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acroeconomics The Multiplier Effect of Fiscal Policy

The Multiplier Effect of Fiscal Policy

We analyze the multiplier effect of fiscal policychanges inovernment expenditure and taxation.

he key result is that an increase in the government budget

eficit causes a proportional increase in consumption.

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Macroeconomics The Multiplier Effect of Fiscal

Keynesian Cross Macroeconomic Model

Consider a standard Keynesian cross macroeconomic mod

which production adjusts to equal demand. Consumption

demandc plus investment demandi plus government

expenditureg equals national income and producty,

c + i + g y.

Investment and government expenditure are exogenous.

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Government Budget Deficit

he government budget deficit is government expenditure g

minus taxest. Government expenditure refers to spending on

oods and services. Transfer paymentssocial security

enefits, unemployment benefits, welfare benefitstogether

ith the interest on government debt are classified as negative

xes.

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Disposable Income Versus National Incom

Disposable incomeydis after-tax income, national income

minus taxes,

ydy t.

We assume that consumption demand is an increasing func

c(yd)

of disposable income.

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Marginal Propensity to Consume

etm pcddenote the marginal propensity to consume out ofisposable income; an increase of disposable income by one

ollar raises consumption demand bym pcd. Let denote the

marginal tax rate, the increase in taxes when national income

ses by one dollar.

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Togetherm pcdand determinem pc, the marginal propen

to consume out of national income, the increase in

consumption demand when national income rises by one dIf national income rises by one dollar, then disposable inco

rises by 1; consequently consumption demand rises by

(1)mpcd= mpc.

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Numerical Example

onsider a numerical model. Suppose that the marginal tax rate

= 1/3, and the marginal propensity to consume out ofisposable income ism pcd= 9/10. If national income rises by

ne dollar, then disposable income rises by 2/3. Consumption

hen rises bym pc=9/102/3=3/5, the marginal propensity

o consume out of national income.

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The Multiplier Effect

and the Consumption Function

The results below are derived entirely from (1), (2), and (3

The first two relationships necessarily hold, as they are

accounting identities. Consequently the consumption

function (3) is the only behavioral relationship. As long as

consumption is determined solely by disposable income, th

results below must hold.

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The Effect of Fiscal Policy on Consumption

We work out the multiplier effect of a change in government

xpenditure and taxation. Let denote the change in a

ariable. If government expenditure changes by gand taxes

hange by t, then gtis the change in the government

udget deficit.

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Consumption and the Deficit

Below we derive the fiscal policy multiplier (8): the multip

effect on consumption of fiscal policy is simply that

consumption changes in proportion to the change in the de

If fiscal policy changes, but without any change in the defi

then consumption is unaffected. If fiscal policy changes an

deficit increases, then consumption rises in proportion.

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Mathematical Derivation

y (1), the change in consumption plus the change in

overnment expenditure equals the change in national income,

c +g= y, (4)

nce investment is exogenous.

y (2), the change in disposable income equals the change in

ational income minus the change in taxes,

yd= yt. (5)

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By (3), the change in consumption is the marginal propens

consume out of disposable income multiplied by the chang

disposable income,

c=m pcdyd.

Substituting from (5) into (4) eliminatesy:

c +g= yd+ t.

Next, eliminateydby substituting from (6):

c +g= c/mpcd+t.

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The Fiscal Policy Multiplier

olving for cthen gives our key result, the fiscal policy

ultiplier:

c= mpcd

1mpcd(gt). (8)

he change in consumption is proportional to the change in the

overnment deficit.

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The Balanced-Budget Multiplier

That thebalance-budget multiplierequals one is an

implication. Suppose that the government expenditure and

taxes both rise by one dollar, so that the government defici

unaffected. By (8), consumption is unaffected. Hence the

national income and product rises by only one dollar, but n

by more.

Although the extra one-dollar production to meet the addit

government demand does increase national income by one

dollar, the one-dollar rise in taxes offsets this increase.

Disposable income is unaffected, so consumption does not

change.14


The Multiplier for Government Expenditure

he fiscal multiplier is consistent with the standard Keynesian

multiplier theory. In the standard theory, an increase in

overnment expenditure has the multiplier effect

y= 1

1mpcg. (9)

ince the change in consumption is c= yg, therefore

c=

mpc

1mpc

g. (10)

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Numerical Example

Although one can show by algebra that the two alternate

expressions (8) and (10) for the multiplier are consistent, h

we just show consistency in a numerical example.

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We continue with the numerical model above. The marginal tax

ate is = 1/3, and the marginal propensity to consume out of

isposable income ism pcd= 9/10, so the marginal propensity

o consume out of national income is

mpc= (1)mpcd= 3/5.

uppose that government expenditure rises by one dollar.

y (9), national income rises by y=1/(13/5) =2 1/2;

hus consumption rises by 1 1/2.

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In the fiscal policy multiplier formula (8), the coefficient

multiplying the change in the deficit is

mpcd/(1mpcd) = (9/10)/(19/10) =9,

so an increase in the government deficit of only one dollar

would raise consumption by nine dollars, a large amount.

However, the increase in the deficit is small: as national inc

rises, taxes rise. The increase in taxes is the marginal tax ra

times the change in national income, t= (1/3)2 1/2=

almost as much as the increase in government expenditure

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he increase in the deficit is only gt=15/6=1/6.

sing (8), we evaluate

c=

mpcd

1mpcd

(gt) =9

1

6= 1

1

2,

hich is consistent with the standard multiplier.

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The Tax Multiplier

Let us consider the effect of a one-dollar cut in the level of

taxes: for any given income, the level of taxes falls by one

dollar, but the marginal tax rate stays constant. The tax cut

causes a multiplier process that raises national income and

product.

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Multiplier Process

nitially, the tax cut raises disposable income by one dollar,

hich raises consumption demand. Firms produce to meet

emand, so national product rises. National income equals

ational product, so national income necessarily rises by the

ame amount. Since national income is higher, consumption

emand increases. Firms produce to meet this additional

emand, so national product rises. National income rises by the

ame amount, which then induces a further increase in

onsumption demand. More demand causes more product,

mplying more income, and in turn yet more demand.

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The following sequence spells out the exact effects:

taxes down by one,

disposable income up, yd= 1

consumption demand up because income up, c1=m pcd

national product up by increase in demand, y1= c1national income up same as product, y1=mpcd

consumption demand up because income up, c2=m pc

product up by increase in demand, y2= c2income up same as product, y2=m pcdmpc

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onsumption demand up because income up, c3=m pcy2roduct up by increase in demand, y3= c3

ncome up same as product, y3=m pcdmpc2

c.

n each round of the multiplier process, the effect on national

ncome and product is less, because the marginal propensity to

onsume is less than one.

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Total Effect

The increase in consumption is the same as the increase in

national income and product. The total increase is sum of

round-by-round increases,

c= y

= y1+y2+y3+y4+

=m pcd+ mpcdmpc + mpcdmpc2 + mpcdmpc

3 +

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Infinite Geometric Sum

he total increase is an infinite geometric sum, an expression of

he form

a + ab + ab2

+ ab3

+ . . .=

a

1b .ere the first term isa=m pcd, and the ratio of successive

rms isb=m pc, so the overall effect on consumption and

ncome is

c= y= mpcd

1mpc. (11)

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Numerical Example

Using our numerical model, we show that the fiscal policy

multiplier (8) is consistent with the tax multiplier (11).

In the numerical model,m pcd= 9/10 andm pc=3/5, so

tax multiplier is

c= y=9

10

1 35=2

1

4.

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ince the tax cut causes national income to increase, taxes rise

y the marginal tax rate times the increase in national income,

/39/4=3/4.

he net decrease in taxes is the one-dollar tax cut less the

/4-dollar rise in taxes, 13/4=1/4. Substituting into (8)

ves

c=

mpcd

1mpcd

(t) =9

1

4=2

1

4.

hus the two multiplier formulas are consistent.

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The Crowding Out of Investment

Seeing one assumption in this analysis is faulty, some criti

have attacked the fiscal policy multiplier theory. They argu

one cannot take investment as exogenous. If the governme

budget deficit increases, this deficit must be financed.

Financing the deficit takes saving from the private sector,

which causes investment to decrease. Fiscal policy crowd

out investment.

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False Criticism

his criticism is, however, faulty. An increase in the

overnment deficit causes income to rise. As income rises,aving rises.

turns out that the increase in saving is exactlyequal to the

ncrease in the deficit. This extra saving finances the higher

eficit, so there is no reason why investment must be crowded

ut.

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We demonstrate this relationship. By definition, saving is

income minus spending. Private saving is disposable incom

minus consumption,s ydc. Rearranging expression (7above yields

gt= ydc s,

Thus the increase in the deficit exactly equals the change i

private saving, and this extra saving finances the deficit.

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