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TA BL E 1
Real Consumer Spending




C
The Effects of an Income Tax on the
Consumption Schedule

(1) (2) (3) (4)
Variable tax
increase
Gross Disposable
Domestic Income
Product Taxes (GDP minus Taxes) Consumption
$ 900 $3,600
$4,500 $3,000
1,000 4,000
5,000 3,300
1,100 4,400
5,500 3,600
Real GDP 1,200 4,800
6,000 3,900
1,300 5,200
6,500 4,200
1,400 5,600
7,000 4,500
1,500 6,000
7,500 4,800
Figure 9 illustrates the second reason why the dis- NOTE: Figures are in billions of dollars per year.
tinction between fixed and variable taxes is important.
This diagram shows two different consumption lines. Notice that each $500 billion increase in GDP in
C1 is the consumption schedule used in previous chap- Table 1 leads to a $300 billion rise in consumer spend-
ters; it reflects the assumption that tax collections are ing. Thus, the slope of line C2 in Figure 9 is $300/$500,
the same regardless of GDP. C2 depicts a more realistic or 0.60, as we observed in the chapter. But in our



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Part 3
236 Fiscal and Monetary Policy



earlier example in Chapter 9, consumption rose by TA BL E 3
$300 billion each time GDP increased $400 billion” Total Expenditure Schedule with a 20 Percent Income Tax
making the slope $300/$400, or 0.75. (See the steeper
(1) (2) (3) (4) (5) (6)
line C1 in Figure 9.) Table 2 compares the two cases ex-
Gross Total
plicitly. In the Chapter 9 example, taxes were fixed at
Domestic Government Expenditures
$1,200 billion and each $400 billion rise in Y led to a C1I1G1
Product Consumption Investment Purchases Net Exports
$300 billion rise in C”as in the left-hand panel of Y C I G (X 2 IM) (X 2 IM)
Table 2. But now, with taxes variable (equal to 20 per-
$4,500 $3,000 $900 $1,300 $5,100
2$100
cent of GDP), each $500 billion increment to Y gives 5,000 3,300 900 1,300 5,400
2100
rise to a $300 billion increase in C”as in the right- 5,500 3,600 900 1,300 5,700
2100
hand panel of Table 2. 6,000 3,900 900 1,300 6,000
2100
6,500 4,200 900 1,300 6,300
2100
7,000 4,500 900 1,300 6,600
2100
TA BL E 2 7,500 4,800 900 1,300 6,900
2100
The Relationship between Consumption and GDP

previous chapters, full employment may occur above
With Fixed Taxes With a 20 Percent
(T 5 $1,200) Income Tax or below Y 5 $6,000 billion. If it is below this level, an
(from Table 1)
(from Table 1, Chapter 9) inflationary gap arises. Prices will probably start to
Y C Y C rise, pulling the expenditure schedule down and re-
ducing equilibrium GDP. If it is above this level, a re-
$4,800 $3,000 $4,500 $3,000
5,200 3,300 5,000 3,300 cessionary gap results, and history suggests that
5,600 3,600 5,500 3,600 prices will fall only slowly. In the interim, the econ-
6,000 3,900 6,000 3,900
omy will suffer a period of high unemployment.
6,400 4,200 6,500 4,200
In short, once we adjust the expenditure schedule
6,800 4,500 7,000 4,500
for variable taxes, the determination of national in-
7,200 4,800 7,500 4,800
Line C1 in Figure 9 Line C2 in Figure 9 come proceeds exactly as before. The effects of govern-
ment spending and taxation, therefore, are fairly
straightforward and can be summarized as follows:
These differences sound terribly mechanical, but Government purchases of goods and services add to
the economic reasoning behind them is vital to under- total spending directly through the G component of
standing tax policies. When taxes are fixed, as in line C 1 I 1 G 1 (X 2 IM). Higher taxes reduce total spend-
C1, each additional dollar of GDP raises disposable in- ing indirectly by lowering disposable income and thus
come (DI) by $1. Consumer spending then rises by reducing the C component of C 1 I 1 G 1 (X 2 IM). On
$1 times the marginal propensity to consume (MPC), balance, then, the government™s actions may raise or
which is 0.75 in our example. Hence, each ad-
ditional dollar of GDP leads to 75 cents more FIGURE 10
spending. But when taxes vary with income, Income Determination with a Variable Income Tax
each additional dollar of GDP raises DI by less
than $1 because the government takes a share 8,000 45°
in taxes. In our example, taxes are 20 percent
C + I + G + (X “ IM )
of GDP, so each additional $1 of GDP gener-
7,000
ates just 80 cents more DI. With an MPC of
0.75, then, spending rises by only 60 cents E
6,000
Real Expenditure




(75 percent of 80 cents) each time GDP rises by
$1. Thus, the slope of line C2 in Figure 9 is only
0.60, instead of 0.75. 5,000
Table 3 and Figure 10 take the next step by
replacing the old consumption schedule with 4,000
this new one in both the tabular presentation
of income determination and the 45o line
3,000
diagram. We see immediately that the equilib-
rium level of GDP is at point E. Here gross do-
mestic product is $6,000 billion, consumption 4,000 6,000 8,000
is $3,900 billion, investment is $900 billion, net Real GDP
exports are 2$100 billion, and government
purchases are $1,300 billion. As we know from NOTE: Figures are in billions of dollars per year.




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Chapter 11 237
Managing Aggregate Demand: Fiscal Policy



lower the equilibrium level of GDP, depending on how noting that GDP does indeed rise by $750 billion as a
much spending and taxing it does. consequence”from $6,000 billion to $6,750 billion.
Notice that the $400 billion tax cut raises GDP by
$750 billion, whereas the multiplier effect of the $400 bil-
MULTIPLIERS FOR TAX POLICY lion increase in government purchases depicted in the
chapter in Figure 2 (page 224) raised GDP by $1,000
Now let us turn our attention, as in the chapter, to billion. This is a specific numerical example of some-
multipliers for tax changes. They are more compli- thing we learned in the chapter. Because some of the
cated than multipliers for spending because they work change in disposable income affects saving rather than
indirectly via consumption. For this reason, we restrict spending, a dollar of tax cut does not pack as much
ourselves to the multiplier for fixed taxes, leaving the punch as a dollar of G. That is why we multiplied the
more complicated case of variable taxes to more ad- $400 billion change in taxes by 0.75 to get the $300
vanced courses. Tax multipliers must be worked out in billion shift of the C schedule shown in Figure 11.
two steps:
1. Figure out how much any proposed or actual
changes in the tax law will affect consumer
FIGURE 11
spending.
The Multiplier for a Reduction in Fixed Taxes
2. Enter this vertical shift of the consumption
schedule in the 45° line diagram and see how 45°
it affects output. C1 + I + G + (X “ IM)

To create a simple and familiar numerical example,
C0 + I + G + (X “ IM)
suppose income taxes fall by a fixed amount at each
Real Expenditure




level of GDP”say, by $400 billion. Step 1 instructs us to
multiply the $400 billion tax cut by the marginal
propensity to consume (MPC), which is 0.75, to get $300
billion as the increase in consumer spending”that is, as $300
the vertical shift of the consumption schedule. billion
Next, Step 2 instructs us to multiply this $300 bil-
lion increase in consumption by the multiplier”
which is 2.5 in our example”giving $750 billion as
the rise in GDP. Figure 11 verifies that this result is
6,000 6,750
correct by depicting a $300 billion upward shift of the Real GDP
consumption function in the 45° line diagram and



| SUMMARY |
1. Precisely how a tax change affects the consumption 3. Because tax changes affect C only indirectly, the multi-
plier for a change in T is smaller than the multiplier for a
schedule depends on whether fixed taxes or variable
change in G.
taxes are changed.
2. Shifts of the consumption function caused by tax policy 4. The government™s net effect on aggregate demand”and
are subject to the same multiplier as autonomous shifts hence on equilibrium output and prices”depends on
in G, I, or X 2 IM. whether the expansionary effects of its spending are
greater or smaller than the contractionary effects of its
taxes.



| KEY TERMS |
Variable taxes 235 Fixed taxes 235




Copyright 2009 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
Licensed to:
Part 3
238 Fiscal and Monetary Policy



| TEST YOURSELF |
1. Which of the following is considered a fixed tax and spending and taxes by $100 billion. What should happen
which a variable tax? to equilibrium GDP on the demand side?
a. The gasoline tax 3. (More difficult) Suppose real GDP is $10,000 billion and
the basic expenditure multiplier is 2. If two tax changes
b. The corporate income tax
are made at the same time:
c. The estate tax
a. fixed taxes are raised by $100 billion,
d. The payroll tax
b. the income-tax rate is reduced from 20 percent to
2. In a certain economy, the multiplier for government pur-
18 percent,
chases is 2 and the multiplier for changes in fixed taxes
will equilibrium GDP on the demand side rise or fall?
is 1.5. The government then proposes to raise both



| DISCUSSION QUESTIONS |
1. When the income-tax rate declines, as it did in the 2. Discuss the pros and cons of having a higher or lower
United States early in this decade, does the multiplier go multiplier.
up or down? Explain why.



| APPENDIX B | Algebraic Treatment of Taxes and Fiscal Policy
In this appendix, we explain the simple algebra be- We can now apply the equilibrium condition:
hind the fiscal policy multipliers discussed in the
Y 5 C 1 I 1 G 1 (X 2 IM)
chapter. In so doing, we deal only with a simplified
Because investment in this example is I 5 900 and net
case in which prices do not change. Although it is pos-
exports are 2100, substituting for C, I, G, and (X 2 IM)
sible to work out the corresponding algebra for the
more realistic aggregate demand-and-supply analysis into this equation gives:
with variable prices, the analysis is rather complicated
Y 5 300 1 0.60Y 1 900 1 1,300 2 100
and is best left to more advanced courses.
0.40Y 5 2,400
We start with the example used both in the chapter
Y 5 6,000
and in Appendix A. The government spends $1,300
billion on goods and services (G 5 1,300) and levies an
This is all there is to finding equilibrium GDP in an
income tax equal to 20 percent of GDP. So, if the sym-
economy with a government.
bol T denotes tax receipts,
To find the multiplier for government spending, in-
T 5 0.20Y crease G by 1 and solve the problem again:
Y 5 C 1 I 1 G 1 (X 2 IM)
Because the consumption function we have been
working with is Y 5 300 1 0.60Y 1 900 1 1,301 2 100
C 5 300 1 0.75DI 0.40Y 5 2,401

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