A basket of goods and services costs \(100 in the United States costs 800 pesos in Mexico, and the current nominal exchange rate is 10 pesos per U.S. dollar. Over the next five years, the cost of that market basket rises to \)120 in the United States and 1,200 pesos in Mexico, although the nominal exchange rate remains at 10 pesos per U.S. dollar. Calculate the following.

a. The real exchange rate now and five years from now, if ' 'today's price index in both countries is 100

b. Purchasing power parity today and five years from now

The real exchange will be$PesosperU.S.dollar\times \frac{AggregateindexlevelintheU.S.}{AggregateindexlevelintheMexico}$

The aggregate price level in the U.S. and Mexico today is 100.

The real exchange rate now is 10$\left(10\times \frac{100}{100}=10\right)$ .

The aggregate price index after five years in the U.S. will be 120 $\left(100\times \frac{120}{100}=120\right)$; the cost of the basket after five years divided by the cost of the basket today then multiplied by 100 gives the price index after five years. The aggregate price index after years in Mexico will be 150$\left(100\times \frac{1,200}{800}=150\right)$ . The real exchange rate after five years is 8 $\left(10\times \frac{120}{150}=8\right)$.

The cost of the basket of goods and services today in the U.S. is $100, and in Mexico is $800; the purchasing power parity will be 8 pesos per U.S. dollar$\left(\frac{800}{100}=8\right)$ . After five years, the basket of goods and services in the U.S. will be $120, Mexico will be $1200 and the purchasing power parity will be 10 pesos per U.S. dollar$\left(\frac{1200}{120}=10\right)$ .