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(1)

ICU winter 2011, Principles of Macroeconomic December 20, 2011

Quiz #1 Solution

Problem 1 (8pts×4) (References: topic 2 and chapter 2)

(a) U.S. Air Force belongs to the U.S. government, so its purchase of the airplane from Boeing is government spending of the U.S.

(b) Japan Airlines is a foreign firm, and its purchase of the airplane from Boeing is an export of the U.S.

(c) American Airlines is a U.S. firm and airplanes are its capital, thus its purchase of the airplane from Boeing is an investment of the U.S.

(d) Because the airplane is built now but sold next year, it is an inventory and thus is an investment of the U.S.

Problem 2 (8pts×5) (References: topic 2 and chapter 2)

2009 (base year) 2010

price quantity price quantity

Rice $5,000 /ton 10 tons $6,600 /ton 10 tons

PC $1,000 /PC 50 PCs $900 /PC 60 PCs

(a) Nominal GDP of 2009 and real GDP of 2010:

2009 2009 2009 2009 2009 5000 10 1000 50 $100, 000

rice rice PC PC

NGDP =P Q +P Q = × + × =

2010 2009 2010 2009 2010 5000 10 1000 60 $110, 000

rice rice PC PC

RGDP =P Q +P Q = × + × =

(b) Growth rate of real GDP in 2010:

2010 2009 2010 2009

2010

2009 2009

$1

100% 100%

110, 000 100, 000

100% 100, 000 0%

RGDP RGDP RGDP GDP

g RGDP P

N NGD

− −

= × = ×

= × − =

Note that we have used in the above calculation. This is because 2009 is the base year and thus the nominal and real GDP of this year are the same.

2009 N 2009

RGDP = GDP

(c) First we compute the nominal GDP of 2010 as follows:

2010 2010 2010 2010 2010 6600 10 900 60 120, 000

rice rice PC PC

NGDP =P Q +P Q = × + × = .

GDP deflator in 2010 is 2010 2010

2010

120, 000 12

100 100

110, 000 11 GDPdef NGDP

RGDP

= = × = × .

1

(2)

Thus the price level had risen in 2010 by

2010

12 1

100 (%) 100 100 (%) 100 (%)

11 11 9.1%

GDPdef = × = × =

The price level is an average of the two prices Price and PPC. Although P2010PC <P2009PC , but P2010rice>P2009rice and the increase in Pricedominated the decrease in PPC, thus the price level had risen in 2010.

(d) Comparing the quantities produced in the two years 2009 and 2010, we observe that but

2010 2009

rice rice

Q =Q Q2010PC >Q2009PC , thus if the level of well-being is measured by the quantities of goods, the level of well-being was higher in 2010 than in 2009.

Problem 3 (8+10+10 pts) (References: topic 3 and chapter 3)

(a) Since the government follows a balanced budget rule, the change in taxes must always equal the change in government spending, thus ∆ = ∆T G .

(b)

We have learned that S=I r( )=YC Y( − −T) G (see slide #54 of the lecture note of topic 3). So, other things being the same, G S and

(note that I is a decreasing function in r, so I and r must always move in opposite directions). However, in this case we have and T at the same time, which affect each of I and r in opposite directions. Therefore, to analyze the responses of I and r to the policy, we need to look more closely at the quantitative effects of and T on the I and r. From the above equation, an increase of G by reduces I by , and an increase of T by raises

,I , & r

↑⇒ ↓ ↓ ↑

G , , &

T↑⇒ ↑ ↑S I r

G

G

GG ∆ = ∆T

r

I,S G

ΔG T

S’’ S’ S

The new equilibrium MPC

×ΔG

I(r) E

E’

The original equilibrium

I I’ r’

r

2

(3)

I by MPC×∆ (where: MPC<1 is the marginal propensity to consume, see slide G

#45). So the total effect of the policy on I is ,

(recall ), and thus the effect on r is positive. We conclude that

( 1)

MPC×∆ −∆ =G G MPC− ×∆ < 0G 1

MPC < investment

falls and the interest rate rises in response to the policy. The effects of the policy are shown graphically in the above figure.

(c) We can see that the results in (b) depend crucially on MPC. If MPC is close to 0, then 1

MPC is large, and thus, quantitatively, the effects of the policy on I and r are large. Conversely, if MPC is close to 1, then MPC1 is small, and thus the effects of the policy on I and r are quantitatively small. In the extreme case in which MPC=1, the policy have no effects on I and r, because in this case the effects and exactly cancel out each other.

G T

3

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