The Economist calculates the Big Mac Index as a manifestation of the Law of One Price (LOOP). The purpose of the index is to estimate the over-/undervaluation of a currency.
Specifically, it calculates the price of a McDonald’s Big Mac across the four largest metro areas in a given country. These prices, along with the theory of LOOP, imply a theoretical value of the currency—what the value of the currency should be. We can then compare this LOOP-implied currency value to the actual value to determine the over-/undervaluation of a currency.
Suppose that the four-metro average price of a Big Mac in the United States is $4.35.
Suppose that the four-metro average price of a Big Mac in China is 18.90¥. Suppose that the foreign exchange rate is 7.10¥/$ (i. e., the yuan price of the dollar, i. e., how many yuans it takes to purchase a one-dollar bill).
1. What is the LOOP-implied FX rate?
2. Is the yuan over- or undervalued?
3. By how much is the yuan over/undervalued?
4. Do you think the Big Mac is a proper good to use for LOOP?
5. Can you think of a better good to use? Explain.