The Law of One Price
Law of One Price
In competitive markets free of transportation costs and barriers to trade, identical products sold in different countries must sell for the same price when their price is expressed in the same currency.
The law of one price states that in competitive markets free of transportation costs and barriers to trade (such as tariffs), identical products sold in different countries must sell for the same price when their price is expressed in terms of the same currency.8 For example, if the exchange rate between the British pound and the dollar is £1 = $2.00, a jacket that retails for $80 in New York should sell for £40 in London (because $80/2.00 = £40). Consider what would happen if the jacket cost £30 in London ($60 in U.S. currency). At this price, it would pay a trader to buy jackets in London and sell them in New York (an example of arbitrage). The company initially could make a profit of $20 on each jacket by purchasing it for £30 ($60) in London and selling it for $80 in New York (we are assuming away transportation costs and trade barriers). However, the increased demand for jackets in London would raise their price in London, and the increased supply of jackets in New York would lower their price there. This would continue until prices were equalized. Thus, prices might equalize when the jacket cost £35 ($70) in London and $70 in New York (assuming no change in the exchange rate of £1 = $2.00).
Purchasing Power Parity
One in which few impediments to international trade and investment exist.
If the law of one price were true for all goods and services, the purchasing power parity (PPP) exchange rate could be found from any individual set of prices. By comparing the prices of identical products in different currencies, it would be possible to determine the “real” or PPP exchange rate that would exist if markets were efficient. (An efficient market has no impediments to the free flow of goods and services, such as trade barriers.)
A less extreme version of the PPP theory states that given relatively efficient markets—that is, markets in which few impediments to international trade exist—the price of a “basket of goods” should be roughly equivalent in each country. To express the PPP theory in symbols, let P$ be the U.S. dollar price of a basket of particular goods and P¥ be the price of the same basket of goods in Japanese yen. The PPP theory predicts that the dollar/yen exchange rate, E$/¥, should be equivalent to:
Thus, if a basket of goods costs $200 in the United States and ¥20,000 in Japan, PPP theory predicts that the dollar/yen exchange rate should be $200/¥20,000 or $0.01 per Japanese yen (i.e., $1 = ¥100).
ANOTHER PERSPECTIVE China Renminbi as Reserve Currency: Yuan a Bet?
Given China’s importance in international trade, it is very likely that the role of yuan will continue to expand in the foreign exchange market. A new study from the Brookings Institution suggests that in the long run, the ascendance of the yuan to reserve-currency standing is likely. It notes that of the six largest economies in the world, China is the only one whose currency does not have reserve status. Getting there will require overcoming two main challenges. First, exchange rate flexibility and financial market development, to improve the cost/benefit trade-off and secondly, strengthening the banking system; developing deep and liquid government and corporate bond markets, as well as foreign exchange spot and derivative markets. Attaining reserve currency status has intangible benefits, including prestige, as well as tangible ones. To the extent that this status results in a greater denomination of trade transactions in China’s own currency, domestic importers and exporters would face lower currency risk. The potential costs of having a reserve currency include reduced control of the currency’s external value and possibly a more volatile exchange rate.
Every year, the newsmagazine The Economist publishes its own version of the PPP theorem, which it refers to as the “Big Mac Index.” The Economist has selected McDonald’s Big Mac as a proxy for a “basket of goods” because it is produced according to more or less the same recipe in about 120 countries. The Big Mac PPP is the exchange rate that would have hamburgers costing the same in each country. According to The Economist, comparing a country’s actual exchange rate with the one predicted by the PPP theorem based on relative prices of Big Macs is a test of whether a currency is undervalued or not. This is not a totally serious exercise, as The Economist admits, but it does provide a useful illustration of the PPP theorem.
Relative currency values according to the Big Mac index for January 11, 2012, are reproduced in Table 10.1. To calculate the index, The Economist converts the price of a Big Mac in a country into dollars at current exchange rates and divides that by the average price of a Big Mac in America (which was $4.20). According to the PPP theorem, the prices should be the same. If they are not, it implies that the currency is either overvalued against the dollar or undervalued. For example, the average price of a Big Mac in Australia was A$4.94 at the euro/dollar exchange rate prevailing January 11, 2012. Dividing this by the average price of a Big Mac in the United States gives 1.176 (i.e., 4.94/4.20), which suggests that the Australian dollar was overvalued by 17.6 percent against the U.S. dollar.
TABLE 10.1 The Big Mac Index, January 11, 2012
Source: The Economist, www.economist.com/node/21542808. Copyright © 2012 The Economist Newspaper Limited, London.
The next step in the PPP theory is to argue that the exchange rate will change if relative prices change. For example, imagine there is no price inflation in the United States, while prices in Japan are increasing by 10 percent a year. At the beginning of the year, a basket of goods costs $200 in the United States and ¥20,000 in Japan, so the dollar/yen exchange rate, according to PPP theory, should be $1 = ¥100. At the end of the year, the basket of goods still costs $200 in the United States, but it costs ¥22,000 in Japan. PPP theory predicts that the exchange rate should change as a result. More precisely, by the end of the year:
Thus, ¥1 = $0.0091 (or $1 = ¥110). Because of 10 percent price inflation, the Japanese yen has depreciated by 10 percent against the dollar. One dollar will buy 10 percent more yen at the end of the year than at the beginning.