What does purchasing power parity holding mean?

This economics article goes over a question dealing with purchasing power parity.  Purchasing power parity  (PPP) considers how much money would be necessary to purchase the identical goods and services in two different countries.  Sometimes this can then be used to calculate an exchange rate. Using this calculated PPP rate, the given amount of money has the same purchasing power in both countries.  It is rare, however, for purchasing power parity to hold and differences in purchasing power imply that goods and services are relatively cheaper in some countries compared to others.

An example question with purchasing power parity holding is given below

a) A can of soda costs $1.50 in the United States and 24 pesos in Mexico. What would the peso-dollar exchange rate be if purchasing-power parity holds?
b) If a monetary expansion caused all prices in Mexico to double, so that soda rose to 48 pesos, what would happen to the peso-dollar exchange rate?

To answer this question we need to make the price of soda the same (regardless of the currency/exchange rate) in both countries.

A)  Purchasing power parity holding means that the can of soda should cost $1.50 in both countries.  For this to hold, $1.50 must equal 24 pesos, so $1 would have to be 16 pesos (24/1.50) which is the exchange rate: $1 for 16 pesos or 1 peso for $.0625 (1/16).

B) All prices in Mexico double, so $1.50 equals 48 pesos, so $1 equals 32 pesos or 1 peso equals $.03125.

Note that the exchange rates exactly doubled (or halved depending on how you look at it) given this monetary policy.  As long as purchasing power parity holds, calculating the changes will always be this easy.

Why would purchasing power hold?  Because of arbitrage.  Imagine someone wanted to buy Soda near the US/Mexico border.  If soda costs $1 in the US but $.50 in Mexico, then that person can buy lots of soda in Mexico and bring it to the US and sell it for more than $.50 but less than $1.  They can continue doing this until the relative price is the same (which is the definition for purchasing power parity).

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