S-191
1. An economy has a marginal propensity to consume of 0.6, real GDP equals $500
billion, and the government collects 20% of GDP in taxes. If government purchas-
es increase by $10 billion, show the rounds of increased spending that take place by
completing the accompanying table. The first and second rows are filled in for you.
In the first row, the increase in government purchases of $10 billion raises real
GDP by $10 billion, taxes increase by $2 billion, and YD increases by $8 billion; in
the second row, the increase in YD of $8 billion increases consumer spending by
$4.80 billion (MPC × change in disposable income).
a. What is the total change in real GDP after the 10 rounds? What is the value of the
multiplier? What would you expect the total change in real GDP to be, based on
the multiplier formula? How do your two answers compare?
b. Redo the accompanying table, assuming the marginal propensity to consume is
Change Change Change
in G in real in Change
or C GDP taxes in YD
Rounds (billions of dollars)
1 ΔG = $10.00 $10.00 $2.00 $8.00
2 ΔC = 4.80 4.80 0.96 3.84
3 ΔC =
?
?
?
?
Appendix: Taxes
and the Multiplier 13 A
CHAPTER
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Solution
S-192 CHAPTER 13 APPENDIX TAXES AND THE MULTIPLIER
1. Here is the completed table:
. . .
Sum
for 10 $19.20
rounds
a. The total change in real GDP after the 10 rounds is $19.20 billion. The multiplier
is 1.923 [1/(1 − (0.6 × (1 − 0.2)))]. We would expect the total change in real
b. Here is the table redone:
Change in Change in
G or C real GDP Change in taxes Change in YD
Rounds (billions of dollars)
1 ⌬G = $10.00 $10.00 $2.00 $8.00
2 ⌬C = 4.80 4.80 0.96 3.84
3 ⌬C = 2.30 2.30 0.46 1.84
Change in Change in
G or C real GDP Change in taxes Change in YD
Rounds (billions of dollars)
1 ⌬G = $10.00 $10.00 $1.00 $9.00
2 ⌬C = 6.75 6.75 0.68 6.08
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Solution
2. Calculate the change in government purchases of goods and services necessary to
close the recessionary or inflationary gaps in the following cases. Assume that the
short-run aggregate supply curve is horizontal, so that the change in real GDP arising
from a shift of the aggregate demand curve equals the size of the shift of the curve.
a. Real GDP equals $100 billion, potential output equals $160 billion, the govern-
2. a. The economy is facing a recessionary gap; real GDP is less than potential
output. Since the multiplier for a change in government purchases is
2.5 [1/(1 − (0.75 × (1 − 0.2)))], an increase in government purchases of
goods and services of $24 billion will increase real GDP by $60 billion and
close the recessionary gap.
tionary gap.
CHAPTER 13 APPENDIX TAXES AND THE MULTIPLIER S-193
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