4-4a Purchasing Power Parity

David R. Frazier Photolibrary, Inc./Alamy

Pharmaceuticals Trade in Global Markets.

the bike at a competitive price. According to the law of one price, identical goods should sell for the same price in different countries according to the local currencies. Suppose one is located in the United States and could purchase a bike for $150 in the United States, but it sells for €100 in Europe. If the exchange rate were $1.40 per euro, then the cost of the bike in Europe, in dollars, would be $140 (i.e., €100 3 $1.40/€). This comparison shows that it is cheaper to purchase the bike from the European supplier. Because it is likely that shipping costs would be higher from Europe to the United States than within the United States, the $10 difference in price may be attributable to shipping costs. If the law of one price holds, this comparison should be true. If not, one could make arbitrage profits by purchasing bikes in Europe and selling them in the United States for less than U.S. bike vendors. Over time, the price of European bikes would rise in price due to higher (arbitrage) demand, and U.S. bike prices would fall due to lower demand; eventually prices in Europe and the United States would converge.

The law of one price is the underlying principle of the purchasing power parity (PPP) theory. By comparing the prices of identical goods in different countries, assuming efficient markets that arbitrage away price differences, the real or PPP exchange rate can be computed. Of course, markets are not perfectly efficient due to imperfections, such as trading costs (e.g., the bicycle’s shipping costs in the above example) or other costs. 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? Given an exchange rate

law of one price

principle stating that identical goods should sell for the same price in different countries according to local currencies

arbitrage

buying goods in a lower priced market and selling them in a higher priced market to make profits

purchasing power parity (PPP)

theory stating that a basket of goods should have approximately the same prices across different countries

big mac index

calculation using the cost of a McDonald’s restaurant sandwich to assess the relative values of currencies

of $1.40 per euro, the French Big Mac in dollars costs $3.50. The Economist computes the parity ratio of foreign cost (in dollars) to U.S. cost, or $3.50/$3.80 5 0.92.9 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 Economist10, 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 $4.43/$4.20 5 1.05. 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:

PUS(1 1 IUS) 5 (1 1 p)PE(1 1 IE), (4.1)

where PUS 5 price index of U.S. goods in dollars PE 5 price index of European goods in dollars IUS 5 inflation rate in the United States in dollar terms IE 5 inflation rate in Europe in euro terms p 5 percentage change in the euro, which equals the forward premium [(F 2 S)/S] 3 100 with F the forward dollar/euro exchange rate and S the spot dollar/euro exchange rate.

Given an exchange rate of $1.40 per euro, an initial PPP with PUS 5 $140 and PE 5 €100 or $140, and 10 percent U.S. inflation and 0 percent European inflation, we have

$140(1.10) 5 (1 1 p) $140(1),

such that the forward premium p 5 [($154 2 $140)/$140] 3 100 5 10 percent. Hence, the value of the euro will increase by 10 percent against the dollar over the next year due to U.S. inflation. After this adjustment in exchange rates, the purchasing power of buyers will be the same for both U.S. and European goods.

An important lesson here is that if one country’s inflation rate exceeds other countries’ inflation rates, then it will experience depreciation of its currency relative to foreign currencies. A simple way to write this idea (approximately at least) is: X 5 IDomestic