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Final Exam, Spring 2010. Daytime MBA. Each question 10 points. 100 points total. SHOW WORK.
1.
Steve and Erwan have the following production possibilities schedule
Beef
Poultry
Steve
10/hour
8/hour
Erwan
8/hour
7/hour
a. 2 points. Suppose Steve and Erwan do NOT trade and they each spend 4 hours a day making
beef and 4 hours a day making poultry. How much beef and poultry do Steve and Erwan
each produce (and immediately consume).
Steve makes 4*10 = 40 units of beef and 4*8 = 32 units of poultry. Erwan makes 4*8 = 32
units of beef and 4*7 = 28 units of poultry.
b. 4 points. Prior to trade, what is the cost of Beef in units of Poultry for Steve? What is the
cost of Beef in units of Poultry for Erwan?
It takes Steve 6 minutes (=60/10) to make one unit of beef and 7.5 minutes (=60/8) to make
one unit of poultry. If Steve makes one more unit of beef he loses 0.80 units of poultry
(=6/7.5).
It takes Erwan 7.5 minutes to make one more unit of beef and 8.57 minutes (=60/7) to make
one more unit of poultry. If Erwan makes one more unit of beef he loses 0.875 units of
poultry (=7.5/8.57).
c. 4 points. Now Suppose Steve and Erwan start to trade. What does Steve export to Erwan?
What does Erwan export to Steve? Explain why.
Steve exports beef to Erwan because he is the low cost producer of beef (0.80 compared to
0.875). Erwan exports poultry to Steve because he is the low cost producer of poultry
(1/0.875 compared to 1/0.80).
2. Steve and Erwan have the following production possibilities schedule
Consumption today
Consumption tomorrow
Steve
10.00/hour
10.20/hour
Erwan
8.00/hour
8.40/hour
a. 2 points. Suppose Steve and Erwan do NOT trade and they each spend 4 hours a day making
Consumption today and 4 hours a day making Consumption tomorrow. How many units of
Consumption today and Consumption tomorrow do Steve and Erwan each produce.
Steve makes 4*10 = 40 units of consumption today and 4*10.2 = 40.8 units of consumption
tomorrow. Erwan makes 4*8 = 32 units of consumption today and 4*8.4 = 33.6 units of
consumption tomorrow.
b. 4 points. Prior to trade, what is the implied interest rate for Steve? What is the implied
interest rate for Erwan?
The interest rate is the number of units of consumption tomorrow a person foregoes to
have one more unit of consumption today.
It takes Steve 6 minutes (=60/10) to make one unit of consumption today and 5.88 minutes
(=60/10.2) to make one unit of consumption tomorrow. If Steve wants one more unit of
consumption today, he must forego 1.02 units of consumption tomorrow (=6/5.88). The
interest rate for Steve is 2 percent.
It takes Erwan 7.5 minutes (=60/8) to make one unit of consumption today and 7.143
minutes (=60/8.4) to make one unit of consumption tomorrow. If Erwan wants one more
unit of consumption today, he must forego 1.05 units of consumption tomorrow
(=7.5/7.143). The interest rate for Erwan is 5 percent.
c. 4 points. Now Suppose Steve and Erwan start to trade. Who runs a trade deficit? Explain
why.
Steve is the low cost producer of consumption today (1.02 compared to 1.05) so he exports
consumption today to Erwan. This means that Erwan runs a trade deficit. (Erwan will
export consumption tomorrow to Steve).
3. On January 1, 2008, the price of a Big Mac is $3.00 in the United States and the exchange rate is
1.5 U.S. dollars per English pound. The inflation rate in the United States in 2008 is 2 percent
and the inflation rate in England in 2008 is 4 percent. Assume purchasing power parity holds.
a. 5 points. What is the price of a Big Mac in England on January 1, 2008 and January 1, 2009
If purchasing power parity holds, then a Big Mac costing $3.00 in the U.S. must cost 2 English
pounds on 1/1/2008 if the exchange rate is 1.5 U.S. dollars per English pound on that date.
If the inflation rate in England is 4 percent in 2008, then the big Mac will cost 2.08 English
pounds (=2 * 1.04) on 1/1/2009.
Note that the price of a Big Mac on 1/1/2009 is $3.06 given the inflation rate in the US is 2
percent. We will use this in the next question.
b. 5 points. What is the Exchange rate in U.S. dollars per English pound on January 1, 2009.
Assuming purchasing power parity holds on 1/1/2009, the exchange rate must be set such
that no profits can be made buying and selling Big Mac costing $3.06 in the US and 2.08
English pounds in England. It must be that $3.06 = 2.08 pounds. The exchange rate is $1.47
dollars per English pound.
(It is not a surprise that the pound depreciated relative to the US dollar – the inflation rate
was higher in England than the U.S.)
4. On January 1, 2009, one English pound can buy 1.5 U.S. dollars. The one-year real risk-free
interest rate in England and the United States is 3 percent. The expected inflation rate in 2009 is
1 percent in the United States and the expected inflation rate in England is 5 percent. Assuming
that the Fisher equation, purchasing power parity, and covered interest party all hold, what is
the forward exchange rate in dollars per pound for January 1, 2010, when contracted on January
1, 2009.
From the Fisher equation, the nominal interest rate in the U.S. is equal to 4.03 percent, that is
1.0403 = (1.03)*(1.01). The nominal interest rate in England is equal to 8.15 percent, that is
1.0815 = (1.03)*(1.05).
(1 + iUS) * Spot $/pound = (1 + iEngland) * Forward$/pound
(1.0403) * 1.5
= (1.0815) * Forward
Forward = 1.443$/pound
5. You have been given the following information for the country of Costa Rica:
Year
Apple Prices
Apple Quantities
Banana Prices
Banana Quantities
2000
3
4
5
6
2001
3.2
4.1
5.2
6.1
Fill out the following table (in your blue book), make sure to show work.
Year
Expenditures on
Apples
Expenditures on
Bananas
Nominal GDP
2000
12 = 3*4
30 = 5*6
42 = 12 + 30
2001
13.12 = 3.2*4.1
31.72 = 5.2*6.1
44.84 = 13.12 + 31.72
6. Given your answer from question 5, fill out the following table in your blue book. Make sure to
show work.
Year
Growth Rate of
Real GDP
(in Percent)
Inflation Rate
(in Percent)
2000
1.91%
4.76%
Growth rate of real GDP and inflation – use expenditure share method.
Expenditure share on apples in 2000 is 12/42 = 0.286.
Expenditure share on bananas in 2000 is 0.714 = 1.0 – 0.286
Growth rate of GDP = 0.286*(4.1/4) + 0.714*(6.1/6) – 1.0 = 0.0191. 1.91%
Inflation rate = 0.286*(3.2/3) + 0.714*(5.2/5) – 1.0 = 0.0476. 4.76%
7. Given your answer from questions 5 and 6, fill out the following table in your blue book. Make
sure to show work.
Note that real GDP = nominal GDP in the base year; then real GDP computations should simply
preserve growth rates.
Year
Real GDP,
BASE YEAR 2000
Real GDP,
BASE YEAR 2001
2000
42.00
44.00 = 44.84/1.0191
2001
42.802 = 42*1.0191
44.84
8. Explain why government tax revenues and deficits are not the same thing as “government
spending” in the National Income and Product Accounts.
The government has two roles: to redistribute income among agents and to buy and maintain
public goods (such as national defense). The purchase and maintenance of public goods is
Government Spending in the NIPA. The government runs a deficit if the sum of its spending
AND its transfers is greater than its tax revenues collected.
9. An acquaintance named Lutz hands you the following data on sources of income in the year
2009 in Germany:
Unambiguous Labor Income
60 Marks
Unambiguous Capital Income
25 Marks
Ambiguous Income Source 1
7 Marks
Ambiguous Income Source 2
8 Marks
Total Income
100 Marks
Using the method we discussed in class and in the book, estimate the fraction of total income
accruing to capital in Germany in 2009. Show work.
The method we discussed in class sets
α = Unambiguous capital income / (Total income – ambiguous income)
= 25 / (100 - 7- 8) = 25/85 = 0.294
10. You have been told that a firm produces output Y using Labor L according to the production
function: Y = 100 Lα. The available data suggest α=0.5 for this firm. You also know that the
marginal cost of an additional unit of labor is $15. How many units of labor (fractional units of
labor are OK) should the firm employ to maximize profits? Show work!
A firm profit maximizes when the marginal product of labor is equal to the wage.
The marginal product of labor is the derivative = α*100*Lα-1
Profit maximization implies: α*100*Lα-1 = 15. Substituting α=0.5 gives 50* L-0.5 = 15.
Reducing gives L-0.5 = 0.3. This can be solved a few ways, but the most straightforward
is L = 0.3-1/0.5 = 0.3-2 = 11.11.
Do a check: 0.5*100*11.11-0.5 = 15 = the wage.