Question

If a Japanese car costs P*=1,000,000 yen, a similar American car costs P= 20,000, and a dollar can buy 100 yen, e= 100 yen/$. Car is assumed to be identical and japan is next door to New Hampshire for simplicity:

a. What is the real exchange rate? In which country is car more expensive?

b. From which country would you buy and which country would you sell?

c. What would be your profit per car in yen and in $?

d. What would happen to the price of the car in japan and the price of the car in the US?

e. why is it called law of one price after such an arbitraging?

f. Why is the relationship between real and exchange rate, E, and nominal exchange rate, e, as a result?

Answer 1

a. The real exchange rate = eP*/P = 100*1000000/20000= 5000

The cost of American cars = eP= 100*20,000=2000000 yen

and cost of japanese cars = 1000,000 yen

Therefore, American cars are more expensive that the Japanese cars.

b. The cars from Japan should be purchased and Japan should sell the cars.

c. The profit per car in yen = 2000000-1000000= 1000000 yen

The profit per car in dollar = P-P*/e= 20000-10000=10000 dollars

d. Price of Japanese car in America = P*/e = 10000 dollars

and price of American car in Japan = eP = 2000000 yen

e. When law of one price does not exists in two different markets, then arbitrage profits will hold until price in both markets become identical. Here,same case exists as American cars are expensive than Japanese cars and therefore, it is profitable for customers to purchase Japanese cars in both American and Japanese markets until price of American cars become exactly the same as price of Japanese cars.

f. Real exchange rate is defined as the ratio of price of a product in a home country versus foreign country multiplied by nominal exchange rate

Mathematically, real exchange rate can be explained as,

   RER= eP*/P, where e= nominal exchange rate , P*= price in domestic country and P = price in a foreign country

From the results of part a), , RER = 5000= 50*100=50e where e=100