Download Chapter 8 - Dr. George Fahmy

Chapter 8
Fiscal Policy
Chapter Summary
1.
2.
3.
4.
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6.
7.
The imposition of taxes on consumers shifts the consumption line downward
since a tax increase causes less consumer spending at each level of output.
Government transfers to individuals are viewed as a negative tax. Thus, an
increase in government transfers shifts the consumption line upward since there
is more consumer spending at each level of output.
Government spending and taxes affect the location of the aggregate spending
line (C + I + Xn + G). An increase in government spending shifts the aggregate
spending line upward by the increase in government spending. An increase in
taxes shifts the aggregate spending line downward by the increase in taxes times
the MPC.
When an inflationary or recessionary gap occurs, government can initiate
changes in government spending and/or taxes––lassifled as a discretionary fiscal
policy and thereby alter the location of the aggregate spending line.
A change in government spending has the same multiplier effect upon
equilibrium output as does a similar change in investment spending. A change in
lump-sum taxes has a smaller multiplier effect upon equilibrium output than
does a similar change in government spending. The lump-sum tax multiplier is
–MPC/(l – MPC) or MPC(k).
An income tax (t) affects the value of the expenditure (a) and the lump-sum tax
multipliers (A,). When there is an income tax, the expenditure multiplier is
l / [1 – MPC + t(MPC)] and the lump-sum tax multiplier is –MPC/[l – MPC +
t(MPC)].
When output falls, government transfers (such as unemployment insurance)
increase and government tax receipts from income taxes decrease. Such
automatic changes in net tax revenues lessen economic fluctuations and are
classified as built-in stabilizers.
Important Terms
Action lag. Government does not respond quickly to a recessionary or inflationary
gap.
Built-in stabilizers. Automatic changes in net tax revenues that result from a change
in the level of output; built-in stabilizers moderate changes in aggregate spending
during an expansion or recession and thereby help stabilize output.
Discretionary fiscal policy. Government implements a change in government
spending and/or taxes to eliminate a recessionary or inflationary gap.
Income tax. A tax imposed upon the amount of income received.
Lump-sum tax. A fixed-sum tax imposed on individuals which is unrelated to the
amount of income received.
Net tax revenues. The net tax receipts of government, which equals gross tax
receipts less government transfers.
Tax multiplier. The multiplier effect on output of a change in lump-sum taxes. The
lump-sum tax multiplier is
-MPC/(l MPC) or -MPC(k) when there is no income tax.
Outline of Chapter 8: Fiscal Policy
8.1 Government Net Tax Revenues and the Consumption Function
8.2 Government Expenditures, Taxes, and the Level of Output
8.3 Discretionary Fiscal Policy
8.4 Fiscal Policy Multipliers
8.5 Built-in Stabilizers
8.6 Implementing Discretionary Fiscal Policy
8.1 GOVERNMENT NET TAX
CONSUMPTION FUNCTION
REVENUES
AND
THE
Tax revenues finance government expenditures and government transfer payments to
the private sector Government transfer payments can be viewed as a government
outlay or as a negative tax. (The latter view can be seen when we look at net tax
revenues as equal to the sum of gross tax revenues less transfer payments.) In the
model of economic activity presented here, (1) tax collections and transfer payments
occur between the government and individuals, and (2) net tax revenues consist of
income taxes plus lump-sum taxes less transfer payments. We shall assume that
lump-sum taxes and transfer payments are legislated; thus, they are unrelated to the
level of output. Net tax revenues fall when transfer payments increase, and rise when
greater per capita taxes are imposed. With respect to income tax receipts, net tax
revenues increase when output increases and more taxes are collected or when
government imposes a higher income tax rate. In Fig. 8-1, a decrease in transfer
payments, ceteris paribus, increases net tax revenues and shifts consumption line C1
downward to C2 ; the downward shift from C1 to C2 equals the increase in transfer
payments times the marginal propensity to consume. An increase in the income tax
rate shifts consumption line C1 downward to C3 and reduces its slope.
EXAMPLE 8.1. Suppose C = 0.90Yd (individuals consume 0.90 of their disposable
income). When there are no taxes and individuals receive an income equal to the
value of output (Yd = Y, since taxes equal 0), consumption is $90 and $126 when
output is $100 and $140, respectively. Consumption line C1 in Fig. 8-1 represents the
relationship of consumption and output in a no-tax economy. When a lump-sum tax
of $20 is introduced into this economy (Yd = Y – $20), consumption is $72 when
output is $100 [C = 0.90($100 - $20) = $72], and $108 when output is $140 [C =
0.90($140 - $20) = $108]. Consumption line C2 indicates the amount consumed at
each level of output when there is a $20 lump-sum tax. Note that the distance
between consumption line C1 and C2 is $18, which equals the $20 lump-sum tax times
the 0.90 marginal propensity to consume. An increase or decrease in lump-sum tax
revenues shifts the consumption function by the MPC times the change in lump-sum
tax revenues. When there is a 20% income tax rate, no lump-sum taxes, and
C = 0.90Yd (Yd = Y – 0.20Y), consumption is $72 when output is $100
[C = 0.90($l00 - 0.2{$l00}) = $72], and $100.80 when output is $140. C3 is the
consumption line when there is a 20% income tax rate. Note that consumption line C3
is less steeply sloped than consumption lines C1 and C2, for which there is no income
tax.
8.2 GOVERNMENT EXPENDITURES, TAXES, AND THE LEVEL
OF OUTPUT
Taxes reduce personal disposable income and therefore consumption and
aggregate spending, whereas government expenditures increase aggregate spending.
The influence of taxes and government expenditures upon aggregate spending is
shown in Fig. 8-2 in the shift of aggregate spending line (C + I + Xn + G). An
increase in net lump-sum tax revenues, ceteris paribus, shifts aggregate spending line
(C + I + Xn + G) downward to (C + I + Xn + G)', since higher taxes reduce consumer
disposable income and therefore consumer spending at each level of output. An
increase in government spending, ceteris paribus, shifts aggregate spending line (C +
I + Xn + G) upward to (C + l + Xn + G)". It therefore follows that the government can
alter the economy’s equilibrium level of output by changing its expenditures or net
tax revenues. Such governmental actions are classified as discretionary fiscal policy.
EXAMPLE 8.2. A $20 increase in investment spending or net exports, ceteris
paribus, shifts the aggregate spending a line (C + I + Xn + G)' in Fig. 8-3 upward to
(C + I + Xn + G)" and increases the equilibrium level of output $40. A $20 increase in
government spending, ceteris paribus, would also shift aggregate spending line (C + I
+ Xn + G)' in Fig. 8-3
upward $20 to (C + I + Xn + G)" and increase equilibrium
output $40. Thus, increased government expenditures can raise output when there is
unemployment because of inadequate private sector spending. Government
expenditures can be lowered when there is excessive private-sector spending.
EXAMPLE 8.3. Government expenditures inject spending into the circular flow,
whereas taxes represent a leakage from the circular flow. An increase in government
spending in Fig. 8-4 shifts injection line (I + X + G) upward to (I + X + G)', and the
equilibrium level of output increases from Y0 to Y1. An increase in taxes shifts
leakage line (S + M + T) upward to (S + M + T)', where it intersects injection line
(I + X + G) at I’2 which is below the initial Y0 level of output.
8.3 DISCRETIONARY FISCAL POLICY
Discretionary fiscal policy involves intentional changes in government spending
and/or net tax revenues in order to alter the level of aggregate spending. We have
already found that an increase in government spending and/or a decrease in lumpsum taxes shifts the aggregate spending line upward and raises the equilibrium level
of output, while a decrease in government spending and/or an increase in lump-sum
taxes shifts the aggregate spending line downward and lowers the equilibrium level
of output. The government can use discretionary fiscal actions to eliminate an
inflationary or recessionary gap.
EXAMPLE 8.4. Suppose there are only lump-sum taxes; the MPC is 0.80; the
aggregate spending line is (C + I + Xn + G) in Fig. 8-5; the equilibrium level of
output is $700; there is a $50 recessionary gap since full employment exists at the
$750 level of output. The $750 full-employment level is achieved by any of the
following discretionary fiscal actions which shift the aggregate spending line upward
to (C + I + X, + C)'.
Discretionary Policy A: Increase in Government Spending. A $10 increase in
government spending, ceteris paribus, shifts aggregate spending line (C + I + Xn +
G) upward $10 to (C + I + X,, + G)', and the economy reaches the $750 fullemployment level of output.
Discretional Policy B: Decrease in Lump-Sum Taxes. A $12.50 decrease in lump-sum
taxes reduces net lump-sum tax revenues $12.50 and shifts the consumption line
upward $10 (0.80 7 $12.50). The aggregate spending line (C + I + Xn + G) shifts
upward $10 to (C + I + Xn + C)', and the economy reaches the $750 full-employment
level of output.
Discretionary Policy C: increase in Government Transfer Payments. A $12.50
increase in government transfers reduces lump-sum tax revenues $12.50 (since some
tax receipts are returned to the private sector) and shifts the consumption line upward
$10 (0.80 x $12.50); the aggregate spending line (C + I + Xn + G) shifts upward $10
to C + I + Xn + G)', and the economy reaches the $750 full employment level of
output.
8.4 FISCAL POLICY MULTIPLIERS
A change in government expenditures or in lump-sum tax revenues has a
multiplier effect upon the equilibrium level of output. The size Of the multiplier
effect depends upon whether (1) there is a change in government spending or in net
lump-sum tax revenues, or (2) there is an income tax. In Example 8.4, a $10 increase
in government spending or a $12.50 decrease in net lump-sum tax revenues raises the
equilibrium level of output $50 for an economy in which there are no income taxes.
The value of the multiplier for the increase in government spending is 5 (Y/G =
$50/$10 = 5), while the value of the multiplier for the $12.50 decrease in net lumpsum tax revenues is –4 (Y/T = +$50/– $12.50 = –4). When there is no income tax,
a change in government spending has the same multiplier effect [k = 1/(1 MPC)] as
does a similar change in investment spending or net exports. The value of the
multiplier is smaller for changes in net lump-sum tax revenues; the tax multiplier (kt)
is – MPC(k) or – MPC/(l – MPC) for an economy with no income tax.
EXAMPLE 8.5. Suppose (1) there is a $60 recessionary gap since the equilibrium
level of output is $700 and the 1-employment level of output is $760; (2) the
government expenditure multiplier is 4 since the MPC is 0.75 and there is no income
tax [k = 1/(1 - MPC); k = 1/(1 – 0.75); k = 4]; and (3) the value of the net lump-sum
tax revenue multiplier is –3 since the MPC is 0.75 and there is. no income tax [kt =
–MPC(k); k1 = 0.75(4); kt = –3].
The $60 recessionary gap is eliminated and full-employment output is reached
by increasing aggregate spending $60. This is achieved by raising government
expenditures $15 or by decreasing net lump-sum tax revenues $20. The required $15
increase in government spending is found by substituting Y = +$60 and k = 4 into
the equation Y = k(G). The required $20 decrease in net lump-sum tax revenues is
found by substituting Y = +$60 and kt = –3 into the equation Y = kt(T).
An income tax reduces the value of both the expenditure and the lump sum tax
revenue multiplier since amount of taxes paid to government is directly related to
income earned. For example, when the income tax rate is 20% and personal income
increases $10, tax payments to the government rise $2 and personal disposable
income increases $8 rather than $10. Thus, an increase in personal income results in
smaller increments in induced consumption, and there for results in a smaller
multiplier effect. When there is an income tax, the equation for the expenditure
multiplier is k = 1/[1 – MPC + MPC(t)], where t is the income tax rate. The equation
for the lump-sum tax multiplier is kt = –MPC(k) or MPC/[l – MPC + MPC(t)].
EXAMPLE 8.6. The expenditure multiplier is 4 when the MPC is 0.75 and there is
no income tax: k = 1/(l – MPC); k = l/(1 – 0.75); k = 4. The expenditure multiplier is
2.5 when the MPC is 0.75 and the income tax rate (t) is 0.20: k = 1/[1 – MPC +
MPC(t)]; k = 1/[1 – 0.75 + 0.75(0.20)] k – 2.5. The tax multiplier is –3 when the
MPC is 0.75 and there is no income tax [kt = –MPC(k); kt = 0.75(4); kt = –3], and –
1.875 when the MPC is 0.75 and income tax rate is 0.20[kt = – MPC(k); kt = –
0.75(2.5); kt = –1.875].
A discretionary fiscal action has a smaller effect upon equilibrium output when
there is an income tax since an some tax reduces the value of the expenditure and the
lump-sum tax multiplier In Example 8.5, aggregate spending must increase $60 to
reach the full-employment level of output. This is achieved by a $15 increase in
government expenditures or a $20 decrease in net lump-sum tax revenues when there
is no income tax. However, when there is a 1% income tax rate, the expenditure
multiplier is 2.5, while the tax multiplier is 1.875. With an income tax rate of 20%,
government expenditures must increase $24 rather than $15 or net lump-sum tax
revenues must decrease $32 rather than $20 to raise aggregate spending $60.
8.5 BUILT-IN STABILIZERS
Personal income taxes and various government transfers automatically change
the level of net tax revenues when the economy moves away from (or toward) the
full-employment level of output. For example, government collects smaller revenues
from income taxes when output decreases; lump-sum tax revenues so fall when
output decreases because of increased government transfer payments to individuals in
the form of unemployment insurance benefits, food stamps, and other government
assistance programs. Because such automatic changes in net tax revenues, consumer
disposable income is not completely dependent on the level of output, consumer
spending is more stable over the business cycle, and the amplitude of economic
fluctuations is lessened.
EXAMPLE 8.7. Suppose the government guarantees that it will pay unemployed
members of the labor force one-third of their weekly income up to a maximum of
$150 per week for a period not to exceed six months. When economic activity falls
and people lose their jobs. government automatically pays these benefits to those who
have become unemployed. It therefore follows that government’s net tax revenues
fall during a recession because it is collecting less income tax revenue and it is
making a larger number of transfer payments to more unemployed individuals. Thus,
hen a recession occurs, there is not as large a decline in personal disposable income
as there would be if unemployment insurance benefits and other social welfare
programs did not exist. During a recession, unemployment insurance payments
moderate the decline in consumers’ disposable income, the decline in aggregate
consumption, and the depth id duration of a recession.
EXAMPLE 8.8. Suppose equilibrium output is initially $500 billion and lump-sum
tax revenues are $50 billion. he following situations show the effect that a $20 billion
decrease in investment and net export spending has upon equilibrium output when (1)
there are no built-in stabilizers (2) there in an income tax, and (3) there is an income
tax and unemployment insurance.
Situation I: No Built-in Stabilizer Suppose the MPC is 0.75 and there are no
income taxes or entitlement programs such as unemployment insurance. A $20
billion decrease in investment and net export spending decreases the equilibrium
level of output by $80 billion, calculated as follows: The expenditure multiplier is 4
since k = 1/(1 – MPC); k = 1/(1 – 0.75); k = 4. The change in output is –$80 billion
since Y = k[(I +X)1; Y = 4(–$20 billion); Y = –$80 billion.
Situation II: An Income Tax as a Built-in Stabilizer Suppose the MPC is 0.75,
the income tax rate is 20%, and there are no entitlement programs such as
unemployment insurance. Since the multiplier is now 2.5, a $20 billion decrease in
investment and net export spending lowers equilibrium output $50 billion, calculated
as follows: The expenditure multiplier is 2.5 since k = 1/[l – MPC + t(MPC)1;
k = 1/(1 – 0.75 + 0.15); k = 2.5. The change in output is –$50 billion since Y =
k[I + X]; Y = 2.5(–$20 billion): Y = –$50 billion.
Situation III: An Income Tax and Unemployment Insurance as Built-in
Stabilizers. Suppose the MPC is 0.75, the income tax rate is 20%, and unemployment
insurance payments increase $10 billion when aggregate spending falls $30 billion. A
$20 billion decrease in investment and net export spending is accompanied by a $10
billion increase in government transfers because of the decline in output. Equilibrium
output falls $31.25 billion, calculated as follows:
The expenditure multiplier is 2.5. Y = k(I + X) + –MPC(k)(T); Y = 2.5(–$20
billion) + –0.75(2.5)(–$10 billion); Y = –$50 billion + $18.75 billion; Y = -$31.25
billion.
8.6 IMPLEMENTING DISCRETIONAL FISCAL POLICY
Since discretionary changes in tax revenues and government expenditures have a
multiplier effect upon equilibrium output, it would appear that government has the
ability to maintain full-employment output by manipulating its net tax revenues
and/or spending. Fiscal policy, however, is not as easily implemented or as successful
as our analysis here suggests. Suppose a recessionary gap exists. Will Congress and
the administration agree on an immediate course of action? In reality, an action lag is
likely to occur because of conflicting priorities. For example, some individuals may
advocate increased government expenditures on public goods, such as the rebuilding
of roads, bridges, or water lines, while others may prefer government expenditures on
services such as public education. Another group may advocate expanded welfare
services, or reduced tax rates for middle-income workers, or a lower capital gains tax
rate to encourage investment spending. And once a fiscal plan of action is reached
and implemented, will Congress and the administration be prepared to scale down or
eliminate any of these stimulative fiscal measures should the fiscal stimulus
eventually become excessive?
Besides political priorities, we must also recognize that economic activity exists
in a dynamic, changing environment, where other variables may change. Thus, while
a fiscal stimulus may close a recessionary gap and bring the economy to full
employment, ceteris paribus, it is possible that investment and/or net export spending
may increase after the fiscal stimulus is implemented, which would result in an
inflationary gap. (See Example 8.9.) In addition, economists are uncertain about the
output level at which full employment exists and have been unable to establish
precise values for multipliers for the U.S. economy. Lastly, many economists believe
that aggregate supply is positively sloped rather than horizontal as output approaches
its full-employment level.
EXAMPLE 8.9. Suppose the equilibrium level of output is $500 billion, the
expenditure multiplier is 2.5, and the full-employment level of output is $550 billion.
Policymakers have agreed to increase government expenditures on the infrastructure
in selected cities by $20 billion to close the recessionary gap. Equilibrium output is
expected to increase $50 billion as a result of this fiscal stimulus, which would bring
output to its full-employment level. Suppose, however, that shortly after the fiscal
stimulus is passed by Congress and signed into law, the U.S. dollar depreciates 10%
and U.S. exports rise. Aggregate spending is now excessive; government must now
implement a fiscal action which reduces aggregate spending in order to avert an
increase in the price level. Either taxes must be increased or government spending
reduced.
Solved Problems
GOVERNMENT NET TAX REVENUES AND THE
CONSUMPTION FUNCTION
8.1.
Why is a government transfer payment considered a negative tax?
There are numerous sources of government revenues: personal and
corporate income taxes, consumption taxes (e.g.. a sales tax), import duties,
inheritance taxes, etc. The majority of tax revenues come from those who have
the ability to pay. i.e., taxes are imposed upon those who earn income and
those who possess wealth. Some individuals in a society have little or no
income and wealth. Government makes money transfers to such economically
disadvantaged individuals, in the form of unemployment insurance, social
security payments, and various government assistance programs. Government
transfers are a negative tax since government is making payments to
(transfers), rather than collecting revenues from. some individuals in the
economy.
8.2.
What is the difference between a lump-sum tax and an income tax?
A lump-sum tax is a fixed-sum tax that is unrelated to income. An income
tax is related directly to earned income. In the case of a proportional income
tax the government collects a fixed percent of income earned, while for a
progressive income tax the rate of taxation increases with the level of income.
Lump-sum taxes and proportional and progressive income taxes are illustrated
in Fig. 8-6. Note that lump-sum taxes remain at $1000 as income increases
from $10,000 to $11,000. When there is a 10%. proportional income tax rate,
tax payments increase from $1000 to $1100 as income increases from $10.000
to $11,000. When the tax rate is 10% on the first $10,000 earned and 20% on
income greater than $10.000, tax payments increase from $1000 to $1200
when income increases from $10,000 to $11 000
8.3.
Suppose the equation for consumer spending is C = $10 billion + 0.75Y4.
(a) Find C when there are no taxes or transfers and output is $800 billion and
$840 billion.
(b) Find C when there is a $40 billion lump-sum tax and output is $800 billion
and $840 billion.
(c) Find C when there is a 20% income tax and output is $800 billion and $840
billion.
(d) Plot the consumption and output levels calculated in (a), (b), and (c), and
label them C1, C2, and C3.
(e) What effect do lump-sum and income taxes have upon the consumption
line?
(a) Since disposable income (Yd) equals the income (Y) earned in producing
output (Y) when there are no taxes and transfers, the consumption
equation can be stated as C = $10 billion + 0.75Y. C = $610 billion when
Y = $800 billion, and $640 billion when Y = $840 billion.
(b) The consumption equation is now stated as C = $10 billion + 0.75(Y - $40
billion) when there is a $40 billion lump-sum tax. since Y, now equals Y $40 billion. C = $580 billion when Y = $800 billion. and $610 billion
when Y = $840 billion.
(c) The consumption equation is now stated as C = $10 billion + 0.75(Y 0.20Y) when there is a 20% income tax, since Yd now equals Y - t(Y).
where the decimal value for t of 20% is 0.20. Thus, C = $490 billion when
Y = $800 billion, and $514 billion when Y = $840 billion.
(d) See Fig. 8-7.
(e) Consumption line C1 shifts downward $30 billion to C2 when a $40 billion
lump-sum tax is added. The $30 billion downward shift from C1 to C2
equals the 0.75 MPC times the $40 billion lump-sum tax. When a 20%
income tax is added consumption line C1 shifts downward to C3 and
becomes less steeply sloped.
8.4.
what happens to a positively sloped consumption line when there is
(a) A $20 increase in lump-sum taxes ceteris paribus?
(b) A $20 increase in government transfers, ceteris paribus?
(c) A decrease in the income tax rate. ceteris paribus?
(a) There is a parallel downward shift of the consumption line equal to the $20
increase in lump-sum takes times the MPC.
(b) There is a parallel upward shift of the consumption line equal to the $20
increase in government transfers times the MPC.
(c) The consumption line shifts upward and becomes more steeply sloped.
GOVERNMENT EXPENDITURES, TAXES, AND THE LEVEL Of OUTPUT
8.5.
How do the following events affect a (C + I + Xn + G) aggregate spending line?
(a) A $15 increase in government spending.
(b) A $10 decrease in investment spending.
(c) A $15 decrease in net tax revenues when the marginal propensity to
consume is 0.80.
(a) The aggregate spending line shifts by G, the amount of the change in
government spending. In this case there is a corresponding $15 upward
shift of the aggregate pending line.
(b) Changes in investment shift the aggregate spending line by I. Here, there
is a $10 downward shift of the aggregate spending line.
(c) Changes in lump-sum taxes shift the aggregate spending line by
–MPC(T). Since net tax revenues decrease $15, there is a $12 upward
shift of the aggregate spending line [$12 = -0.80(-$15)].
8.6.
(a) What happens to a (C + I + Xn +G) aggregate spending line when there is
a $10 decrease in investment spending and a $10 increase in government
spending, ceteris paribus?
(b) How can government spending be used to stabilize aggregate spending?
(a) There is no shift (change) of the aggregate spending line since the $10
decrease in investment is exactly offset by the $10 increase in government
spending.
(b) Government spending can be changed to stabilize aggregate spending to
offset increases or decreases in private-sector spending. For example,
government expenditures could be increased when investment pending
decreases as in part (a); it follows that government expenditures would
need to decrease when private-sector spending increases.
8.7.
In a closed-economy model where there arc no imports or exports, the leakageinjection approach to equilibrium output requires that leakages (household
saving plus taxes) equal injections (investment plus government expenditures).
(a) Why are taxes classified as a leakage and government spending as an
injection?
(b) At the equilibrium level of output of $580 in Fig. 8-S, leakages (S + T) of
$60 equal injections (I + G) of $60. When the MPC is 0.80, what effect
does the following have upon the equilibrium level of output: (1) a $12
increase in government spending? (2) a $15 decrease in lump-sum taxes?
(a) When government imposes taxes and does not spend these incremental
tax revenues, payments made in producing output are not returned to the
business sector That is, there is a leakage from the circular flow just as
there is when individuals save some of their disposable income.
Government expenditures inject spending into the circular flow in the
same way that investment does.
(b) A $12 increase in government expenditures shifts the injection line (I + G)
in Fig. 8-8. upward $12 to (I + G)' ; the equilibrium level of output
increases $60, from $580 to $640. A $15 decrease in lump-sum taxes
shifts the leakage line (S + T) downward $12 to (S + T)' [Lump-sum
tax changes shift the leakage line by –MPC(T)––in this situation by
–0.80(–$15)]; (I + G) and (S + T)' intersect at the $640 output level. and
the equilibrium level of output increases from $580 to $640.
DISCRETIONARY FISCAL POLICY
8.8
Suppose there is full employment at the $600 level of output and the MPC is
0.80.
(a) Does the aggregate spending line (C + I + Xn + G) in Fig. 8-9 depict the
existence of an inflationary or recessionary gap?
(b) What discretionary fiscal action can government implement to close this
gap?
(c) What discretionary fiscal action is needed when investment spending
decreases $5?
(a) There is a $60 inflationary gap since the equilibrium level of output is $660
and full-employment output is $600.
(b) Government spending should be decreased $12 since the necessary
decrease in aggregate spending is $60 and the multiplier is 5 [Y = k(G);
–$60 = 5(G); G –$12]. An alternative fiscal action is a $5 increase in
lump-sum taxes since the tax multiplier is -4 (Y = kt(T); -$60 = 4(T);
T = +$15].
(c) The inflationary’ gap is $35 rather than $60 since the $5 decrease in
investment spending lowers aggregate spending $25. To close the smaller
inflationary gap, lump-sum taxes need to be increased $8.75. or
government expenditures need to be reduced $7.
8.9.
Suppose full-employment output is $1300; C = $10 + 0.80 Yd; I = $150; Xn =
$50; G = $150; Yd = Y - T, where lump-sum taxes (T) equal $150.
(a) Find the equilibrium level of output by equating output (Y) with aggregate
spending (C + I + Xn + G). How is the government financing its
expenditures?
(b) Is there an inflationary or recessionary gap?
(c) What change in government spending is needed to bring output to its fullemployment level flow are government expenditures being financed after
this change in government spending?
(a) The consumption equation is C = $10 + 0.80(Y - $150) since lump-sum
taxes equal $15O. The equilibrium level of output can be determined as
follows:
Y = C + I + Xn + G
Y = $10 +0.80(Y - $150) + $150 +$50 + $150
Y – 0.80Y = $360 - $120
0.20Y = $240
Y = $240/0.20 = $1200
Government expenditures of $150 are being financed by the $150 collected
from lump-sum taxes.
(b) There is a recessionary gap since equilibrium output is $100 below the lullemployment level of output.
(c) Government spending should be increased $20 to bring output to its fullemployment level [Y k(G); $l00 = 5(G); G = $20]. The government
is now spending $170 and collecting $150 in lump-sum taxes. The $20
government deficit is financed by borrowing $20, i.e., the government is
borrowing the additional $20 saved by consumers.
8.10. Figure 8-10 illustrates a closed economy with a full-employment level of
output of $800; the MPC equals 0.80, the leakage line is (S + T)', and the
injection line is (I + G)'.
(a) Is there an inflationary or recessionary gap?
(b) What change in government spending is needed to bring output to its full
employment level?
(c) What happens to the leakage and injection lines as a result of this fiscal
action?
(a) There is a recessionary gap since the $700 equilibrium level of output is
below the $800 full-employment level of output.
(b) Government spending must increase $20 since Y = k(G); $100 = 5(G).
and G = $20. (The multiplier is 5 since the MPC is 0.80.)
(c) There is no change in the (S + T)' leakage line. The injections line (I + C)'
shifts upward $20 to (I + G)" so that leakages equal injections at the $800
level of output.
8.11. What effect will each of the following events have upon the equilibrium level
of output?
(a) An increase in lump-sum taxes, ceteris pa rib its.
(b) An increase in government spending, ceteris paribus,
(c) An equal increase in government spending and lump-sum taxes. ceteris
paribus.
(a) An increase in lump-sum taxes reduces consumer saving and spending A
decrease in consumer spending would result in a lower level of output.
(b) Increased government spending raises aggregate spending and therefore the
level of output.
(c) The multiplier effect of a change in taxes is less than the multiplier effect of
a change in government spending. Since there is an equal increase in
lump-sum taxes (which reduces spending) and government spending
(which increases spending), there should he a net increase in the level of
output.
FISCAL POLICY MULTIPLIERS
8.12. Suppose the equilibrium level of output is 5700, consumption is $570,
investment is 570, government spending is $60, lump-sum taxes equal $60. and
there is no income tax.
(a) Find the lump-sum tax and expenditure multipliers when the MPC is 0.80.
(b) What effect does a $10 increase in government spending have upon the
equilibrium level of output?
(c) Find the change in consumption and saving as a result of the $10 increase
in government spending.
(d) How is government paying for its expenditures before and after the $10
increase in government spending?
(e) Suppose lump-sum taxes are increased $10 to finance the $10 increase in
government spending. What effect does an equal increase in government
spending and taxes have upon the equilibrium level of output?
(a) when the MPC is 0.80 and there is no income tax. the tax multiplier is -4
and the expenditure multiplier is 5[kt = –MPC/(1 - MPC), kt = -0.80/(l 0.80), kt = -0.80/0.20 -4]; [k = 1/(1 - MPC), k = 1/(1 - 0.80). k = 1/0.20 =
5].
(b) The equilibrium level of output increases $50 (Y = k(G): Y = 5($10) =
$50).
(c) Since the MPC is 0.80 and the NIPS is 0.20.80% of the increase in income
is consumed. while 20% of the increase in income is saved. Thus,
consumption increases $40 while saving increases $10.
(d) Government expenditures are equal to lump-sum tax revenues before the
$10 increase in government spending. With no change in lump-sum tax
revenues. government expenditures exceed lump-sum taxes by $10 after
the $10 increase in government spending. There is a $10 deficit which is
financed by her-rowing the additional $10 saved by individuals.
(e) An increase in lump-sum taxes lowers aggregate spending. whereas an
increase in government expenditures raises aggregate spending. Since the
lump-sum multiplier is smaller than the expenditures multiplier, the $10
increase in lump-sum axes and government spending raises the
equilibrium level of output $10[Y = k(G) + kt(T); Y = 5($10) + (4)($l0) = + $10].
8.13. (a) Find the expenditure and lump-sum tax multipliers when there is no
income tax and the MPC is (1)0.50, (2)0.75. and (3)0.90.
(b) What is the relationship of the lump-sum tax and expenditure multiplier?
(a) The equation for the expenditure multiplier is k = 1/(1 - MPC) when there is
no income tax. The expenditure multiplier is (1)2 when the MPC is
0.50(2)4 when the MPC is 0.75, and (3)10 when the MPC is 0.90. The
equation for the lump-sum tax multiplier is kt = -MPC(k), or -MPC/(1 -
MPC) when there is no income tax. The lump-sum tax multiplier is (1) - 1
when the MPC is 0.50 (2) -3 when the MPC is 0.75, and (3) -9 when the
MPC is 0.90.
(b) The lump-sum tax multiplier is always smaller than the expenditure
multiplier. When there is no income tax. the lump-sum tax multiplier is
always negative and one less than the expenditure multiplier.
8.14. Suppose there is a $50 recessionary gap. the MPC is 0.80, and there is no
income tax.
(a) Find the necessary change in (1) government spending or (2) lump-sum
taxes to bring output to its full-employment level.
(b) Suppose tax revenues currently equal government expenditures. Can a
fiscal action he initiated which brings output to its full-employment level
without incurring a deficit, i.e., an action whereby there is an equal
change in lump-sum taxes and government spending?
(c) Why might the fiscal measures in part (a) be preferable to the equal
change in taxes and government spending in part (b)?
(d) Which fiscal action is preferable: a change in government spending or a
change in lump-sum taxes?
(a) Output must increase $50 to close the recessionary gap.
(1) Government spending must increase $10 since kG = Y ; 5G =
$50; G = $10.
(2) Lump-sum taxes must be lowered $12.50 since ktT = Y ; -4T =
$50; T = -$12.50.
(b) A $50 increase in government expenditures and a $50 increase in lumpsum taxes raise output $50: Y = kG + ktT and thus $50 = 5G + -4T;
and when G must equal T. substituting G for T we have $50 = 5G
+ -4G and $50 = G.
(c) An equal change in government spending or taxes requires a larger
expansion in government taxes anti expenditures than does a change in
government spending or taxes. which results in a budget deficit.
Assuming that we wish to achieve full employment without an increase in
taxes. a tax cut and/or an increase in government spending are the most
viable policy alternatives.
(d) A tax cut returns funds to the private sector and expands consumer
spending, while an increase in government spending increases the size of
the public section There should be increased government spending when
there 5 a recognized need for increased public-sector goods.
8.15. (a) Find the value of the expenditure multiplier when the MPC is 0.80 and the
income tax rate is (1) 0.10, (2)0.25, and (3)0.50.
(b) what happens to the value of the expenditure multiplier when the income
tax rate is increased?
(c) suppose there is a 5100 recessionary gap. What change in government
spending, is needed to bring output to its full-employment level when the
income tax rate is (1) 0.10, (2)0.25, and (3)0.50?
(a) The equation for the expenditure multiplier is 1/[1 - MPC + (t) MPC when
there is an income tax. The value of the expenditure multiplier is (1)3.57
when the income tax rate is (1) 0.10, (2) 0.25, and (3) 1.67 when the
income tax rate is 0.50,
(b) An increase in the income tax rate reduces the value of the expenditure
multiplier.
(c) The required increase in government expenditures is Found by solving the
equation Y = kG for G. substituting $100 for Y. Using the
multipliers determined in part (b) we find that government spending must
increase (1) $28.0l when [he income tax rate is 0.10,(2)$40 when the
income tax rate is 0.25, and (3) $59.88 when the income tax rate is 0.50.
BUILT-IN STABILIZERS
8.16. why are government’s net tax revenues directly related to the level of output?
Net tax revenues, the sum of tax revenues less government transfers. are
directly related to the level of output because of income taxes and government
transfer programs. Income tax revenues increase with output since individuals
and corporations have larger income flows and therefore pay more taxes to
government; likewise. income tax revenues fall when there is a decrease in the
level of output. Government transfer payments decline as output increases. and
rise as output falls More government assistance is provided when the level of
output falls. since more individuals become eligible for unemployment
insurance, food stamps. Medicaid. And other welfare payments. Such transfer
payments decline as the economy recovers and more individuals obtain gainful
employment. Therefore. net tax revenues decrease when output declines and
increase when output rises.
8.17. Suppose investment spending decreases, ceteris paribus.
(a) what should happen to the levels of output and of employment?
(b) What should happen to net tax revenues when the level of output declines
and there is a federal program of unemployment insurance for
unemployed members of the labor force?
(c) What should happen to income tax revenues when the output level
declines?
(d) Why are income taxes and unemployment insurance classified as built-in
stabilizers?
(a) A decrease in investment spending shifts the aggregate spending tine
downward and lowers the equilibrium level of output. Since employment
is tied directly to the level of output, larger number of the labor force will
be unemployed.
(b) Unemployment compensation is paid to members of the labor force when
they become unemployed and are unable to find another job. Thus. when
a decrease in investment spending causes equilibrium out-put to fall and
unemployment to increase. net tax revenues decline as a result of
automatic increases in unemployment insurance transfer payments made
to those who have lost their jobs.
(c) Since output is falling, government receives less income tax revenues.
(d) A change in output results in an automatic change in tax receipts and
transfers which dampen the expanding or contracting effect of spending
changes; i.e.. some fiscal policy is automatic or built in. The decrease in
output results in lower net tax revenues since less income taxes are
collected and more transfer payments are made to a larger number of
unemployed individuals. Such decreases in net tax revenues are automatic
and do not require Congressional approval.
IMPLEMENTING DISCRETIONARY FISCAL POLICY
8.18. (a) Since tax revenues are impacted by built-in stabilizers, would it be
advisable to support a proposal to balance the budget annually?
(b) Would it be advisable to have a balanced budget over the business cycle?
(a) A requirement that the federal budget balance annually would aggravate
inflationary and recessionary situations. For example. tax revenues
automatically fall in a recession due to built-in stabilizers. If government
spending were cut at the same time as this decrease in tax revenue, the
equal decreases in taxes and government spending would have a negative
effect upon an already contracting economy. Similarly, tax revenue
increases during an economic expansion would necessitate additional
government spending to keep the budget in balance, which could result in
excessive aggregate spending and therefore inflation. Given the
procyclical nature of net tax revenues. an annually balanced budget would
likewise be procyclical and thereby create greater fluctuations in the level
of economic activity.
(b) A proposal to balance the budget over the business cycle overcomes the
disadvantages of an annually balanced budget by allowing for deficits
during contractions, surpluses during expansions, and balancing the
budget over the business cycle. Budget deficits during periods of rising
unemployment are counter-cyclical because the decline in aggregate
spending is offset in pan by a fall in tax revenues; surpluses during an
economic expansion dampen the increase in aggregate spending and
thereby reduce inflationary pressures. balancing the budget over the
business cycle. while appealing may not be practical. Recession and
inflationary gaps are not necessarily of the same magnitude and duration.
so it would be difficult to ensure that tax receipts will equal government
expenditures during each complete business cycle.
Multiple Choice Questions
1.
When there is an increase in lump-sum taxes, the consumption function
(a) Shifts upward by the increase in taxes, ceteris paribus,
(b) Shifts downward by the increase in taxes, ceteris paribus,
(c) Shifts upward by the MPC times the increase in taxes. ceteris paribus.
(d) Shifts downward by the MPC times the increase in taxes, ceteris paribus.
2.
Which of the following statements is true?
(a) An increase in lump-sum taxes increases personal disposable income,
ceteris paribus.
(b) A decrease in welfare payments increases personal disposable income,
ceteris paribus.
(c) An increase in social security payments increases personal disposable
income, ceteris paribus.
(d) An increase in the income tax rate increases personal disposable income,
ceteris paribus.
3.
An increase in government spending, ceteris paribus, shifts the aggregate
spending line
(a) Upward by the increase in government spending,
(b) Downward by the increase in government spending,
(c) Upward by the increase in government spending times the expenditure
multiplier,
(d) Downward by the increase in government spending times the expenditure
multiplier.
4.
In the leakages-injection approach to income determination, an increase in
lump-sum taxes, ceteris paribus, shifts
(a) the investment plus government spending line upward,
(b) the investment plus government spending line downward,
(c) the saving plus taxes line to the right,
(d) the saving plus taxes line to the left.
5.
An inflationary gap can be eliminated by
(a) equal increases in net tax revenues and government spending,
(b) an increase in government spending and a decrease in lump-sum taxes,
(c) equal decreases in net tax revenues and government spending.
(d) a decrease in lump-sum taxes.
6.
Suppose the full-employment level of output is $680, the equilibrium level of
output is $600, the MPC is 0.80, and there is no income tax. Full-employment
output can be achieved by a $16 increase in government spending or which of
the following changes in net lump-sum tax revenues?
(a) A $20 decrease,
(b) A $20 increase,
(c) A $l6 increase.
(d) A l6 decrease.
7.
Suppose the full-employment level of output is $680, the equilibrium level of
output is $600, the MPC is 0.80. and there is a 0.25 income tax. Fullemployment output can be achieved by a
(a)
(b)
(c)
(d)
8.
$20 increase in government spending,
$25 increase in government spending,
$30 increase in government spending.
$32 increase in government spending.
which of the following situations results in a $50 increase in the equilibrium
level of output when the MPC is 0.80 and there is no income tax?
(a) A $10 increase in both net lump-sum tax revenues and in government
spending,
(b) A $12.50 increase in both net lump-sum tax revenues and in government
spending.
(c) A $12.50 increase in net lump-sum tax revenues and a $30 increase in
government spending,
(d) A $12.50 increase in net lump-sum tax revenues and a $20 increase in
government spending.
9.
A discretionary fiscal action involves
(a) automatic changes in net tax revenues that result from the income tax
structure,
(b) payment of unemployment insurance,
(c) a Congressionally mandated change in the level of government spending or
net tax revenues,
(d) payment of social security to retired individuals.
10. Built-in stabilizers are
(a) discretionary fiscal actions available to the President,
(b) increased government spending on public works projects,
(c) a change in the income tax rate,
(d) changes in net tax revenues that are the result of a change in the level of
economic activity.
True or False Questions
11. An increase in the income tax rate shifts the consumption tine downward and
makes the consumption line more steeply sloped.
12. Fiscal policy refers to any change in government tax revenue and/or in
government spend-mg.
13. Net tax revenues fall when a decrease in economic activity results in automatic
increases in tax payments.
14. When there is no income tax and the MPC is 0.80, a $10 increase in transfer
payments shifts the aggregate spending line upward by $8.
15. when there is no income tax and the MPC is 0.75, a $10 decrease in net tax
revenues results in a $30 increase in the equilibrium level of output.
16. An increase in taxes, ceteris paribus, shifts the leakage line (S + M + T)
rightward, which results in an increase in the equilibrium level of output.
17. A managed change in government spending and/or tax revenue is a discretionary
fiscal policy.
18. When the MPC is 0.75 and the income tax rate is 0.20, the lump-sum tax
multiplier is -3.
19. when the MPC is 0.75 and the income tax rate is 0.20, a $10 increase in
government spending, ceteris paribus. increases the equilibrium level of output
$30.
20. The availability of food stamps is an example of a discretionary fiscal action.
Answers to Multiple Choice and True or False Questions
1.
2.
3.
4.
5.
(d)
(c)
(a)
(a)
(c)
6.
7.
8.
9.
10.
(a)
(d)
(d)
(c)
(d)
11.
12.
13.
14.
15.
(F)
(T)
(F)
(T)
(T)
16.
17.
18.
19.
20.
(F)
(T)
(F)
(F)
(F)