the level of saving changes in anticipation of future increases in
taxes. However, a permanent tax cut can lead to a change in permanent income and
therefore, a relatively significant change in consumption.
MULTIPLE-CHOICE QUESTIONS
1. On a Fisher diagram, the endowment point of the household
a) is a point below the budget constraint.
b) is a point above the budget constraint.
c) is the point at which a saver maximizes utility.
d) is a point on the budget constraint.
2. The real interest rate is denoted by ρ. What is the slope of the budget constraint?
a) 1/(1+ρ)
b) -1/(1-ρ)
c) -(1+ρ)
d) 1/(1-ρ)
3. The household’s rate of time preference is given by
a) the slope of the budget constraint.
b) the slope of the indifference curves.
c) the real rate of interest.
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d) the slope of the 450 line.
4. Other things being equal, a decrease in the real rate of interest
a) rotates the budget constraint anticlockwise about the endowment point.
b) generates a parallel shift in the budget constraint, rightward.
c) changes the slope of indifference curves.
d) moves the budget constraint away from the endowment point.
5. An increase in the level of income in period one (present period)
a) does not affect the optimum consumption choice of the household.
b) is likely to increase both current and future consumption.
c) is likely to decrease both current and future consumption.
d) shifts the budget constraint downward.
6. According to Keynes, the main determinant of the consumption level is
a) current income.
b) initial wealth.
c) permanent income.
d) the rate of interest.
7. Empirical research shows that the long-run marginal propensity to consume
a) is larger than the short-run marginal propensity to consume.
b) is smaller than the short-run marginal propensity to consume.
c) has always been equal to the long-run average propensity to consume.
d) has been equal to the short-run marginal propensity to save.
8. According to the permanent income hypothesis
a) a permanent change in actual income has no impact on the level of consumption.
b) an increase in transitory income has a greater impact on saving than on consumption.
c) a temporary change in income has a greater impact on consumption.
d) neither actual income nor transitory income has any impact on consumption or saving.
9. Transitory income is
a) average annual income over one's lifetime.
b) the difference between actual income and permanent income.
c) income generated by the assets.
d) the sum of labour income and the returns on assets.
10. According to the life cycle theory,
a) the MPC out of labour income is low when the household is young.
b) the MPC out of assets is low when the household is old.
c) the MPC out of labour income is constant over the lifetime.
d) the MPC out of assets depends on the age of the household.
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PROBLEMS
1. A consumer has period one income of $40,000, period two income of $60,000 and the
interest rate is 10%. The consumer prefers to consume the same amount in periods one
and two.
a) Provide an equation for the intertemporal budget line.
b) Graph the budget line and draw in an appropriately place indifference curve.
c) Determine period one and period two consumption.
d) Determine the amount of period one saving or borrowing.
2. Within the framework of the intertemporal choice model, explain the impact of a
decrease in the real interest rate on consumption and saving, in the case of a borrower.
3. Using the two-period intertemporal choice model, explain the effect of a decrease in
the level of income in period one (present period) on current saving if the household is
a saver.
4. “A household facing a liquidity constraint will always be constrained to consume at the
endowment point.” Do you agree? Explain why.
5. State which theory of consumption is consistent with each of the following
consumption functions and why. Y = labour income; A = assets; Yp = permanent
income; t refers to time.
a) C = 0.5At + 0.25Y
b) Ct = 0.9 Yt p
c) Ct = 100 + 0.8Yt
6. Suppose that period one income equals period two income and suppose also that the
consumer chooses to consume an amount equal to his or her income in each period.
a) Is this individual better off if interest rates rise?
b) Is this individual worse off if interest rates fall?
Prove both of these answers graphically.
7. Draw an intertemporal budget line for a consumer who has the same income in periods
one and two on the assumption that they can earn only 2% on savings but they pay
10% on borrowing.
ANSWER SECTION
Answers to multiple-choice questions:
1. d (see pages 185-186)
2. c (see page 185)
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3.
4.
5.
6.
7.
8.
9.
10.
b
a
b
a
a
b
b
d
(see page 186)
(see page 186)
(see page 190)
(see page 193)
(see page 193)
(see page 196)
(see page 196)
(see pages 197-198)
Answers to problems:
1. a) The equation for the intertemporal budget line is
c1 + ( c 2/ 1.10) = $40,000 + ( $60,000 / 1.10 ) = $104,545
b) Graph the budget line and draw in an appropriately place indifference curve.
c) Period one and period two consumption both equal $54,761.66
d) Period one borrowing equals $14,761.66.
2. In an intertemporal choice model, the real interest rate is a determinant of the slope of
the household budget constraint. A decrease in the real interest rate decreases the slope
of the budget constraint. As a consequence, the budget constraint rotates anticlockwise
about the endowment point. In the case of a borrower, the new budget constraint will
be tangent to a higher level indifference curve. As a result, present consumption will
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increase (savings will decrease) and future consumption will decrease. However, the
net effect on future consumption may differ, depending on the household’s preferences.
3. A decrease in the level of income in period one (present period) shifts the budget
constraint downward. The new budget constraint will be parallel to the original budget
constraint. The new budget constraint will be tangent to a lower level indifference
curve. As a result, the household moves to the lower level indifference curve. Both
present (or current) consumption and savings decrease as a result of the decrease in
income level. Future consumption also decreases.
4. No, the statement is not true. Whether the household is constrained to the endowment
point or not depends on whether the liquidity constraint is binding or not. For a person
(household) who chooses to consume less than the income in the first period, the
liquidity constraint is not binding. Therefore, the household’s consumption is not
constrained to the endowment point. However, if the consumer wants to borrow
(consume more than the current income) in the first period, then the liquidity constraint
is binding. In that case, the liquidity constraint constrains the household to the
endowment point.
5. a) C = 0.5At + 0.25Y. This equation represents a consumption function consistent with
the life cycle hypothesis, because consumption (C) depends on the level of assets
(A) and the level of income. The marginal propensity to consume out of assets is
relatively higher (0.5) and the marginal propensity to consume out of income is
relatively lower (0.25). Therefore, this can be thought of as a consumption function
for an old age household.
b) Ct = 0.9Yt p. This equation represents a consumption function consistent with
Friedman’s permanent income hypothesis, since consumption depends only on the
permanent income level. Consumption out of permanent income is 0.9.
c) Ct = 100 + 0.8Yt. This equation represents a consumption function consistent with
the Keynesian current income hypothesis. Current consumption depends only on the
current income level. The marginal propensity to consume is 0.8.
6. a) Note that as the budget line gets steeper (as interest rates rise) the consumer can shift
to a new higher indifference curve and is, therefore, better off.
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b) If interest rates fall, the consumer again is made better off because they can now
borrow at a more attractive rate. The same diagram is used but now the consumer’s
choice shifts to a point lower and to the right.
7. The budget line is kinked because the rate earned on savings is lower than the rate paid
on borrowing.
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