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Solutions to Problems
Chapter 24
1a i.
The marginal propensity to consume is 0.5.
mpc = C/Y = 5/10 = 0.5 at all levels of income.
1a ii
Table 1 shows Heron Island's saving at each level of income.
Saving equal disposable income minus consumption expenditure. These amounts run from –5 at zero disposable income to
15 at a disposable income of 40. For each increase in disposable income of $1, saving increases by 50 cents.
Table 1  Problem 1
Heron Island
Disposable Consumption
income
expenditure
($m per year) ($m per year)
5
10
15
20
25
0
10
20
30
40
Saving
($m per
year)
mpc
-5
0
5
10
15
0.5
0.5
0.5
0.5
1a iii Marginal propensity to save is 0.5
The marginal propensity to consume plus the marginal propensity to save equals 1. Because consumption expenditure and
saving exhaust disposable income, 0.5 of each dollar increase in disposable income is consumed and the remaining part (0.5)
is saved.
1b.
The consumption function is drawn in figure 1. Its slope is the same as the marginal propensity to consume, which is 0.5.
Consumption ($m per year)
Heron Island – Problem 1
40
30
C=0.5Y +5
20
C=5
Y=10
10
450
0
0
10
20
30
40
Real GDP($m per year)
Figure 1
1c.
Consumer spending is greater than income for all levels of income below $10 million dollars per year. Dis-saving is shown
by the shaded area in figure 1.
3ai. Autonomous expenditure for Turtle Island is $2.0 billion.
Autonomous expenditure is expenditure that does not depend on real GDP. Autonomous expenditure equals the value of
aggregate planned expenditure when real GDP is zero.
3aii. Marginal propensity to consume is 0.6.
When the country has no imports or exports and no income taxes, the slope of the AE curve equals the marginal propensity
to consume.
mpc = C/YD
= 3.6/6.0
= 0.6
3aiii. When real GDP is $6 billion, aggregate planned expenditure is $5.6 billion per year.
3b. Unplanned inventory investment is negative.
When real GDP is $4 billion, aggregate planned expenditure is $4.4 billion, so firms sell more than they produce. There is a
$0.4 billion unplanned rundown of inventories.
3c. Unplanned inventory investment is positive.
When real GDP is $6 billion, aggregate planned expenditure is less than real GDP, so firms cannot sell all that they produce.
There is a $0.4 billion unplanned accumulation of inventories.
3d. The multiplier is 2.5.
The multiplier
3e.
= 1/(1  mpc)
= 1/(1  0.6)
= 2.5.
Equilibrium expenditure is $5 billion.
At equilibrium:
Y = AE
Y=C+I+G
= 0.6Y + 1.5 + 0.5
0.4Y = 2.0
Y = $5m
5a. The consumption function is for Zeeland is:
C = 100 + 0.9(Y – T).
The consumption function is the relationship between consumption expenditure and disposable income, other things
remaining the same.
5b. The equation to the AE curve is:
AE = 600 + 0.9Y,
where Y is real GDP.
Aggregate planned expenditure is the sum of consumption expenditure, investment, government expenditure, and net
exports. Using the symbol AE for aggregate planned expenditure, aggregate planned expenditure is:
AE = 100 + 0.9(Y – 400) + 460 + 400
AE = 100 + 0.9Y – 360 + 460 + 400
AE = 600 + 0.9Y
5c.
Equilibrium expenditure is $6,000 billion.
At equilibrium:
Y = AE
= 600 + 0.9Y
0.1Y = 600
Y = $6,000 billion
5d. Equilibrium real expenditure decreases by $1,000 billion, and the multiplier is 10.
The multiplier
= 1/(1  mpc)
= 1/(1  0.9)
= 10.
The change in equilibrium expenditure equals the change in investment multiplied by 10.
Ye = I x 10
= 100 x 10
= $1,000b
7a. The quantity demanded increases by $1,000 billion at constant prices.
The increase in investment shifts the aggregate demand curve rightward by the change in investment times the multiplier.
The multiplier is 10 and the change in investment is $100 billion, so the aggregate demand curve shifts rightward by $1,000
billion from AD to AD/. A move from a to b in figure 2. This would only happen if prices were held constant.
7b. In the short-run, real GDP increases by less than $1,000 billion.
Short run equilibrium real GDP is determined by the intersection of the AD curve and the SAS curve. In the short run, the
price level will rise and real GDP will increase but by an amount less than the shift of the AD curve. A move from b to c in
figure 2. In comparative static analysis b is not an equilibrium position, the economy moves from a to c.
7c. In the long-run, real GDP will equal potential GDP, so real GDP does not increase.
Long run equilibrium real GDP is determined by the intersection of the AD curve and the LAS curve. After the initial
increase in investment, money wages increase, the SAS curve shifts leftward from SAS to SAS / in figure 2, and in the long
run, real GDP moves back to potential GDP. A move from c to a/ in figure 2.
7d. In the short run, the price level rises.
7e. In the long run, the price level rises.
AE/(p=100)
AE//(p=102)
AE (p=100)
b
•
E1
c
E2
Antarctica – Problem 8
•
a
•
E0
Expenditure
Expenditure
Zeeland – Problem 7
E2
•
a
•
E0
7000
LAS
SAS/
SAS
a/
•
a
•
•c
104
real GDP
Price level
Price level
•
c
I=1
6000
104
102
100
b
E1
I=100
AE/(p=100)
AE//(p=102)
AE (p=100)
104
102
100
•b
124
LAS
real GDP
SAS/
•
a
•
•c
•b
AD/
AD/
AD
6000
Figure 2
7000
SAS
a/
AD
real GDP
104
Figure 3
124
real GDP