on consumption of a change in current income, expected future income, or wealth depends only on how that change affects the consumer's present value of lifetime resources, or

PVLR.

An Increase in Current Income

Suppose that Prudence receives a bonus at work of

12,000,

which raises her current real income from

42,000

to

54,000.

Her initial assets

(18,000),

future income

(33,000),

and the real interest rate

(10°/o)

remain unchanged; hence the increase of

12,000

in current income implies an equal increase in Prudence's present value of lifetime

resources, or

PVLR.

If she hasn't yet committed herself to her original consump­ tion-saving plan, how might Prudence revise that plan in light of her increased cur­ rent income?

We use the graph in Fig. 4.A.4 to answer this question. In Fig. 4.A.4, BL 1 is

Prudence's original budget line, and point D, where

c

=

45,000

and

cf

=

49,500,

represents Prudence's original, pre-bonus consumption plan. Prudence's bonus will allow her to consume more, both now and in the future, so the increase in her income causes her budget line to shift. To see exactly how it shifts, note that the increase of

12,000

in Prudence's current income implies that her

PVLR

also increases by

12,000.

Because the horizontal intercept of the budget line occurs at

c

=

PVLR,

the bonus

shifts the horizontal intercept to the right by

12,000.

The slope of the budget line,

-( 1

+

r)

=

-1.10,

remains unchanged because the real interest rate r is unchanged.

Thus the increase in current income of

12,000

causes a parallel shift of the budget line to the right by

12,000,

from BL 1 to BL

2.

1 56 Part 2 Long-Run Economic Performance

Figure 4.A.4

An increase in income or wealth

An increase in current income, future income, and/ or initial wealth that raises Prudence's

PVLR by 12,000 causes

the budget line to make a parallel shift to the right by 12,000, from BL 1 to

BL 2. If Prudence's origi­

nal consumption plan

was to consume at point

D, she could move to

point H by spending all the increase on future

consumption and none on current consumption; or she could move to

point K by spending all

the increase on current consumption and none

on future consumption. However, if Prudence has a consumption­

smoothing motive she will move to point J,

which has both higher

current consumption and higher future consump­

tion than D. Point J is

optimal because it lies where the new budget

line B L 2 is tangent to an

indifference curve, IC**.

56,100 .. . . ' . . . . ,. . 49,500 . . .. ,. . . . .. . . .. . . . .. 0 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ...., ' 45,000 51,000 57,000 PVLR Increases by 12,000 Ic** Ic* 90,000 102,000 Current consumption, c

That shift demonstrates graphically that, after receiving her bonus, Prudence can enjoy greater current and future consumption. One strategy for Prudence, repre­ sented by point K on the new budget line

BL

2, is to use the entire bonus to increase

her current consumption by 12,000 while leaving her future consumption unchanged. Another strategy, represented by point H on

BL 2,

is to save all of her bonus while keeping her current consumption unchanged, and then use both the bonus and the interest of 1,200 earned on the bonus to increase her future consump­ tion by 13,200.

If Prudence operates under a consumption-smoothing motive, she will use her bonus to increase

both

her current consumption and (by saving part of her bonus) her future consumption, thereby choosing a point on

BL

2 between point K (consume the

entire bonus) and point H (save the entire bonus). If her indifference curves are as shown in Fig. 4.A.4, she will move to J, where her new budget line,

BL

2, is tangent to

the indifference curve

IC**.

At J, current consumption,

c,

is 51,000, future consump­ tion,

cf,

is 56,100, and saving, s, is 54,000 - 51,000 == 3000. Both current and future

consumption are higher at J than at D (where

c ==

45,000 and

cf ==

49,500). Pru­ dence's current saving of 3000 at J is higher than her saving was at D (where she dis­ saved by 3000) because the increase in her current consumption of 6000 is less than

the increase in her current income of 12,000. This example illustrates that an increase in current income raises both current consumption and current saving.

An Increase in Future Income

Suppose that Prudence doesn't receive her bonus of 12,000 in the current period, so that her current income,

y,

remains at its initial level of 42,000. Instead, because of an improved company pension plan, she learns that her future income will increase by 13,200, so

yf

rises from 33,000 to 46,200. How will this good news affect Pru­

Chapter 4 Consumption, Savi ng, and I nvestment 1 57

At a real interest rate of 10°/o, the improvement in the pension plan increases the present value of Prudence's future income by 13,200/1.10, or 12,000. So, as in the case of the current-period bonus just discussed, the improved pension plan raises Prudence's

PVLR

by 12,000 and causes a parallel shift of the budget line to the right by that amount. The effects on current and future consumption are there­ fore exactly the same as they were for the increase of 12,000 in current income

(and Fig. 4.A.4 applies equally well here).

Although increases in current income and expected future income that are equal in present value will have the same effects on current and planned future consumption, the effects of these changes on current saving are different. Previ­

ously, we showed that an increase in current income raises current saving. In con­ trast, because the increase in future income raises current consumption (by 6000 in this example) but doesn't affect current income, it causes saving to fall (by 6000, from -3000 to -9000). Prudence knows that she will be receiving more income in the future, so she has less need to save today.

An Increase in Wealth

Changes in wealth also affect consumption and saving. As in the cases of current and future income, the effect of a change in wealth on consumption depends only on how much the

PVLR

changes. For example, if Prudence finds a passbook savings

account in her attic worth 12,000, her

PVLR

increases by 12,000. To illustrate this sit­ uation, we use Fig. 4.A.4 again. Prudence's increase in wealth raises her

PVLR

by

12,000 and thus shifts the budget line to the right by 12,000, from

BL

1 to

BL 2.

As

before, her optimal consumption choice goes from point D (before she finds the passbook) to point J (after her increase in wealth). Because the increase in wealth raises current consumption (from 45,000 at D to 51,000 at J) but leaves current income (42,000) unchanged, it results in a decline in current saving (from -3000 at D to -9000 at J). Being wealthier, Prudence does not have to save as much of her cur­ rent income (actually, she is increasing her dissaving) to provide for the future.

The preceding analyses show that changes in current income, future income, and initial wealth all lead to parallel shifts of the budget line by the amount that they change the

PVLR.

Economists use the term

income effect

to describe the impact of any change that causes a parallel shift of the budget line.

The Permanent Income Theory

In terms of our model, a temporary increase in income represents a rise in cur­ rent income,

y,

with future income,

yf,

held constant. A permanent increase in

income raises

both

current income,

y, and

future income,

yf.

Therefore a perma­ nent one-unit increase in income leads to a larger increase in

PVLR

than does a

temporary one-unit increase in income. Because income changes affect con­ sumption only to the extent that they lead to changes in

PVLR,

our theory pre­ dicts that a permanent one-unit increase in income will raise current and future consumption more than a temporary one-unit increase in income will.

This distinction between the effects of permanent and temporary income changes is emphasized in the

permanent income theory

of consumption and saving, developed in the 1950s by Nobel laureate Milton Friedman. He pointed out that income should affect consumption only through the

PVLR

in a many-period ver­

sion of the model we present here. Thus permanent changes in income, because they last for many periods, may have much larger effects on consumption than

1 58 Part 2 Long-Run Economic Performance

temporary changes in income. As a result, temporary income increases would be mostly saved, and permanent income increases would be mostly consumed.7

Consumption and Saving over Many Periods: The Life-Cycle Model

The two-period model suggests that a significant part of saving is intended to pay for retirement. However, it doesn't reflect other important aspects of a consumer 's lifetime income and consumption patterns. For example, income typically rises over most of a person's working life, and people save for reasons other than retire­ ment. The

life-cycle model

of consumption and saving, originated in the 1950s by Nobel laureate Franco Modigliani and his associates, extends the model from two periods to many periods and focuses on the patterns of income, consumption, and saving throughout an individual's life.

The essence of the life-cycle model is shown in Fig. 4.A.5. In Fig. 4.A.5(a), the typ­ ical consumer's patterns of income and consumption are plotted against the con­

sumer's age, from age twenty (the approximate age of economic independence) to age eighty (the approximate age of death). Two aspects of Fig. 4.A.5(a) are significant.

First, the average worker experiences steadily rising real income, with peak earnings typically occurring between the ages of fifty and sixty. After retirement, income (excluding interest earned from previous saving) drops sharply.

Second, the lifetime pattern of consumption is much smoother than the pattern of income over time, which is consistent with the consumption-smoothing motive discussed earlier. Although shown as perfectly flat in Fig. 4.A.5(a), consumption, in reality, varies somewhat by age; for example, it will be higher during years of high child-rearing expenses. An advantage of using the life-cycle model to study con­ sumption and saving is that it may be easily modified to allow for various patterns

of lifetime income and consumption.

The lifetime pattern of saving, shown in Fig. 4.A.5(b ), is the difference between the income and consumption curves in Fig. 4.A.5(a). This overall hump-shaped pattern has been confirmed empirically. Saving is minimal or even negative during the early work­ ing years, when income is low. Maximum saving occurs when the worker is between

ages fifty and sixty, when income is highest. Finally, dissaving occurs during retirement as the consumer draws down accumulated wealth to meet living expenses.

An important implication of the hump-shaped pattern of saving is that national saving rates depend on the age distribution of a country's population. Countries with unusually young or unusually old populations have low saving rates, and countries with relatively more people in their middle years have higher saving rates.

Bequests and Saving

We have assumed that the consumer plans to spend all of his or her wealth and income during his or her lifetime, leaving nothing to heirs. In reality, many people leave bequests, or inheritances, to children, charities, and others. To the extent that consumers desire to leave bequests, they will consume less and save more than when they simply consume all their resources during their lifetimes.

7Friedman also provided some of the first empirical evidence for this theory. For example, he found that the consumption of farm families, on average, responded less to changes in income than did the consumption of nonfarm families. Friedman's explanation was that, because farm incomes depend heavily on weather and crop prices, both of which are volatile, changes in farm incomes are much

more likely to be temporary than are changes in nonfarm incomes. Current changes in farm incomes have a smaller effect on the PVLR and therefore have a smaller effect on current consumption.

Figure 4.A.S

Life-cycle consumption, income, and saving

(a) Income and consump­

tion are plotted against

age. Income typically rises gradually throughout

most of a person's work­ ing life and peaks shortly before retirement. The

desire for a smooth pat­ tern of consumption

means that consumption varies less than income over the life cycle. Con­

sumption here is constant.

(b) Saving is the differ­

ence between income and consumption; the saving pattern is hump-shaped.

Early in a person's work­ ing life consumption is larger than income, so

saving is negative. In the

middle years saving is positive; the excess of

income over consumption is used to repay debts

incurred earlier in life and to provide for retirement. During retirement people dissave.

Chapter 4 Consumption, Savi ng, and I nvestment 1 59

Saving Consumption Dissaving : _{: Dissaving} 20 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 40 60 65 • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • . • • • • • • • • • • . • • • Income 80 20 • • • • • • • • • . • • • • • • • • • • • • • • • 40 60 65 Saving 80 Age Age Ricardian Equivalence

One of the most significant results of analyzing our model is that changes in income or wealth affect desired consumption only to the extent that they affect the con­ sumer's

PVLR.

The point made by advocates of Ricardian equivalence, discussed in Chapter

4,

is that, holding current and future government purchases constant,

a

In document Macroeconomics 7e Abel Bernanke Croushore (Page 182-186)