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Solutions to Problems
Chapter 25
1.
Given for the Zap economy :
mpc  0.9
I  $50b
G  $40b
T  $40b
1a. Equilibrium expenditure decreases by $100 billion.
Zap has no induced taxes or imports, so the government expenditures multiplier is;
1
1  mpc
1

1  0 .9
 10
multiplier 
The multiplier tells us that when government expenditures decrease by $10 billion, equilibrium expenditure decreases by 10
times as much or $100 billion.
Y
G
Y  G  multiplier
multiplier 
 $10b  10
 $100b
1b. Government expenditures multiplier is 10.
1c. Equilibrium expenditure increases by $90 billion.
The autonomous tax multiplier is;
 mpc
1  mpc
0 .9

1  0 .9
 9
multiplier 
When autonomous taxes are cut by $10 billion, equilibrium expenditure changes by 9 times the change in autonomous taxes. A
cut in autonomous taxes of $10 billion will increase equilibrium expenditure by $90 billion.
Y
T
Y  T  (9)
multiplier 
 ($10b)  (9)
1d.
 $90b
Autonomous tax multiplier is 9.
1e. Equilibrium expenditure decreases by $10 billion.
The decrease in government expenditures decreases equilibrium expenditure by $100 billion and the cut in taxes increases
equilibrium expenditure by $90 billion. So together, equilibrium expenditure decreases by $10 billion.
3a. The quantity of real GDP demanded increases by $100 billion at constant prices.
When government expenditures increase by $10 billion, at the price level 100, equilibrium expenditure increases by 10 times as
much, or $100 billion.
3b. The aggregate demand curve shifts rightward by $100 billion at each price level.
The AE curve shifts upward by $10 billion from AE to AE/, equilibrium expenditure at constant prices increases by $100 billion,
and the AD curve shifts rightward by $100 billion from AD to AD/ (see figure 1).
3c. In the short run, real GDP increases by less than the $100 billion increase in the quantity of real GDP demanded.
In the short run, short-run aggregate supply and aggregate demand determine real GDP. Because the short-run aggregate supply
curve slopes upward, the price level rises and real GDP increases but by less than $100 billion. The Zap economy moves from a
to c in figure 1.
3d. In the long run, the increase in real GDP will be zero. Real GDP will return to potential GDP.
In the short run, real GDP exceeds potential GDP and wage rates will start to rise. The short-run aggregate supply will begin to
decrease and the price level will rise. The short-run aggregate supply will continue to decrease and the price level will continue
to rise until real GDP equals potential GDP. The Zap economy moves from c to a / in figure 1.
3e. The price level rises.
In the short run, aggregate demand and short-run aggregate supply determine the price level. Because the short-run aggregate
supply curve slopes upward and because aggregate demand increases, the price level rises (see figure 1).
3f. The price level rises.
In the long run, aggregate demand and long-run aggregate supply determine the price level. The short-run aggregate supply curve
shifts leftward because the money wage rate rises. Because the long-run aggregate supply curve is vertical and because aggregate
demand increases, the price level rises. And it rises by more in the long run than it does in the short run (see figure 1).
Zip – Problem 4
AE/(p=100)
AE//(p=102)
AE (p=100)
b
•
E1
c
E2
•
a
•
E0
Expenditure
Expenditure
Zap – Problem 3
•
G=-$5B
LAS
SAS/
SAS
a/
•
a
•
•c
Y1 Y2 Y0
real GDP
Price level
Price level
•
b
E0
Y0 Y2 Y1
104
102
100
•
c
E2
G=$10b
AE (p=100)
AE//(p=98)
AE/(p=100)
a
E1
LAS
SAS
SAS/
•b
AD/
100
98
96
•b
•c
•a
• a/
Y0 Y2 Y1
real GDP
Given :
b  0 .9
t  0.333
m  0 .1
C  $29b
I  $100b
G  $160b
T  $10b
therefore :
T  0.3Y  10
and :
C  0.9YD  29
 0.9[Y  T ]  29
 0.9[Y  (0.3Y  10)]  29
 0.9Y  0.3Y  9  29
 0.6Y  20
and :
M  0.1Y  60
AD
AD/
AD
5.
real GDP
Y1 Y2 Y0
real GDP
5a. Equilibrium real GDP is $600 billion.
Equilibrium expenditure occurs when aggregate planned expenditure equals real GDP.
At equilibrium :
Y  AE
C  I G  X M
 0.6Y  20  100  160  80  (0.1Y  60)
 0.5Y  300
0.5Y  300
300
0 .5
 $600b
Y
5b. The government has a surplus of $50 billion.
When a government’s revenues exceed its outlays the government has a budget surplus.
government budget balance  T  G
 (tY  T )  G
 13  600  10  160
 200  10  160
 $50b
5c. The country has a balance of trade deficit of $40 billion.
When the value of a country’s imports is greater than the value of its exports the country has a current account deficit.
balanceof trade  X  M
 80  ( mY  M )
 80  0.1  600  60
 80  60  60
 $40b
7.
Given the marginal rate of tax is reduced to 25 percent for the country in question 5.
7a. Equilibrium real GDP increases by $106b
The lower marginal rate of tax increases the size of the multiplier and the equilibrium level of real GDP given the levels of
autonomous expenditures.
At equilibrium :
Y  AE
1
1  b(1  t )  m
1
 (29  9  100  160  80  60) 
1  0.9(1  0.25)  0.1
1
 300 
0.425
 $706b
 (C  bT  I  G  X  M ) 
7b. The government surplus falls by $23.5 billion.
The new lower level of taxation revenue with the new marginal rate of taxation is $26.5 billion. This is a fall in the budget
surplus of $23.5 billion.
government budget balance  T  G
 (tY  T )  G
 0.25  706  10  160
 186.5  160
 $26.5b
7c. The country’s trade balance deficit increases by $10.6 billion.
The marginal propensity to import is 0.1. Imports will increase by 10% of any increase in real GDP.
M  0.1 Y
 0.1 106
 $10.6b
9,
Given:
At potential real GDP the unemployment rate is 5.5% and the government budget is balanced at 20 per cent of potential real
GDP. A 1percentage point increase (decrease) in unemployment decreases (increases) the budget balance by 2 percentage points.
G = 0.2Y + 0.01Y)xUcyclic
T = 0.2Y - 0.01YxUcyclic
9a. The budget balance as a percentage of GDP is shown in table 1. A negative value is a budget deficit.
The budget balance column was calculated using the formula:
Government Budget Balance = T  G
= [0.2Y - 0.01YxUcyclic]  [0.2Y + 0.01YxUcyclic]
= 0.02YxUcyclic
Table 1  Problem 9
Year
1
2
3
4
5
6
7
UnemploymentUnemploymentUnemployment
(actual rate) (natural rate) (cyclical rate)
5
5.5
-0.5
6
5.5
0.5
7
5.5
1.5
6
5.5
0.5
5
5.5
-0.5
4
5.5
-1.5
5
5.5
-0.5
9b. The deficit increases as the unemployment rate increases and the level of real GDP decreases.
The relationship between the unemployment rate and the budget balance is shown in figure 3.
Budget
balance
(%GDP)
1
-1
-3
-1
1
3
1
Unemployment & Budget balance
Automatic stabilizers – problem 9
8
4
Budget balance (%GDP)
2
0
-2
-4
Figure 3
Unemployment rate
6
1
2
3
4
5
6
7 Year