CH04 Consumption and Saving

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Chapter 4

Consumption,Saving, and

Investment


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Copyright 2005 Pearson Addison-Wesley. All rights reserved. 4-3

4.1 Consumption and Saving

The importance of consumption and saving

Desired consumption: consumption amount desired byhouseholds

Desired national saving: level of national saving whenconsumption is at its desired level, Sd= Y- Cd- G (4.1)

The consumption and saving decision of an individualA person can consume less than current income (saving is

positive)A person can consume more than current income (saving is

negative)

Trade-off between current consumption and futureconsumptionThe price of 1 unit of current consumption is 1 + runits of

future consumption, where ris the real interest rateConsumption-smoothing motive: the desire to have a

relatively even pattern of consumption over time


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Effect of changes in current incomeIncrease in current income: both consumption

and saving increase (vice versa for decrease incurrent income)

Marginal propensity to consume (MPC) =fraction of additional current income consumedin current period; between 0 and 1

Aggregate level: When current income (Y)

rises, Cd

rises, but not by as much as Y, so Sd

rises


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Figure 4.1(a) The index of consumer sentiment,January 1987December 1994


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Figure 4.1(b) Total consumption expenditures andconsumption expenditures on durable goods, 19871994


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Effect of changes in expected futureincomeHigher expected future income leads to more

consumption today, so saving falls

Application: consumer sentiment and the199091 recession; sharp contraction inconsumer sentiment in 1990 led to fall inconsumer spending

Effect of changes in wealth

Increase in wealth raises current consumption,so lowers current saving


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Effect of changes in real interest rateIncreased real interest rate has two opposing

effectsSubstitution effect: Positive effect on saving, since

rate of return is higher; greater reward for savingelicits more saving

Income effectFor a saver: Negative effect on saving, since it takes less

saving to obtain a given amount in the future (targetsaving)

For a borrower: Positive effect on saving, since the higherreal interest rate means a loss of wealth

Empirical studies have mixed results; probably a

slight increase in aggregate saving


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Taxes and the real return to savingExpected after-tax real interest rate:

ra-t = (1 - t)i- e (4.2)

Simple examples: i= 5%, e = 2%; ift= 30%, ra-t

= 1.5%; ift= 20%, ra-t= 2%

In touch with the macroeconomy: interest ratesDiscusses different interest rates, default risk, term

structure (yield curve), and tax statusSince interest rates often move together, we frequently

refer to the interest rate


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Table 4.1 Calculating After-Tax Interest Rates


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Fiscal policyAffects desired consumption through changes in current

and expected future income

Directly affects desired national saving, Sd = Y- Cd - G

Government purchases (temporary increase)HigherG financed by higher current taxes reduces after-tax

income, lowering desired consumption

Even true if financed by higher future taxes, if people realizehow future incomes are affected

Since Cddeclines less than G rises, national saving (Sd= Y-Cd - G) declines

So government purchases reduce both desired consumptionand desired national saving


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TaxesLump-sum tax cut today, financed by higher future

taxes

Decline in future income may offset increase incurrent income; desired consumption could rise or fall

Ricardian equivalence proposition If future income loss exactly offsets current income gain,

no change in consumption

Tax change affects only the timing of taxes, not their

ultimate amount (present value) In practice, people may not see that future taxes will rise if

taxes are cut today; then a tax cut leads to increaseddesired consumption and reduced desired national saving


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Application: a Ricardian tax cut?The Economic Growth and Tax Relief Reconstruction

Act (EGTRRA) of 2001 gave rebate checks to taxpayersand cut tax rates substantially

From the first quarter to the third quarter, government

saving fell $245 billion (at an annual rate) but privatesaving increased $212 billion, so national savingdeclined only $33 billion, a result consistent withRicardian equivalence

Most consumers saved their tax rebates and did notspend them

As a result, the tax rebate and tax cut did not stimulatemuch additional spending by households


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Application A Ricardian Tax Cut?


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4.2 Investment

Why is investment important?

Investment fluctuates sharply over the business cycle,so we need to understand investment to understand thebusiness cycle

Investment plays a crucial role in economic growth

The desired capital stockDesired capital stock is the amount of capital that allows

firms to earn the largest expected profitDesired capital stock depends on costs and benefits of

additional capitalSince investment becomes capital stock with a lag, thebenefit of investment is the future marginal product ofcapital (MPKf)


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4.2 Investment

The user cost of capital

Example of Kyle's Bakery: cost of capital, depreciation rate,and expected real interest rate

User cost of capital = real cost of using a unit of capital for aspecified period of time

uc= rpK+ dpK= (r+ d)pK (4.3)

Determining the desired capital stock (Fig. 4.2)Desired capital stock is the level of capital stock at which MPKf

= ucMPKf falls as Krises due to diminishing marginal productivityucdoesn't vary with K, so is a horizontal line

IfMPKf> uc, profits rise as Kis added (marginal benefits >marginal costs)

IfMPKf< uc, profits rise as Kis reduced (marginal benefits replacement cost, then firmshould invest more

Tobins q = capitals market value divided by itsreplacement costIfq < 1, don't invest

Ifq > 1, invest more


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4.2 Investment

Stock price times number of shares equals firms market

value, which equals value of firms capitalFormula: q = V/ (pKK), where Vis stock market value of firm,

Kis firms capital,pK is price of new capital

SopKKis the replacement cost of firms capital stock

Stock market boom raises V, causing q to rise, increasing

investmentData show general tendency of investment to rise when

stock market rises; but relationship isnt strong becausemany other things change at same time

This theory is similar to text discussionHigherMPKf increases future earnings of firm, so VrisesA falling real interest rate also raises Vas people buy stocks

instead of bonds

A decrease in the cost of capital,pK, raises q


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Figure 4.4 An increase in the expectedfuture MPK raises the desired capital stock


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4.2 Investment

From the desired capital stock to investment

The capital stock changes from two opposing channelsNew capital increases the capital stock; this is gross investmentThe capital stock depreciates, which reduces the capital stockNet investment = gross investment (I) minus depreciation:

Kt+1 - Kt = It - dKt (4.5), where net investment equals the change in the capital stock

Fig. 4.5 shows gross and net investment for the United StatesRewriting (4.5) gives It= Kt+1 - Kt+ dKt

If firms can change their capital stocks in one period, then the desiredcapital stock (K*) = Kt+1, so It = K*- Kt + dKt (4.6)

Thus investment has two partsDesired net increase in the capital stock over the year (K*- Kt)

Investment needed to replace depreciated capital (dKt)Lags and investment

Some capital can be constructed easily, but other capital may takeyears to put in place

So investment needed to reach the desired capital stock may bespread out over several years


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Figure 4.5 Gross and net investment, 19292002


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4.2 Investment

Investment in inventories and housingMarginal product of capital and user cost also

apply, as with equipment and structures


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4.3 Goods Market Equilibrium

The real interest rate adjusts to bring the goods

market into equilibriumgoods market equilibrium condition : Y

= Cd + Id+ G (4.7)Differs from income-expenditure identity, as goods

market equilibrium condition need not hold; undesiredgoods may be produced, so goods market won't be inequilibrium

Alternative representation: sinceSd= Y- Cd - G, Sd= Id (4.9)

The saving-investment diagramPlot Sd vs. Id (Key Diagram 3; Fig. 4.6)Equilibrium where Sd = Id

How to reach equilibrium? Adjustment ofr


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Key Diagram 3 The saving investment diagram


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Figure 4.6 Goods market equilibrium


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Table 4.3 Components of AggregateDemand for Goods (An Example)


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Shifts of the saving curveSaving curve shifts right due to a rise in current output,

a fall in expected future output, a fall in wealth, a fall ingovernment purchases, a rise in taxes (unless Ricardianequivalence holds, in which case tax changes have noeffect)

Example: Temporary increase in governmentpurchases shifts S leftResult of lower savings: higherr, causing crowding out

ofI

Shifts of the investment curveInvestment curve shifts right due to a fall in the effective

tax rate or a rise in expected future marginal productivityof capitalResult of increased investment: higherr, higherS and I


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Figure 4.7 A decline in desired saving


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Figure 4.8 An increase in desired investment


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Application: Macroeconomic consequences of the

boom and bust in stock pricesSharp changes in stock prices affect consumption

spending (a wealth effect) and capital investment (viaTobins q)

Consumption and the 1987 crashWhen the stock market crashed in 1987, wealth declined by

about $1 trillionConsumption fell somewhat less than might be expected, and

it wasnt enough to cause a recession

There was a temporary decline in confidence about the future,but it was quickly reversedThe small response may have been because there had been a

large run-up in stock prices between December 1986 andAugust 1987, so the crash mostly erased this run-up


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Figure 4.9 Real U.S. stock prices and theratio of consumption to GDP, 19872002


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Consumption and the rise in stock market wealth in the

1990sStock prices more than tripled in real termsBut consumption was not strongly affected by the runup in

stock prices

Consumption and the decline in stock prices in the early

2000sIn the early 2000s, wealth in stocks declined by about $5

trillionBut consumption spending increased as a share of GDP in

that period

Investment and Tobins qInvestment and Tobins q were not closely correlated following

the 1987 crash in stock pricesBut the relationship has been tighter in the 1990s and early

2000s, as theory suggests


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Figure 4.10 Investment and Tobins q, 19872002


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Appendix 4A

A Formal Modelof Consumption

and Saving


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Appendix 4.A: A Formal Model of Consumption and Saving

How much can the consumer afford? The budget constraint (BC)Current income y; future income yf; initial wealth a

Choice variables: af= wealth at beginning of future period; c=current consumption; cf= future consumption

af = (y+ a - c)(1 + r), so cf = (y+ a - c)(1 + r) + yf (4.A.1) the BC

The budget lineGraph budget line in (c, cf) space (Fig. 4.A.1)

Slope of line = -(1 + r) Present values

Present value is the value of payments to be made in the future interms of today's dollars or goods

Example: At an interest rate of 10%, $12,000 today invested for

one year is worth $13,200 ($12,000

1.10); so the present valueof $13,200 in one year is $12,000General formula: Present value = future value / (1 + i), where

amounts are in dollar terms and iis the nominal interest rateAlternatively, if amounts are in real terms, use the real interest rate

rinstead of the nominal interest rate i


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Figure 4.A.1 The budget line


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Present value and the budget constraintPresent value of lifetime resources: PVLR= y+ yf/(1+r) + a (4.A.2)

Present value of lifetime consumption: PVLC= c+ cf

/(1+r) (4.A.3)The budget constraint means PVLC= PVLRc+ cf/(1+r) = y+ yf/(1+r) + aHorizontal intercept of budget line is c= PVLR, cf= 0

What does the consumer want? Consumer preferences Utility = a persons satisfaction or well-being (indifference curve, IC) Graph a persons preference for current vs. future consumption using ICAn IC shows combinations ofcand cf that give the same utility (Fig. 4.A.2)A person is equally happy at any point on an IC Three important properties of ICs

Slope downward from left to right: Less consumption in one period

requires more consumption in the other period to keep utility unchangedICs that are farther up and to the right represent higher levels of utility,

because more consumption is preferred to lessICs are bowed toward the origin, because people have a consumption-

smoothing motive, they prefer consuming equal amounts in each periodrather than consuming a lot one period and little the other period



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Figure 4.A.2 Indifference curves


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The optimal level of consumption Optimal consumption point is where the budget line is tangent to an IC (Fig.

4.A.3)

Thats the highest IC that its possible to reachAll other points on the budget line are on lower ICs The Effects of Changes in Income and Wealth on Consumption and

Saving The effect on consumption of a change in income (current or future) or

wealth depends only on how the change affects the PVLRAn increase in current income (Fig. 4.A.4)

Increases PVLR, so shifts budget line out parallel to old budget line If there is a consumption-smoothing motive, both current and future

consumption will increase Then both consumption and saving rise because of the rise in current

incomeAn increase in future income

Same outward shift in budget line as an increase in current income

Again, with consumption smoothing, both current and future consumptionincrease Now saving declines, since current income is unchanged and current

consumption increasesAn increase in wealth

Same parallel shift in budget line, so both current and future consumptionrise

Again, saving declines, since crises and yis unchanged



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Figure 4.A.3 The optimal consumptioncombination

Fi 4 A 4


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Figure 4.A.4 An increase in income or wealth

A di 4 A A F l M d l f C ti d S i


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The permanent income theoryDifferent types of changes in income

Temporary increase in income: yrises and yf is unchanged

Permanent increase in income: Both yand yf rise

Permanent income increase causes bigger increase in PVLRthan atemporary income increase

So current consumption will rise more with a permanent income

increaseSo saving from a permanent increase in income is less than from

a temporary increase in income

This distinction between permanent and temporary income changeswas made by Milton Friedman in the 1950s and is known as the

permanent income theoryPermanent changes in income lead to much larger changes in

consumption

Thus permanent income changes are mostly consumed, whiletemporary income changes are mostly saved




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Consumption and Saving Over Many Periods: The Life-CycleModel

Life-cycle model was developed by Franco Modigliani andassociates in the 1950sLooks at patterns of income, consumption, and saving over an

individuals lifetimeTypical consumers income and saving pattern shown in Fig. 4.A.5Real income steadily rises over time until near retirement; at retirement,

income drops sharplyLifetime pattern of consumption is much smoother than the income

pattern In reality, consumption varies somewhat by age For example, when raising children, household consumption is

higher than average

The model can easily be modified to handle this and othervariationsSaving has the following lifetime pattern

Saving is low or negative early in working lifeMaximum saving occurs when income is highest (ages 50 to 60)Dissaving occurs in retirement


Fi 4 A 5 Lif l ti


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Figure 4.A.5 Life-cycle consumption,income, and saving

Fi 4 A 5 Lif l ti


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Figure 4.A.5 Life-cycle consumption,income, and saving (contd)



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Bequests and savingWhat effect does a bequest motive (a desire to leave an

inheritance) have on saving?Simply consume less and save more than without a bequest

motive

Ricardian equivalence

We can use the two-period model to examine Ricardianequivalence

The two-period model shows that consumption is changedonly if the PVLRchanges

Suppose the government reduces taxes by 100 in the current

period, the interest rate is 10%, and taxes will be increased by110 in the future period

Then the PVLRis unchanged, and thus there is no change inconsumption


Appendix 4 A: A Formal Model of Consumption and Saving


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Excess sensitivity and borrowing constraintsGenerally, theories about consumption, including the

permanent income theory, have been supported bylooking at real-world dataBut some researchers have found that the data show

that the impact of an income or wealth change isdifferent than that implied by a change in the PVLRThere seems to be excess sensitivity of consumption to

changes in current incomeThis could be due to short-sighted behavior

Or it could be due to borrowing constraintsBorrowing constraints mean people cant borrow as

much as they want. Lenders may worry that a consumerwont pay back the loan, so they won't lend




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If a person wouldnt borrow anyway, the

borrowing constraint is said to be nonbindingBut if a person wants to borrow and cant,

the borrowing constraint is bindingA consumer with a binding borrowing constraint

spends all income and wealth on consumptionSo an increase in income or wealth will be entirely

spent on consumptionThis causes consumption to be excessively

sensitive to current income changesHow prevalent are borrowing constraints?

Perhaps 20% to 50% of the U.S. populationfaces binding borrowing constraints




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The Real Interest Rate and theConsumption-Saving Decision

The real interest rate and the budget line(Fig. 4.A.6)When the real interest rate rises, one point

on the old budget line is also on the newbudget line: the no-borrowing, no-lending

pointSlope of new budget line is steeper



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The substitution effect

A higher real interest rate makes future consumptioncheaper relative to current consumption

Increasing future consumption and reducing currentconsumption increases saving

Suppose a person is at the no-borrowing, no-lending pointwhen the real interest rate rises (Fig. 4.A.7)

An increase in the real interest rate unambiguouslyleads the person to increase future consumptionand decrease current consumption

The increase in saving, equal to the decrease incurrent consumption, represents the substitutioneffect


Figure 4 A 6 The effect of an increase in


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Figure 4.A.6 The effect of an increase inthe real interest rate on the budget line

Figure 4 A 7 The substitution effect of an


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Figure 4.A.7 The substitution effect of anincrease in the real interest rate



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The income effectIf a person is planning to consume at the no-borrowing, no-lending point, then a rise in thereal interest rate leads just to a substitution

effectBut if a person is planning to consume at a

different point than the no-borrowing, no-lending point, there is also an income effect




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The intuition of the income effect

If the person originally planned to be a lender, therise in the real interest rate gives the person moreincome in the future period; the income effectworks in the opposite direction of the substitution

effect, since more future income increases currentconsumption

If the person originally planned to be a borrower,the rise in the real interest rate gives the person

less income in the future period; the income effectworks in the same direction as the substitutioneffect, since less future income reduces currentconsumption further



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The income and substitution effects together

Split the change in the budget line into two parts(Fig. 4.A.8)A budget line with the same slope as the new budget

line, but going through the original consumption point(BLint)

The substitution effect is shown by the change frombudget line BL1 to budget line BLint, with theconsumption point changing from point D to point P

The income effect is shown by the change from

budget line BLint to budget line BL2, with consumptionpoint changing from point Pto point Q




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The substitution effect decreases current

consumption, but the income effect increases currentconsumption; so saving may increase or decrease

Both effects increase future consumption

For a borrower, both effects decrease current

consumption, so saving definitely increases but theeffect on future consumption is ambiguous

The effect on aggregate saving of a rise in the realinterest rate is ambiguous theoretically

Empirical research suggests that savingincreases

But the effect is small

Figure 4 A 8 An increase in the real interest rate with


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Figure 4.A.8 An increase in the real interest rate withboth an income effect and a substitution effect

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