Big Mac Exchange Rate Theory

Roberto ChangEcon 336

February 2012

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.

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

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.

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

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.

Current Big Mac Prices

• Price of a Big Mac in the US: $ 4.07

• In China: 14.7 Yuan

• Let x = the exchange rate (Yuan per $) that makes the two prices equal. Then

14.7 Yuan = x times $ 4.07i.e. x = 14.7/4.07 = 3.61 Yuan/$

Is the Yuan Undervalued?

• So, according to the Big Mac Theory, the “equilibrium” Yuan/dollar exchange rate should be 3.61

• Yesterday: market exchange rate is 6.30 Yuan/dollar

• So, according to this, the Yuan is about 43 percent undervalued relative to the dollar!

Big Mac Index, June 2009 (from The Economist)