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Midterm Exam
Economics 112
Principles of Macroeconomics
I. Short Calculations (10 points each)
A. The price of a Big Mac in Hong Kong is $9.90. The price of a Big Mac in
Germany is DM4.90 (DM is the abbreviation for DeutschMark or German mark).
The nominal exchange rate between Hong Kong and Germany is such that 4.675
Hong Kong Dollars are necessary to buy 1 German mark. What is the real Big
Mac Exchange rate (treating Hong Kong as the domestic country)?
The real exchange rate is HK:DEUBIGMAC = eHK:DEU * (PHKBIGMAC / PDEUBIGMAC) where
eHK:DEU is the HK$: DM exchange rate. In this case eHK:DEU = (1/4.675) =.214. The
Big Mac exchange rate is HK:DEUBIGMAC =.432=.214*9.90/4.90.
B. In 1997, the velocity in Germany and Hong Kong was the same as in 1996. The
real exchange rate between the two countries was the same in 1996 and 1997.
Money growth in Germany was 5% and money growth in Hong Kong was 7%.
Assume both countries had the same real growth rates (1%), what is the growth
rate of the Hong Kong-Germany nominal exchange rate (treating Hong Kong as
the domestic country).
We know that g = ge +  - *. If real exchange rate remains constant then,
ge = *- 
We also know that with constant velocity,  =gM - gY, if both countries have the same
growth rate of money we know that *-  = gM* - gM, in this case .05-.07=-.02.
II. Graphical Questions (15 points each)
A. Consider two countries, Austria and Bulgaria, which have no population growth
and no technology growth. Austrians and Bulgarians have the same production
function and technology level. Austrians and Bulgarians also invest the same
percentage of income (i.e. sAUS = sBUL). However, the weather is so bad in
Bulgaria, that capital has a faster depreciation rate in Bulgaria than in Austria.
Explain in words (no more than 4 sentences) and 1 graph which country will have
the highest steady state output per worker.
A graph of this model is:
dBULk
i
dAUSk
k
In each period, both countries contribute the same share of output to investment, but
Bulgaria must contribute a greater share of that just to replacing lost capital. When
Bulgaria reaches that level of capital such that its investment share is equal to its
capital replacement needs, Austrian gross investment will still be above its capital
replacement needs. Austria will still be able to conduct net investment and its capital
stock and output will grow beyond Bulgaria.
B. Consider the effect of an expansion in the investment schedule on a small open
economy's real exchange rate and net exports. Due to an expansion in business
optimism, the amount of investment that a country's businesses will want to
engage in at any interest rate expands. Assume that national savings remain
constant. What is the effect of this expansion on net exports and the real exchange
rate? Explain with two graphs and at most 5 sentences.
S
r
NFI1
r*
NFI0
I1
I0

NFI1
NFI0
1
0
NX
A boom in confidence increases the amount of domestic investment that will be done
at the world interest rate. This reduces the net amount of funds available for foreign
investment and reduces the supply of domestic currency in foreign exchange markets.
Purchasers of domestic currency will pay a higher price for the currency (the
exchange rate will rise) and domestic goods will be less competitive. Net Exports will
drop.
III. Longer Questions (25 points each)
A. i) The capital stock in Hong Kong is K =100 Units and the Labor supply is L =
100 units. Calculate output if the production function is:
Y K L
Y = 100.
ii) The consumption function is:
C = 20 + .5(Disposable Income)
If taxes are T = 0 and government spending is G = 20. What are consumption,
the budget deficit, private saving, and national saving?
Disposable income = Y - T = 100 - 0 = 100. C = 20+ .5*100 = 70. Private Saving =
Y - T - C = 100 -70 = 30. The budget deficit = G - T = 20. National saving = Private
Saving - Budget Deficit = 10.
iii) The investment function is:
I = 30-100r
The net real interest rate prevailing in Global markets is r = .1. What will
investment be? What will Net Exports be? What will the trade deficit be?
What will net foreign investment be?
Invest will be I=30-100*.1 = 30-10 = 20. Net Exports = Y - C - I - G = 100 70 - 20 -20 = -10. The trade deficit = 10. Net foreign investment = -10.
iv) Assume that net exports are given by:
NX = 100 (1 - )
What is the real exchange rate?
Net Exports = -10 = 100(1-)  =1.10
v) Now assume that the government raises taxes sufficient to close the budget
deficit. What is the new level of net exports and the new real exchange rate?
T = 20, Budget Deficit = 0. Disposable Income = 100 - 20 = 80. C = 60. I = 20,
G = 20. NX = 100 - 60-20-20 = 0. 0 = 100(1-)  =1.
B. Unemployment and Output per Worker
i)
Compare two countries, France and Hong Kong. In France and Hong
Kong, 1% of the countries employed people become laid off in every
quarter. However, in France the unemployment benefits are substantially
more generous than Hong Kong. In France, 5% of unemployed people find
a job every quarter, while in Hong Kong, the job finding rate is 10%. What
are the steady state unemployment rates in France and Hong Kong.
French Steady State Unemployment = .01/(.01+.05) = .166.
Hong Kong Steady State Unemployment = .01/(.01+.10) = .091.
ii)
Assume production of goods in services in France and Hong Kong are
given by the function:
Yt  K t Et
Where Et is the number of employed people. Show that we can write
output per person in the labor force as:
yt  1  u k t
y
Y

L
where yt is output per person in the labor force; k is capital per person in
the labor force and u is the unemployment rate. Calculate the ratio of
output per person in the labor force in France to output per person in
the labor force and Hong Kong when both have the same level of k
(capital per person in the labor force) and the unemployment rate is at
its long run level.
K E
K
E
L U


 k
 k  1 u
L
L
L
L
y France

y HK
k  1  u France
k  1  u HK

1  u France
1  u HK

.833
 .957
.909
iii) Assume that the investment rate in France and Hong Kong is 20% (i.e. the
ratio of investment per person in the labor force to output per person in the
labor force is .2). Assume the depreciation rate in both countries is 10% and
technology growth and labor force growth is zero. Calculate steady state
output per person in the labor force in France and Hong Kong when
unemployment is at its steady state level. Explain why the ratio of French
steady state output per person in the labor force to Hong Kong steady state
output per person in the labor force is smaller than your answer to question ii).
s k ss  1  u  dk ss 

s
s
 1  u  k ss   1  u  1  u  k ss  1  u  y ss
d
d
s
 (1  u )  y ss
d
yFrancess =(.2/.1)*.833=1.667
yHKss =(.2/.1)*.909=1.818
SS
y France
1.667

 .916  .957
SS
1.818
y HK
Because the employment rate is higher in Hong Kong, than in France, output
and gross investment per person in the labor force is higher in Hong Kong
than in France. Because Gross Investment per Person in the Labor Force in
Hong Kong is Higher than in France at all levels of capital stock, when
French capital per person in the labor force reaches steady state, Hong Kong
capital per person in the labor force is still growing. Hong Kong will achieve
a higher capital per person in the labor force in steady state which will
reinforce the fact that employment per person in the labor force is also higher
in Hong Kong.