Question

8. Purchasing-power parity

Using data from The Economist's Big Mac Index for 2016, the following table shows the local currency price of a Big Mac in several countries as well as the actual exchange rate between each country and the United States. At the time of the data collection, a Big Mac would have cost you $4.93 in the United States and GBP 2.89 in the United Kingdom. The actual exchange rate between the British pound and the U.S. dollar was $1.63 per pound. The dollar price of a Big Mac purchased in the United Kingdom was, therefore, computed as follows:

Dollar price of a Big Mac in the United KingdomDollar price of a Big Mac in the United Kingdom	=  =	GBP 2.89×$1.63GBP 1.00GBP 2.89×$1.63GBP 1.00
	=  =	$4.71$4.71

For the price you paid for a Big Mac in the United States, you could have purchased a Big Mac in the United Kingdom and had some change left over for fries!

Complete the final column of the table by computing the dollar price of a Big Mac for the countries where this amount is not given.

Note: Round your answers to the nearest cent.

	Big Mac Index: January 2016
	Local Price	Actual Exchange Rate	Dollar Price
	(Foreign currency)	(Dollars per unit of foreign currency)	(Dollars)
The Eurozone	3.72	1.10
Switzerland	6.50	1.02
United Kingdom	2.89	1.63	4.71
Poland	9.60	0.36	3.46
China	17.60	0.16	2.82

Source: “Currency Comparison, To Go,” The Economist, last modified January 7, 2016, accessed July 8, 2016, http://www.economist.com/blogs/graphicdetail/2016/01/daily-chart-7.

Purchasing-power parity (PPP) theory states that exchange rates would need to equalize the prices of goods in any two countries. For the dollar price of a Big Mac to be the same in both countries, a U.S. citizen would need to be able to convert $4.93 into exactly GBP 2.89. To find the exchange rate at which hamburger purchasing power is the same in both countries, divide the price in the United States by the price in the United Kingdom:

PPP Exchange Rate (U.S. Dollars per British pound)PPP Exchange Rate (U.S. Dollars per British pound)	=  =	$4.93GBP 2.89$4.93GBP 2.89
	=  =	$1.71 per pound$1.71 per pound

The exchange rate that would have equalized the dollar price of a Big Mac in the United States and the Eurozone (that is, the PPP exchange rate for Big Macs) is   . This change would mean that the euro had   against the dollar.

If Big Macs were a durable good that could be costlessly transported between countries, which of the following would present an arbitrage opportunity? Check all that apply.

Exporting Big Macs from Switzerland to China

Exporting Big Macs from the Eurozone to the United States

Exporting Big Macs from the United Kingdom to Poland

Answer 1

a) The complete table is below: (using the same calculation given in the question)

	Big Mac Index: January 2016
	Local Price	Actual Exchange Rate	Dollar Price
	(Foreign currency)	(Dollars per unit of foreign currency)	Formula: Local currency * actual exchange rate (Dollars)
The Eurozone	3.72	1.10	4.09
Switzerland	6.50	1.02	6.63
United Kingdom	2.89	1.63	4.71
Poland	9.60	0.36	3.46
China	17.60	0.16	2.82

b) The exchange rate that would have equalized the dollar price of a Big Mac in the United States and the Eurozone (that is, the PPP exchange rate for Big Macs) is 1.33. This change would mean that the euro had advantage/appreciated against the dollar.

Answer: The PPP calculation is below:

PPP Exchange Rate (U.S. Dollars per Euro (euro zone's currency))	=	$4.93, Euro 3.72
Formulae: Rate of big mac in U.S / local euro currency value: 4.93/3.72	=	$1.33 per euro

C) If Big Macs were a durable good that could be costlessly transported between countries, then we can compare arbitrage opportunities on the basis of dollar price in (a) answer table.

Exporting big macs from Switzerland to China will not be a good option as big mac is expensive in Switzerland than in China. Hence, it will not be beneficial to export the product to China. Same is the case between UK and Poland. However, it would be great arbitrage opportunity to export big mac to United states as in dollar terms big mac is cheap ($4.09) in euro zone than in United states ($4.93). Hence, it will be beneficial for a company to export big mac to US, so that they earn the benefits of it being expensive in US.