Download Spring 2012, Problem Set 3 Prof. Hui He

ECON131
Principles of Macroeconomics
Spring 2012, Problem Set 3
Suggested Answer
Prof. Hui He
Due on March 19, 2012
Topic: aggregate demand and measurement of GDP
Question 2-4 on page 167 and question 1-3 on page 173 on the textbook.
Question 2 on page 167 (5points)
Answer: In ordinary language, an investment is the purchase of any asset, irrespective of
whether the asset is newly produced or used, or whether it is a real thing or a financial
instrument. Economists restrict the term to the purchase of new, physical assets,
including plant and equipment, inventory and housing. For an economist, investment is
an increase in the capital stock.
(a) Investment.
(b) Not investment (financial asset, not physical).
(c) Not investment (previously produced asset, not new).
(d) Investment.
(e) Not investment (previously produced asset, not new).
Question 3 on page 167 (5 points)
Answer: Line C0 is the consumption function for Simpleland. The marginal propensity to
consume can be calculated from the data for any pair of years. For example, for the
period 2006–2007:
MPC = [C(2007) – C(2006)]/[Y(2007) – Y(2006)]
= (2,160 – 1,920)/(2,700 – 2,400) = 240/300 = 0.8
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Question 4 on page 167 (5 points)
Answer: As shown on Figure 6 in the text (page 162), the consumption function shifts
down when the price level rises, from C0 to C2.
Question 1 on page 173 (8points)
Answer: (a) Included: GDP rises by $25,000.
(b) Not included, because it was produced in another country. Actually, it is
included as part of C, but then deducted as part of IM, which enters negatively in
C + I + G + (X - IM).
(c) Not included, since it was not produced this year.
(d) Included: GDP rises by $500 million (in investment, I).
(e) Not included; it’s a government transfer payment.
(f) Included, as investment in inventory: GDP rises by $15 million.
(g) Included, as consumption (legal services): GDP rises by $10,000.
(h) Not included: previously produced.
Question 2 on page 173 (6 points)
Answer: GDP as the Sum of Final Demands (all figures in millions)
Source
Specific
Super
Motors
Duper
Total
C
4.8
14.0
18.8
I
0.8
0.8
G
0.0
X
1.2
1.2
Y
20.8
GDP as the Sum of Incomes (all figures in millions)
Source
Wages
Interest
Rent
Profits
Y
Specific
Motors
3.8
0.1
0.2
2.7
Super
Duper
4.5
0.2
1.0
1.3
Farmers
0.7
2.0
4.3
Total
8.3
1.0
3.2
8.3
20.8
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Note: Profits were computed as follows:
Revenues
– Wages
– Interest
– Rent
– Intermediate Goods
= Profits
Specific
Motors
6.8
–3.8
–0.1
–0.2
2.7
Super
Duper
14.0
–4.5
–0.2
–1.0
–7.0
1.3
Farmers
7.0
–0.7
–2.0
4.3
Question 3 on page 173 (6 points)
Answer: GDP as the Sum of Final Demands (all figures in millions)
GDP as the Sum of Incomes (all figures in millions)
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Personal income = National income + Transfer payments
= 20.1 + 1.2 = 21.3
Disposable income = Personal income - Taxes
= 21.3 - 1.33 = 19.97
(since taxes are 10% of wages + interest + rent, which total 13.3)
Note: Profits were computed as follows:
(Note that there is a typo in the table above. Depreciation -0.6 should belong to Specific
Motors and -0.2 goes to Super Duper)
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Topic: demand-side equilibrium
Question 1, 2, 4, 5, 6, and 7 on page 192-193 and question 4 on page 194 on the textbook
Question 1 on page 192 (5 points)
Answer:
FIGURE 1
The original equilibrium GDP is at Y = 3,800, where spending equals output. This
is shown by the intersection of the lower of the two expenditure lines in the graph
above with the 45° line. The MPC calculated from the data is 0.90, so the
multiplier is 10. If investment spending rises by $20 (to $260) the equilibrium
GDP will increase by $20×10 = $200, which is represented by a vertical shift (by
$20) to the upper expenditure function in the diagram.
Question 2 on page 192 (5points)
Answer: In question 2, the marginal propensity to consume is lower than it was in
question 3 (0.6 versus 0.9), but in this case there is induced investment
(investment which changes as GDP changes), while in question 3 investment was
constant. The two changes cancel each other, and the expenditure schedule is the
same in both questions. So Figure 1 applies to Question 2, and the equilibrium
GDP is 3800.
Question 4 on page 192 (5 points)
Answer: Y = C + I + G + (X – IM)
C = 300 + 0.75DI
5
C = 300 + 0.75(Y – 1200)
C = 300 + 0.75Y – 900
C = -600 + 0.75Y
Y = -600 + 0.75Y + 900 + 1300 – 100
Y = 0.75Y + 1500
0.25Y= 1500
Y = (1/0.25)  1500
Y = 4  1500 = 6000
This algebraic model yields the same equilibrium GDP as Table 26-2. (The
solution is also given in the Appendix.)
Question 5 on page 192 (5 points)
Answer: Y = C + I + G + (X - IM)
C = 300 + 0.75DI
C = 300 + 0.75(Y - 1,200)
C = 300 + 0.75Y - 900
C= -600 + 0.75Y
Y= -600 + 0.75Y + 1,100 + 1,300 - 100
Y = 0.75Y + 1,700
0.25Y = 1,700
Y = 4 × 1,700 = 6,800
This algebraic model yields the same equilibrium GDP as Table 3 and Figure 10
in the chapter.
Compared to the answer to Test Yourself Question 4, we find $800 more in GDP
from a $200 increase in I. Thus this question demonstrates that the multiplier of 4
applies to changes in I as well as to changes in C.
Question 6 on page 192 (10 points)
Answer: Y = C + I + G + (X – IM)
C = 200 + 0.8(Y – 1000)
C = 200 + 0.8Y – 800
C = –600 + 0.8Y
Y = –600 + 0.8Y + 600 + 1000 + 100
Y = 1100 + 0.8Y
0.2Y= 1100
Y = 5*(1100) = 5500
The multiplier is 5. If G rises by $100, Y will increase by $500 (5  $100). Table
26-3 and Figure 26-10 in the text. This question demonstrates that the multiplier
applies to changes in I as well as changes in C.
If G and T each increase by $100 Y will increase by $100 as demonstrated below:
Y = C + I + G + (X – IM)
C = 200 + 0.8(Y – 1100)
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C = 200 + 0.8Y – 880
C = –680 + 0.8Y
Y = –680 + 0.8Y + 600 + 1100 + 100
Y = 1120 + 0.8Y
0.2Y= 1120
Y = 5*(1120) = 5600
Question 7 on page 193 (10 points)
Answer:
FIGURE 3
Question 4 on page 194 (10 points)
Answer: (a) Y = C + I + G + (X – IM)
C = 50 + 0.75(Y – 200)
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C = 50 + 0.75Y – 150
C = –100 + 0.75Y
Y = –100 + 0.75Y + 500 + 300 + 0
Y = 0.75Y + 700
0.25Y= 700
Y = (1/0.25)  700
Y = 4  700 = 2800
(b) There is a recessionary gap of 200.
(c) The last five lines in 4(a) above are replaced by:
Y = –100 + 0.75Y + 600 + 300 + 0
Y = 0.75Y + 800
0.25Y= 800
Y = (1/0.25)  800
Y = 4  800 = 3200
(d) There is now an inflationary gap of 200.
Topic: AS-AD equilibrium
Question 1 and 3 on page 217 on the textbook.
Question 1 on page 217 (5 points)
Answer:
FIGURE 1
Equilibrium real output is $3,000, while the price level is 100. Since full
employment is at $2,800 billion, there is an inflationary gap of 200.
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Question 3 on page 217 (10 points)
Answer:
FIGURE 2
(a) In Chapter 26, Test Yourself Question 2, the marginal propensity to consume
was 0.9, and the (oversimplified) multiplier was therefore 10. The table in this
question confirms that when investment rises by 20, from 240 to 260,
aggregate demand rises by 200 at any given price level. For example, at a
price level of 105, aggregate demand rises from 3,770 to 3,970.
(b) Initial equilibrium: P = 100, Y = 3,800. Eventual equilibrium: P = 110, Y =
3,940. The multiplier, taking account of price increases, is 140/20 = 7, which
is less than 10.
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