Given that these imperfections are not large and

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Given that these imperfections are not large and markets are fairly efficient, a basket of goods should have approximately the same prices across different countries. If the prices of goods change in one country but not in other countries, the exchange rate of the country’s local currency should likewise change with foreign currencies to maintain PPP.
4-4a-(i) The Big Mac Index In 1986, The Economist began publishing the big mac index based upon McDonald’s restaurant sandwich consisting of a number of goods. What if the Big Mac costs $3.80 in the United States but €2.50 in France?
the parity ratio of foreign cost (in dollars) to U.S. cost, or . Since this ratio should be 1 under PPP, in our example the euro is undervalued by 8 percent against the dollar. Again, market imperfections, such as transportation costs, taxes, and the like, could explain all or part of this difference. Differential costs of the Big Mac over time and across nations should be related to changes in currency values as PPP tends to push prices up or down to one price. According to The Economist , on January 11th, 2012, the average dollar price in major U.S. cities for a Big Mac was $4.20. At that time, the average euro price was €3.49, which translates to $4.43 given an exchange rate of $1.27. Again, the actual PPP ratio is computed as foreign cost (in dollars) to U.S cost (in dollars), which equals . Because this ratio is greater than 1 by 5 percent, the euro was 5 percent overvalued. Based on the cited Big Mac Index, Norway’s kroner was overvalued by 63 percent and Switzerland’s franc by 58 percent; but other countries’ currencies were undervalued against the dollar, such as Malaysia’s ringgit by 57 percent, South Africa’s rand by 53 percent, and Hong Kong’s dollar by 52 percent. The Brazilian real and Israeli new shekel were near parity and neither over- nor undervalued. While it would not be practical to purchase Big Macs in undervalued currency countries and sell them in overvalued currency countries to earn arbitrage profits, it is possible to buy and sell the basket of ingredients required to make a Big Mac. Consequently, if price differentials like these existed in traded goods markets, short-run differences should be reversed over time. 4-4a-(ii) Inflation and PPP Consider what would happen if inflation caused the prices of U.S. goods to increase 10 percent over the next year, but no inflation occurred in Europe. Higher U.S. prices would motivate consumers to purchase European goods. To do this, consumers would sell dollars and buy euros, resulting in a decline in value of the dollar (due to increased supply) against the euro (due to increased demand). This would continue over time until PPP was once again achieved. We can compute how much the dollar will decline by using the following PPP equation: (4.1) Given an exchange rate of $1.40 per euro, an initial PPP with and or $140, and 10 percent U.S. inflation and 0 percent European inflation, we have

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