Finance 475

Problem Set #2

1)      Suppose that the annualized inflation in the US is 3% while annual inflation in Europe is 1%.  If the current exchange rate is $1.40 per Euro, that would you expect the exchange rate to be in one year?  If the exchange rate one year from now turns out to be $1.50 per Euro, what has happened to the real exchange rate?

2)      Suppose that The United States and Japan only produce one good Roller Skates.  Further, assume that Japanese produced roller skates and American roller skates are identical in every way. 

a)      If the American price of roller skates is $40 and the Japanese price of roller skates is 4,300 Yen, what should the Dollar/Yen exchange rate be?

b)      Now, suppose that it costs $5/pair to ship roller skates from the US to Japan.  Within what range could the nominal exchange rate fluctuate without creating an arbitrage opportunity in roller skates 

3)      Continuing with the example in (1), suppose that in addition to roller skates, the U.S. and Japan also have roller skating rinks. The price of admission to a roller skating rink is $10/hr. in the US and Y1075 /hr in Japan.  It is costless to ship roller skates overseas, but passenger flights are very expensive.  Therefore, it is safe to assume that nobody will fly to Japan to go roller-skating (or visa versa).

a)      It is reasonable to believe that roller skating rinks and roller skates are used in equal proportions, so assume that the CPI in both Japan and the U.S. is defined as .5 times the cost of roller skates + .5 times the cost of roller skating rink admission.  Calculate the CPI in Japan and the U.S.  What nominal exchange rate is implied by PPP? 

b)      Suppose that the Japanese roller skate producer experience some cost increases, forcing them to raise their price to Y4750.  What should happen to the nominal exchange rate between the U.S. and Japan? What should happen to the real exchange rate between the U.S. and Japan?

4)      Suppose that the U.S. and Mexico produce and consume three goods - Computers, Petroleum, and medical care.  Computers and Petroleum are traded internationally, but medical care is not.   America produces more computers than Mexico, but Kuwait produces more oil.  Consequentially the U.S. exports computers to Mexico and imports oil.  Suppose that the U.S. and Mexican price levels are defined as follows:

P(U.S) = .2*Pm + .6*Pc +.2*Po

P(Mex) = .2*Pm + .2*Pc + .6*Po

Where Pm is the price of medical care, Pc is the price of a computer and Po is the price of oil. The larger share of oil is the Mexican price reflects the fact that oil is a larger component of Mexican output just as computers are a larger component of U.S. output.

Suppose that we have the following information on prices in the U.S. and Mexico

 

U.S. ( in $s)

Mexico ( in Pesos)

Medical Care

750

7312.50

Computers

2,500

24,375

Oil

38

370.50

a)      Calculate the price levels in the U.S. and Mexico.

b)      Calculate the exchange rate implied by the law of one price (the exchange rate that eliminates profitable arbitrage in computers or oil).

c)      Suppose that Howard Dean gets elected President and immediately creates a universal health care system.  The inefficiency of the government program causes the price of medical care to rise in the U.S. to $1000.  What happens to the U.S. price level, the nominal exchange rate and the real exchange rate?

d)      Suppose the conflict in the Middle East causes the price of oil to rise by 10% worldwide.  What should happen to U.S. and Mexican price levels, the nominal exchange rate, and the real exchange rate?

5)      Over the past decade, the U.S. has experienced a significant economic expansion.  GDP growth has averaged around 4-6% per year.  All else equal, this expansion in the U.S. should appreciate the nominal exchange rate (for reasons we will talk about later).  However, growth in the U.S. has not been even across all sectors of the economy.  High tech industries have expanded much more rapidly than traditional manufacturing sectors (in fact, manufacturing has shrunk).  How could this shift in production affect the U.S. exchange rate? (Hint: Think about possible relative price changes).