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The Government and
Fiscal Policy
9
CHAPTER OUTLINE
Government in the Economy
Government Purchases (G), Net Taxes (T), and Disposable
Income (Yd)
The Determination of Equilibrium Output (Income)
Fiscal Policy at Work: Multiplier Effects
The Government Spending Multiplier
The Tax Multiplier
The Balanced-Budget Multiplier
PART III The Core of Macroeconomic Theory
The Federal Budget
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
The Budget in 2009
Fiscal Policy Since 1993: The Clinton, Bush, and Obama
Administrations
The Federal Government Debt
The Economy’s Influence on the Government
Budget
Automatic Stabilizers and Destabilizers
Full-Employment Budget
Looking Ahead
Appendix A: Deriving the Fiscal Policy Multipliers
Appendix B: The Case in Which Tax Revenues
Depend on Income
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PART III The Core of Macroeconomic Theory
fiscal policy The government’s spending and taxing policies.
monetary policy The behavior of the Federal Reserve
concerning the nation’s money supply.
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Government in the Economy
discretionary fiscal policy Changes in taxes or spending that are the result
of deliberate changes in government policy.
Government Purchases (G), Net Taxes (T), and Disposable Income (Yd)
PART III The Core of Macroeconomic Theory
net taxes (T) Taxes paid by firms and households to the government
minus transfer payments made to households by the government.
disposable, or after-tax, income (Yd) Total income minus net taxes:
Y − T.
disposable income ≡ total income − net taxes
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Yd ≡ Y − T
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PART III The Core of Macroeconomic Theory
Over which of the following categories does the government have
more control?
a.
Tax revenue.
b.
Government expenditures.
c.
Tax rates.
d.
The size of corporate profits.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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PART III The Core of Macroeconomic Theory
Over which of the following categories does the government have
more control?
a.
Tax revenue.
b.
Government expenditures.
c.
Tax rates.
d.
The size of corporate profits.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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Government in the Economy
Government Purchases (G), Net Taxes (T), and Disposable Income (Yd)
PART III The Core of Macroeconomic Theory
 FIGURE 9.1 Adding Net Taxes
(T) and Government Purchases (G)
to the Circular Flow of Income
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Government in the Economy
Government Purchases (G), Net Taxes (T), and Disposable Income (Yd)
The disposable income (Yd) of households must end up as either
consumption (C) or saving (S). Thus,
Yd  C  S
PART III The Core of Macroeconomic Theory
Because disposable income is aggregate income (Y) minus net taxes
(T), we can write another identity:
Y  T  C S
By adding T to both sides:
Y  C S  T
Planned aggregate expenditure (AE) is the sum of consumption
spending by households (C), planned investment by business firms (I),
and government purchases of goods and services (G).
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AE  C  I  G
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PART III The Core of Macroeconomic Theory
Select the best answer. Households use their disposable income
(Yd) to do the following:
a.
Consume.
b.
Consume and save.
c.
Consume, save, and pay taxes.
d.
Consume, save, pay taxes, and buy imports.
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PART III The Core of Macroeconomic Theory
Select the best answer. Households use their disposable income
(Yd) to do the following:
a.
Consume.
b. Consume and save.
c.
Consume, save, and pay taxes.
d.
Consume, save, pay taxes, and buy imports.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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Government in the Economy
Government Purchases (G), Net Taxes (T), and Disposable Income (Yd)
budget deficit The difference between what a government spends
and what it collects in taxes in a given period: G − T.
PART III The Core of Macroeconomic Theory
budget deficit ≡ G − T
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Government in the Economy
Government Purchases (G), Net Taxes (T), and Disposable Income (Yd)
Adding Taxes to the Consumption Function
To modify our aggregate consumption function to
incorporate disposable income instead of before-tax income,
instead of C = a + bY, we write
PART III The Core of Macroeconomic Theory
C = a + bYd
or
C = a + b(Y − T)
Our consumption function now has consumption depending
on disposable income instead of before-tax income.
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PART III The Core of Macroeconomic Theory
When government enters the circular flow of income, which of the
following is an expression for planned aggregate expenditure?
a.
Y−T
b.
C+S+T
c.
C+I+G
d.
G–T
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PART III The Core of Macroeconomic Theory
When government enters the circular flow of income, which of the
following is an expression for planned aggregate expenditure?
a.
Y−T
b.
C+S+T
c.
C+I+G
d.
G–T
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Government in the Economy
Government Purchases (G), Net Taxes (T), and Disposable Income (Yd)
Planned Investment
PART III The Core of Macroeconomic Theory
The government can affect investment behavior through its
tax treatment of depreciation and other tax policies.
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Government in the Economy
The Determination of Equilibrium Output (Income)
Y=C+I+G
TABLE 9.1 Finding Equilibrium for I = 100, G = 100, and T = 100
PART III The Core of Macroeconomic Theory
(1)
(2)
(3)
(4)
Output
Net Disposable Consumption
(Income) Taxes
Income
Spending
Y
T
Yd ≡Y  T C = 100 + .75 Yd
(5)
(6)
(7)
(8)
(9)
(10)
Planned
Planned
Unplanned
Saving Investment Government Aggregate
Inventory Adjustment
S
Spending Purchases Expenditure
Change
to DisequiYd – C
I
G
C + I + G Y  (C + I + G)
librium
300
100
200
250
 50
100
100
450
 150
Output ↑
500
100
400
400
0
100
100
600
 100
Output ↑
700
100
600
550
50
100
100
750
 50
Output ↑
900
100
800
700
100
100
100
900
0
Equilibrium
1,100
100
1,000
850
150
100
100
1,050
+ 50
Output ↓
1,300
100
1,200
1,000
200
100
100
1,200
+ 100
Output ↓
1,500
100
1,400
1,150
250
100
100
1,350
+ 150
Output ↓
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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Government in the Economy
The Determination of Equilibrium Output (Income)
 FIGURE 9.2 Finding Equilibrium
Output/Income Graphically
PART III The Core of Macroeconomic Theory
Because G and I are both fixed at
100, the aggregate expenditure
function is the new consumption
function displaced upward by I + G
= 200.
Equilibrium occurs at Y = C + I + G
= 900.
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Government in the Economy
The Determination of Equilibrium Output (Income)
The Saving/Investment Approach to Equilibrium
saving/investment approach to equilibrium:
PART III The Core of Macroeconomic Theory
S+T=I+G
To derive this, we know that in equilibrium, aggregate
output (income) (Y) equals planned aggregate expenditure
(AE). By definition, AE equals C + I + G, and by definition,
Y equals C + S + T.
Therefore, at equilibrium:
C+S+T=C+I+G
Subtracting C from both sides leaves:
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S+T=I+G
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PART III The Core of Macroeconomic Theory
In the circular flow that includes households, firms, and
government, which of the following expressions is the
leakages/injections approach to equilibrium?
a.
Y = C + I + G.
b.
C + S = I + G.
c.
Y = a + bT + I + G.
d.
S + T = I + G.
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PART III The Core of Macroeconomic Theory
In the circular flow that includes households, firms, and
government, which of the following expressions is the
leakages/injections approach to equilibrium?
a.
Y = C + I + G.
b.
C + S = I + G.
c.
Y = a + bT + I + G.
d. S + T = I + G.
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Fiscal Policy at Work: Multiplier Effects
At this point, we are assuming that the government controls G and T. In this
section, we will review three multipliers:
Government spending multiplier
Tax multiplier
PART III The Core of Macroeconomic Theory
Balanced-budget multiplier
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Fiscal Policy at Work: Multiplier Effects
The Government Spending Multiplier
government spending multiplier 
1
PART III The Core of Macroeconomic Theory
MPS
government spending multiplier The ratio of the change in the
equilibrium level of output to a change in government spending.
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Fiscal Policy at Work: Multiplier Effects
The Government Spending Multiplier
TABLE 9.2 Finding Equilibrium after a Government Spending Increase of 50 (G Has
Increased from 100 in Table 9.1 to 150 Here)
(1)
(2)
(3)
(4)
PART III The Core of Macroeconomic Theory
Output
Net Disposable Consumption
(Income) Taxes
Income
Spending
Y
T
Yd ≡Y  T C = 100 + .75 Yd
(5)
(6)
(7)
(8)
(9)
(10)
Unplanned
Planned
Planned
Inventory
Saving Investment Government Aggregate
Change
Adjustment
S
Spending Purchases Expenditure Y  (C + I +
to
Yd – C
I
G
C+I+G
G)
Disequilibrium
300
100
200
250
 50
100
150
500
 200
Output ↑
500
100
400
400
0
100
150
650
 150
Output ↑
700
100
600
550
50
100
150
800
 100
Output ↑
900
100
800
700
100
100
150
950
 50
Output ↑
1,100
100
1,000
850
150
100
150
1,100
0
1,300
100
1,200
1,000
200
100
150
1,250
+ 50
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Equilibrium
Output ↓
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PART III The Core of Macroeconomic Theory
How much of an increase in government spending would be required
to generate a $200 billion increase in the equilibrium level of output?
a.
An amount less than $200 billion in government spending.
b.
An amount greater than $200 billion in government spending.
c.
Exactly $200 billion in government spending.
d. None of the above. Equilibrium output does not change with
changes in government spending.
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PART III The Core of Macroeconomic Theory
How much of an increase in government spending would be required
to generate a $200 billion increase in the equilibrium level of output?
a.
An amount less than $200 billion in government spending.
b.
An amount greater than $200 billion in government spending.
c.
Exactly $200 billion in government spending.
d. None of the above. Equilibrium output does not change with
changes in government spending.
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Fiscal Policy at Work: Multiplier Effects
The Government Spending Multiplier
 FIGURE 9.3 The Government
Spending Multiplier
PART III The Core of Macroeconomic Theory
Increasing government spending by
50 shifts the AE function up by 50.
As Y rises in response, additional
consumption is generated.
Overall, the equilibrium level of Y
increases by 200, from 900 to 1,100.
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Fiscal Policy at Work: Multiplier Effects
The Tax Multiplier
tax multiplier The ratio of change in the equilibrium level of output to
a change in taxes.
 1 
 Y  (initial increase in aggregate expenditure)  

 MPS 
PART III The Core of Macroeconomic Theory
Because the initial change in aggregate expenditure caused by a tax
change of ∆T is (−∆T × MPC), we can solve for the tax multiplier by
substitution:
1 
MPC 


Y  (  T  MPC )  
  T  

 MPS 
 MPS 
Because a tax cut will cause an increase in consumption expenditures
and output and a tax increase will cause a reduction in consumption
expenditures and output, the tax multiplier is a negative multiplier:
tax multiplier  
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 
MPC
MPS
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PART III The Core of Macroeconomic Theory
Which of the following formulas shows the impact of a change in
taxes on equilibrium income?
a.
Y = a + b(Y – T) + I + G
b.
Y = 1/(1 – b) * (a – bT + I + G)
c.
S+T=I+G
d.
– ∆T * (b/1 – b)
e.
C+S=I+G
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PART III The Core of Macroeconomic Theory
Which of the following formulas shows the impact of a change in
taxes on equilibrium income?
a.
Y = a + b(Y – T) + I + G
b.
Y = 1/(1 – b) * (a – bT + I + G)
c.
S+T=I+G
d. – ∆T * (b/1 – b)
e.
C+S=I+G
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Fiscal Policy at Work: Multiplier Effects
The Balanced-Budget Multiplier
PART III The Core of Macroeconomic Theory
balanced-budget multiplier The ratio of change in the equilibrium
level of output to a change in government spending where the change
in government spending is balanced by a change in taxes so as not to
create any deficit. The balanced-budget multiplier is equal to 1: The
change in Y resulting from the change in G and the equal change in T
are exactly the same size as the initial change in G or T.
balanced-budget multiplier  1
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Fiscal Policy at Work: Multiplier Effects
The Balanced-Budget Multiplier
TABLE 9.3 Finding Equilibrium after a Balanced-Budget Increase in G and T of 200 Each
(Both G and T Have Increased from 100 in Table 9.1 to 300 Here)
(1)
(2)
(3)
(4)
PART III The Core of Macroeconomic Theory
Output
Net Disposable Consumption
(Income) Taxes
Income
Spending
Y
T
Yd ≡Y  T C = 100 + .75 Yd
(5)
(6)
(7)
(8)
(9)
Planned
Planned
Unplanned
Investment Government Aggregate
Inventory
Adjustment
Spending Purchases Expenditure
Change
to
I
G
C + I + G Y  (C + I + G) Disequilibrium
500
300
200
250
100
300
650
 150
Output ↑
700
300
400
400
100
300
800
 100
Output ↑
900
300
600
550
100
300
950
 50
Output ↑
1,100
300
800
700
100
300
1,100
0
1,300
300
1,000
850
100
300
1,250
+ 50
Output ↓
1,500
300
1,200
1,000
100
300
1,400
+ 100
Output ↓
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
Equilibrium
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PART III The Core of Macroeconomic Theory
What happens when there is a simultaneous increase in
government spending of $100 and a lump-sum tax of $100?
a.
Equilibrium income would increase by $100, or the amount of
increase in G.
b.
Equilibrium income would decrease by $100, or the amount
of increase in T.
c.
Equilibrium income would decrease by $200, or double the
amount of the increase in T.
d.
Nothing happens. Equilibrium income remains the same
because the amount of government spending (G) is
compensated by the amount of taxation (T).
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PART III The Core of Macroeconomic Theory
What happens when there is a simultaneous increase in
government spending of $100 and a lump-sum tax of $100?
a.
Equilibrium income would increase by $100, or the
amount of increase in G.
b.
Equilibrium income would decrease by $100, or the amount
of increase in T.
c.
Equilibrium income would decrease by $200, or double the
amount of the increase in T.
d.
Nothing happens. Equilibrium income remains the same
because the amount of government spending (G) is
compensated by the amount of taxation (T).
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Fiscal Policy at Work: Multiplier Effects
The Balanced-Budget Multiplier
TABLE 9.4 Summary of Fiscal Policy Multipliers
PART III The Core of Macroeconomic Theory
Policy Stimulus
Multiplier
Government
spending
multiplier
Increase or decrease in the
level of government
purchases: ∆G
1
MPS
Tax multiplier
Increase or decrease in the
level of net taxes: ∆T
 MPC
MPS
Balanced-budget
multiplier
Simultaneous balanced-budget
increase or decrease in the
level of government purchases
and net taxes: ∆G = ∆T
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
1
Final Impact on
Equilibrium Y
G 
T 
1
MPS
 MPC
MPS
G
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Fiscal Policy at Work: Multiplier Effects
The Balanced-Budget Multiplier
A Warning
Although we have added government, the story told about
the multiplier is still incomplete and oversimplified.
PART III The Core of Macroeconomic Theory
We have been treating net taxes (T) as a lump-sum, fixed
amount, whereas in practice, taxes depend on income.
Appendix B to this chapter shows that the size of the
multiplier is reduced when we make the more realistic
assumption that taxes depend on income.
We continue to add more realism and difficulty to our analysis
in the chapters that follow.
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The Federal Budget
federal budget The budget of the federal government.
The “budget” is really three different budgets:
It is a political document that dispenses favors to certain groups or regions and
places burdens on others.
PART III The Core of Macroeconomic Theory
It is a reflection of goals the government wants to achieve.
The budget may be an embodiment of some beliefs about how (if at all) the
government should manage the macroeconomy.
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PART III The Core of Macroeconomic Theory
The federal budget can be conceived as:
a.
A political document that dispenses favors to some groups
and places burdens on others.
b.
A reflection of goals the government wants to achieve.
c.
An embodiment of some beliefs about how (if at all) the
government should manage the macroeconomy.
d.
All of the above.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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PART III The Core of Macroeconomic Theory
The federal budget can be conceived as:
a.
A political document that dispenses favors to some groups
and places burdens on others.
b.
A reflection of goals the government wants to achieve.
c.
An embodiment of some beliefs about how (if at all) the
government should manage the macroeconomy.
d. All of the above.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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The Federal Budget
The Budget in 2009
TABLE 9.5 Federal Government Receipts and Expenditures, 2009 (Billions of Dollars)
PART III The Core of Macroeconomic Theory
Amount
Current receipts
Personal income taxes
828.7
Excise taxes and customs duties
92.3
Corporate income taxes
231.0
Taxes from the rest of the world
12.3
Contributions for social insurance
949.1
Interest receipts and rents and royalties
48.2
Current transfer receipts from business and persons
68.1
Current surplus of government enterprises
− 4.9
Total
2,224.9
Current Expenditures
Consumption expenditures
986.4
Transfer payments to persons
1596.1
Transfer payments to the rest of the world
61.7
Grants-in-aid to state and local governments
476.6
Interest payments
272.3
Subsidies
58.2
Total
3,451.3
Net federal government saving—surplus (+) or deficit (−)
− 1,226.4
(Total current receipts − Total current expenditures)
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
Percentage of Total
37.2
4.1
10.4
0.6
42.7
2.2
3.1
− 0.2
100.0
28.6
46.2
1.8
13.8
7.9
1.7
100.0
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The Federal Budget
The Budget in 2009
PART III The Core of Macroeconomic Theory
federal surplus (+) or deficit (−) Federal government receipts minus
expenditures.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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The Federal Budget
PART III The Core of Macroeconomic Theory
Fiscal Policy Since 1993: The Clinton, Bush, and Obama Administrations
 FIGURE 9.4 Federal Personal Income Taxes as a Percentage of Taxable Income, 1993 I–2010 I
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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The Federal Budget
PART III The Core of Macroeconomic Theory
Fiscal Policy Since 1993: The Clinton, Bush, and Obama Administrations
 FIGURE 9.5 Federal Government Consumption Expenditures as a Percentage of GDP and
Federal Transfer Payments and Grants-in-Aid as a Percentage of GDP, 1993 I–2010 I
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The Federal Budget
PART III The Core of Macroeconomic Theory
Fiscal Policy Since 1993: The Clinton, Bush, and Obama Administrations
 FIGURE 9.6 The Federal Government Surplus (+) or Deficit (–) as a Percentage of GDP, 1993 I–2010 I
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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PART III The Core of Macroeconomic Theory
After a large deficit buildup in the 1980s, the federal government deficit:
a.
Continued to worsen steadily throughout the 1990s and into the
2000s.
b.
Turned into a surplus during the two Clinton administrations.
c.
Was vastly diminished during the G.W. Bush administrations.
d.
Was virtually eliminated by the Obama administration.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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PART III The Core of Macroeconomic Theory
After a large deficit buildup in the 1980s, the federal government deficit:
a.
Continued to worsen steadily throughout the 1990s and into the
2000s.
b. Turned into a surplus during the two Clinton administrations.
c.
Was vastly diminished during the G.W. Bush administrations.
d.
Was virtually eliminated by the Obama administration.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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The Federal Budget
The Federal Government Debt
federal debt The total amount owed by the federal government.
PART III The Core of Macroeconomic Theory
privately held federal debt The privately held (non-governmentowned) debt of the U.S. government.
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The Federal Budget
PART III The Core of Macroeconomic Theory
The Federal Government Debt
 FIGURE 9.7 The Federal Government Debt as a Percentage of GDP, 1993 I–2010 1
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The Economy’s Influence on the Government Budget
Automatic Stabilizers and Destabilizers
automatic stabilizers Revenue and expenditure items in the federal
budget that automatically change with the state of the economy in
such a way as to stabilize GDP.
PART III The Core of Macroeconomic Theory
automatic destabilizer Revenue and expenditure items in the
federal budget that automatically change with the state of the
economy in such a way as to destabilize GDP.
fiscal drag The negative effect on the economy that occurs when
average tax rates increase because taxpayers have moved into higher
income brackets during an expansion.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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PART III The Core of Macroeconomic Theory
Which of the following statements is correct about the government’s
control over its budget?
a.
The government has complete control over the revenue side of
the budget, but not complete control over the expenditure side.
b.
The government has complete control over the expenditure side
of the budget, but not complete control over the revenue side.
c.
The government does not have complete control of either the
revenue side or the expenditure side of the budget.
d.
The size of the government budget, and whether it is in surplus
or deficit, is controlled entirely by Congress, not by the economy.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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PART III The Core of Macroeconomic Theory
Which of the following statements is correct about the government’s
control over its budget?
a.
The government has complete control over the revenue side of
the budget, but not complete control over the expenditure side.
b.
The government has complete control over the expenditure side
of the budget, but not complete control over the revenue side.
c.
The government does not have complete control of either
the revenue side or the expenditure side of the budget.
d.
The size of the government budget, and whether it is in surplus
or deficit, is controlled entirely by Congress, not by the economy.
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
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EC ON OMIC S IN PRACTICE
Governments Disagree on How Much More Spending Is Needed
The U.S. economy is intertwined with the rest
of the world.
PART III The Core of Macroeconomic Theory
For that reason, U.S. government leaders are
concerned not only with their own fiscal
policies but also with those of other
governments (and vice versa).
President Obama was among the strongest
advocates of additional stimulus by
governments in a June 2010 summit of the
G-20.
Spending Fight at G-20
The Wall Street Journal
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The Economy’s Influence on the Government Budget
Full-Employment Budget
full-employment budget What the federal budget would be if the
economy were producing at the full-employment level of output.
PART III The Core of Macroeconomic Theory
structural deficit The deficit that remains at full employment.
cyclical deficit The deficit that occurs because of a downturn in the
business cycle.
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PART III The Core of Macroeconomic Theory
When the economy reaches full employment, the budget deficit is:
a.
A combination of cyclical and structural deficits.
b.
Zero.
c.
Equal to the cyclical deficit.
d. Equal to the structural deficit.
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PART III The Core of Macroeconomic Theory
When the economy reaches full employment, the budget deficit is:
a.
A combination of cyclical and structural deficits.
b.
Zero.
c.
Equal to the cyclical deficit.
d. Equal to the structural deficit.
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Looking Ahead
We have now seen how households, firms, and the government interact in the
goods market, how equilibrium output (income) is determined, and how the
government uses fiscal policy to influence the economy.
PART III The Core of Macroeconomic Theory
In the following two chapters, we analyze the money market and monetary
policy—the government’s other major tool for influencing the economy.
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REVIEW TERMS AND CONCEPTS
automatic destabilizers
privately held federal debt
automatic stabilizers
structural deficit
balanced-budget multiplier
tax multiplier
budget deficit
1. Disposable income Yd ≡ Y − T
cyclical deficit
2. AE ≡ C + I + G
discretionary fiscal policy
3. Government budget deficit ≡ G − T
disposable, or after-tax, income (Yd)
4. Equilibrium in an economy with a
government: Y = C + I + G
federal budget
PART III The Core of Macroeconomic Theory
federal debt
federal surplus (+) or deficit (−)
fiscal drag
5. Saving/investment approach to
equilibrium in an economy with a
government: S + T = I + G
6. Government spending multiplier ≡
fiscal policy
full-employment budget
government spending multiplier
monetary policy
1
MPS
 MPC 

7. Tax multiplier ≡ 

 MPS 
8. Balanced-budget multiplier ≡ 1
net taxes (T)
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CHAPTER 9 APPENDIX A
Deriving the Fiscal Policy Multipliers
The Government Spending and Tax Multipliers
We can derive the multiplier algebraically using our hypothetical
consumption function:
C  a  b(Y  T )
The equilibrium condition is
Y  C I  G
PART III The Core of Macroeconomic Theory
By substituting for C, we get
Y  a  b(Y  T )  I  G
Y  a  bY  bT  I  G
This equation can be rearranged to yield
Y  bY  a  I  G  bT
Y (1  b)  a  I  G  bT
Now solve for Y by dividing through by (1 − b):
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
1
Y 
(a  I  G  bT )
1  b
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CHAPTER 9 APPENDIX A
Deriving the Fiscal Policy Multipliers
The Balanced-Budget Multiplier
It is easy to show formally that the balanced-budget multiplier = 1.
PART III The Core of Macroeconomic Theory
increase in spending:
− decrease in spending:
= net increase in spending
G
C  T ( MPC )
G  T ( MPC )
In a balanced-budget increase, G = T; so we can substitute:
net initial increase in spending:
G − G (MPC) = G (1 − MPC)
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CHAPTER 9 APPENDIX A
Deriving the Fiscal Policy Multipliers
The Balanced-Budget Multiplier
Because MPS = (1 − MPC), the net initial increase in spending is:
G (MPS)
PART III The Core of Macroeconomic Theory
 1 
We can now apply the expenditure multiplier 
 to this net initial
MPS


increase in spending:
 1 
Y  G ( MPS ) 
  G
 MPS 
Thus, the final total increase in the equilibrium level of Y is just equal to the
initial balanced increase in G and T.
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CHAPTER 9 APPENDIX B
The Case in Which Tax Revenues Depend on Income
 FIGURE 9B.1 The Tax Function
This graph shows net taxes (taxes
minus transfer payments) as a
function of aggregate income.
Yd  Y  T
PART III The Core of Macroeconomic Theory
Yd  Y  (200  1 / 3Y )
Yd  Y  200  1 / 3Y
C  100  .75Yd
C  100  .75(Y  200  1 / 3Y )
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CHAPTER 9 APPENDIX B
The Case in Which Tax Revenues Depend on Income
Y  C  I G
Y  100  .75(Y  200  1/ 3Y )  100  100
I
G
C
Y  100  .75Y  150  25Y  100  100
Y  450  .5Y
PART III The Core of Macroeconomic Theory
.5Y  450
 FIGURE 9B.2 Different Tax Systems
When taxes are strictly lump-sum (T = 100)
and do not depend on income, the
aggregate expenditure function is steeper
than when taxes depend on income.
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CHAPTER 9 APPENDIX B
The Case in Which Tax Revenues Depend on Incomes
The Government Spending and Tax Multipliers Algebraically
C  a  b(Y  T )
C  a  b(Y  T0  tY )
C  a  bY  bT0  btY
PART III The Core of Macroeconomic Theory
Through substitution we get
Y  a  bY  bT  btY  I  G
0
C
Solving for Y:
1
Y
(a  I  G  bT0 )
1  b  bt
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CHAPTER 9 APPENDIX B
The Case in Which Tax Revenues Depend on Incomes
The Government Spending and Tax Multipliers Algebraically
This means that a $1 increase in G or I (holding a and T0 constant) will
increase the equilibrium level of Y by
PART III The Core of Macroeconomic Theory
1
1  b  bt
Holding a, I, and G constant, a fixed or lump-sum tax cut (a cut in T0) will
increase the equilibrium level of income by
© 2012 Pearson Education, Inc. Publishing as Prentice Hall
b
1  b  bt
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