A.2. a. The level of GDP per capita in each country, measured in its own currency is
(CPUs per capita ´ Price) + (IC per capita ´ Price) = GDP per capita.
Therefore, Richland’s GDP per capita is 40 and Poorland’s GDP per capita is 4.
b. The market exchange rate is determined by the law of one price. As CPUs are the only traded good, the price of computers should be the same. Consequently, the exchange rate must be
2 Richland dollars to 1 Poorland dollar.
c. To find the ratio of GDP per capita between Richland and Poorland, we must first convert GDP denominations into the same currency. In the analysis that follows, I choose to convert GDP denominations into Poorland dollars, but converting to Richland dollars is equally correct, similar, and will yield the same result. From Part (a), we convert Richland’s GDP per capita, denominated in Richland dollars, into Poorland dollars by multiplying GDP per capita with the market exchange rate. Since from Part (b), we know 2 Richland dollars equals 1 Poorland dollar, we multiply 1/2 to Richland’s GDP per capita, yielding 20 Poorland dollars. Thus, the ratio of Richland GDP per capita to Poorland GDP per capita is 5:1.
d. A natural basket to use is 3 computers and 1 ice cream. The cost of this basket in Richland
is 10 Richland dollars. The cost of this basket in Poorland is 4 Poorland dollars. Equating
the costs of baskets to be one price, the purchasing power parity exchange rate must be
10 Richland dollars: 4 Poorland dollars.
e. To find the ratio of GDP per capita between Richland and Poorland, we must first convert GDP denominations into the same currency. In the analysis that follows, I choose to convert GDP denominations into Poorland dollars, but converting to Richland dollars is equally correct, similar, and will yield the same result. From Part (a), we convert Richland’s GDP per capita, denominated in Richland dollars, into Poorland dollars by multiplying GDP per capita with the PPP exchange rate. Since from Part (d), we know 10 Richland dollars equals 4 Poorland dollars, we multiply 4/10 to Richland’s GDP per capita, yielding 16 Poorland dollars. Thus the ratio of Richland GDP per capita to Poorland GDP per capita is 4:1.