1. (Big Mac) Exchange Rate Theory
Roberto Chang
Econ 336
February 2014

2. The Law of One Price
In Economics, we often postulate the Law of One Price: the same good should sell at the same price in different locations.
Why? If not, there could be arbitrage: you could make a profit by buying the good where it is cheaper and selling it where it is more expensive.

3. Limits to the “Law” Obviously, transportation costs may matter.
But they may not be so important for “big” items (i.e. cars)
You might also find that people cannot easily arbitrage due to e.g. legal issues

4. Nevertheless…
Sometimes (often) economists believe that the Law of One Price must hold at least in the long run, provided one corrects for transportation costs.

5. The Law of One Price in an International Context
One may also believe that the Law of One Price should hold across countries as well.
Now: goods are priced in different currencies
So: one can postulate that exchange rates in the long run adjust so that the Law of One Price holds
 This will lead to a theory of exchange rates in the long run

6. The Big Mac Theory A Big Mac is a standard, homogenous, product
So it should sell for the same price everywhere in the long run
So, in a long run equilibrium, the exchange rate should equalize prices of Big Macs in different countries.

7. Current Big Mac Prices Price of a Big Mac in the US: $ 4.20
In Brazil: BRL
Let x = the exchange rate ($ per BRL) that makes the two prices equal. Then
$ 4.20 = x times BRL
i.e. x = 4.20/13.66 = $/ BRL

8. Is the BRL Overvalued?
So, according to the Big Mac Theory, the “equilibrium” Dollar/BRL exchange rate should be 0.307
Today: market exchange rate was dollar per BRL
So, according to this, the BRL is about 35 percent overvalued relative to the dollar!

9. Big Mac Index, June 2009 (from The Economist)
An example of undervaluation appears in Row 2, where we see that the Buenos Aires correspondent found the same burger cost 11.5 pesos, which, at an actual exchange rate of 3.81 pesos per dollar, worked out to be $3.02 in U.S. currency, or 15%less than the U.S. price. So the peso was 15% undervalued against the U.S. dollar according to this measure, and Argentina’s exchange rate would have had to appreciate to 3.22 pesos per dollar to attain the level implied by a burger-based PPP theory.
An example of overvaluation appears in Row 4, in the case of neighboring Brazil. There a Big Mac cost 8.03 reais, or $4.02 in U.S. currency at the prevailing exchange rate of 2.00 reais per dollar, making the Brazilian burgers 13% more expensive than their U.S. counterparts. To get to its PPP-implied level, and put the burgers at parity, Brazil’s currency would have needed to depreciate to 2.25 reais per dollar.
Big Mac Index, June 2009 (from The Economist)