Download Purchasing Power Parity Page 1 of 3

International Focus
Exchange Rates
Purchasing Power Parity
Page 1 of 3
We’re ready now to discuss the determinants of the foreign exchange rate; that is, how do supply and demand
determine the price of foreign currency? Before we go into an explicit look at supply and demand, let’s consider a
force that moves the foreign exchange rate in the very long run. In the very long run, economists imagine that
exchange rates adjust to equilibrate the cost of living across international boundaries. If countries find that their goods
and services have become very expensive, then what they’ll begin to do is import goods and services from abroad
instead. That action will end up changing prices and exchange rates to the point at which the cost of living is brought
in to equality across international boundaries. We call this phenomenon purchasing power parity. Purchasing power
parity refers to a situation in which the purchasing power of your income in one country is the same as it is in another
country, if you convert your income at the going nominal exchange rate. Prices and exchange rates are in relation
such that the cost of living is the same in Mexico as it is in the US. Now, purchasing power parity is a sophisticated
concept, so we’re going to build it up in bite-size chunks.
Let’s start with what economists call the Law of One Price, and that is the supposition that a particular good, say
oranges, that are freely tradable across international boundaries should have the same price whether you import them
from Mexico or buy them locally in the United States. Here’s a statement of the Law of One Price: the price of
oranges in the US multiplied by pesos per dollar, the nominal exchange rate, should equal the price of oranges
abroad in Mexico. Otherwise, you would image that arbitrage, trade across international boundaries, would eventually
bring these prices and exchange rates into this relationship. We’ll talk about how that arbitrage works in just a
moment, but let’s first use some simple numbers to make sure we’re clear on the concept of the Law of One Price.
If an orange sells for $1.00 in the United States and the peso per dollar exchange rate is 10 pesos per US dollar, then
the Law of One Price says that multiply $1.00 by 10 pesos to the dollar, this orange should be selling for 10 pesos in
Mexico. If not, what’s going to happen? Well, suppose that this orange, instead of selling for 10 pesos, were only
selling for 5 pesos. So oranges are relatively inexpensive in Mexico. What’s going to happen? Everyone is going to
start buying their oranges from Mexico, including people who live in Texas, California and Nebraska. So what’s going
to happen? The reduction in demand for US oranges is going to cause the price of oranges to fall in the United
States. The increase demand for oranges from Mexico is going to cause the price of oranges to rise in Mexico.
Meanwhile, because all of these people in the United States are converting US dollars into Mexican pesos, the peso is
going to appreciate from 10 pesos to the dollar, to 8 pesos, to 6 and so forth. So what happens, as demand shifts for
the relatively low-priced Mexican oranges, the numbers on this side of the equal side are going to fall, and the number
on this side is going to rise, until we have equilibrium established, as in the equation that I've written here. So one
way of solving the problem would be for the price of Mexican oranges to be bid up from 5 pesos per orange to 10
pesos. That would give you one price for oranges, whether they bought in the US or bought in Mexico.
Now, what would keep the Law of One Price from holding? I can think of four things. First of all, what if trade were
blocked between the US and Mexico? Tariffs and quotas could keep this equation from holding. The second thing
that could keep this arbitrage from happening is if oranges have different qualities in the two countries, so that people
like Mexican oranges better or they like US oranges better. If these are not the same goods across international
boundaries, then they wouldn’t be selling for the same price. Another thing that could keep trade from bringing this
equation into equilibrium would be transportation costs, the high cost of shipping oranges from one country to another.
And finally, there could be taxes or other things that would cause the price to be different in the two countries, taxes or
regulations. So trade barriers, differences in quality, transportation costs, this is the kind of stuff that causes oranges
to have different prices across the international boundary.
Now, let’s now go from the Law of One Price applied to oranges to what’s called purchasing power parity. Purchasing
power parity is the same idea as the Law of One Price, only now instead of just talking about oranges, we’re talking
about a basket of goods and services that represents the cost of living. So suppose the cost of living, oranges,
insurance, automobiles, medical care, education in the Unites States cost $1,000.00 a month. $1,000.00 to buy the
cost of living in the US. Well, convert that cost of living into peso, 10 pesos per dollar, then the cost of living would be
10,000 pesos in Mexico if it’s going to be equal to the cost of living in the United States. Well, this is almost never
true. If you look at actual real-world data, purchasing power parity almost never holds across international
boundaries. Why is that? It’s because of transportation costs, trade barriers, differences in quality and finally,
International Focus
Exchange Rates
Purchasing Power Parity
Page 2 of 3
because these indexes that we use to measure the cost of living include different goods in the US than they do in
Mexico. The typical Mexican family consumes a different bundle of goods than the typical family in the United States.
Therefore, the Cost of Living Index, if you compare the US cost of living with the Mexican cost of living, is not directly
comparable, because the bundles represent different goods and services. So this is what we call absolute purchasing
power parity. Absolute purchasing power parity is the law of one price applied to the cost of living, just like our story
with oranges. Still, in the long-run, you would imagine that if the cost of living was a lot higher in the United States
than in Mexico, people in the US would start importing more stuff from Mexico and would put pressure on the
government to lower trade barriers and, in the long-run, this equation would be something that the economy would
approach. Well, typically, that’s true. Typically, economies do move in the direction in the long run, given time,
toward purchasing power parity, toward an alignment of prices and exchange rates that satisfies this equation. But it
takes a long time to get there and anytime you look at the actual data, you’ll find that most economies do not satisfy
this equation.
Well, one equation the economies do tend to satisfy is relative purchasing power parity. Relative purchasing power
parity refers not to price levels, but the way in which prices change; that is, the differences in rates of inflation across
economies. So go back to the Law of One Price equation that says that the cost of things in Mexico should equal the
cost in the US with nominal exchange rate applied, and take the rate of change on both sides, that is, how are things
changing. Well, there’s a simple mathematical principle that says that if you have a product of two numbers, the rate
of change of a product of two numbers is equal to the rate of change of the first number plus the rate of change of the
number that it’s multiplied by. So in this case, as far as Mexicans are concerned, the rate of change of importing
goods from the United States is equal to the rate of change of the exchange rate plus the rate of inflation in the United
States. Now, what happens when you look at the data is that relative purchasing power parity, that is, rates of change
of prices and exchange rates, tends to explain the data pretty well. If you look at the inflation rate in the United States
and the inflation rate in Mexico, the difference between those two inflation rates usually tells you the rate at which the
currency price is changing. If the inflation rate in the United States is 10% and the inflation rate in Mexico is 20%,
then 20%, Mexico’s inflation rate, minus 10%, the US inflation rate, leaves 10%, which is typically the rate at which the
Mexican peso is depreciating. Think about it this way: if you're in a country that has very rapid inflation, what are
people doing? They're trying to avoid inflation by buying goods from abroad. So if you avoid inflation by buying
goods from abroad, you're taking your local currency and buying up foreign currency so you can buy these cheaper
goods from countries where there’s less inflation. But, as everybody does that, dumping their local currency to buy
foreign currency, they wind up driving up the price of foreign currency, causing the local currency to depreciate with
respect to the foreign currency. So counties that have rapid inflation typically experience depreciation of their
currency as people in the country try to avoid the inflation by buying foreign currency so they can import less
expensive goods from abroad. And what ends up happening is the currency typically depreciates at the rate at which
the local inflation rate exceeds the foreign inflation rate, or to write it another way, the rate at which the Mexican peso
depreciates is equal to the difference between Mexico’s inflation rate and the inflation rate in the United States. So if
Mexico’s inflation rate is 10% and the US inflation rate is 4%, then the Mexican peso will be depreciating at an annual
rate of 6% according to relative purchasing power parity. And relative purchasing power parity is a much better
match, a much better theory for explaining the data than is absolute purchasing power parity. Even through the
absolute price levels don’t satisfy that equation, the rate at which these variables change does tend to satisfy this
equation.
Now, let’s get on then to a famous measure of purchasing power parity called the Big Mac Index. Here is a product,
the Big Mac hamburger, that’s pretty much the same wherever in the world you buy it. Dallas, Mexico City, Tokyo,
London, wherever you buy it, this is the same product. So we could look at the dollar price of a Big Mac across
international boundaries to get a sense of whether purchasing power parity is satisfied or not. So let’s take an
example. Suppose in the United States a Big Mac costs $2.50, so that’s the price level from this equation. And
suppose that, in Mexico City, you can buy this same Big Mac for 25 pesos, that’s the Mexican price. Well, the
exchange rate that would give you purchasing power parity, the exchange rate that makes the Mexican Big Mac have
the same price as the US Big Mac, would be 25 pesos per Big Mac divided by $2.50 per Big Mac gives you 10 pesos
to the dollar. So if these are the prices of Big Macs in the two countries, then this is the exchange rate that would
make them have the same price for someone who lived in Texas, whether he bought his Big Mac in Dallas or took his
dollars, bought pesos, and bought the Mexico City Big Mac. This is the purchasing power parity exchange rate. Now,
International Focus
Exchange Rates
Purchasing Power Parity
Page 3 of 3
it turns out that the actual exchange rate between the US and Mexico will very rarely satisfy this equation. Purchasing
power parity is rarely satisfied. However, if the peso were trading at 8 pesos to the dollar today, then we would say
that the peso is overvalued; that is, we’re getting too many dollars per peso relative to the purchasing power parity
exchange rate. And the peso would be expected to depreciate towards the purchasing power parity level in the long
run. That means if you're a currency trader and you want to know what's going to happen to the peso-dollar exchange
rate over time, use the Big Mac standard as a measure of where things might be going. Use purchasing power parity
as a long-run target, because in the long run, arbitrage is going to take us toward that exchange rate. So if we have 8
pesos to the dollar today, that means the peso is too strong, it’s overvalued, and it’s going to tend to depreciate
towards 10 pesos to the dollar, the purchasing power parity exchange rate. On the other hand, if we’ve got 12 pesos
to the dollar today, the peso is undervalued, it’s too weak and, in the long-run, the peso is going to be expected to
appreciate towards 10 pesos to the dollar. Now, the British magazine The Economist publishes the Big Mac Standard
every year and shows how foreign currency prices are lining up with purchasing power parity. So, for example, in the
United States, when this table was printed this year, a Big Mac was selling for a price of $2.44 a sandwich. In Israel,
given the exchange rate between the Israeli shekel and the US dollar, if you converted your US dollars into Israeli
shekels, the price you end up paying for a Big Mac in Israel is $3.50. The shekel price multiplied by shekels per dollar
means you need $3.50 to get the shekels to buy that Big Mac in Tel Aviv. In Britain, too, you’d end up paying more for
the Big Mac. That means the British pound is overvalued, it needs to depreciate to make the London price of a Big
Mac equal to the price of a Big Mac in Dallas. On the other hand, if you were in the Philippines, you’d be able to get a
Big Mac for the equivalent of $1.36. That means the Philippine peso is undervalued. It needs to appreciate to make
the price of the sandwich in Manila equal to the price of the sandwich in Dallas. Now, an undervalued currency is
expected to appreciate, so foreign currency traders will look at this measure of purchasing power parity and say,
“Whoa! The Philippine peso is undervalued, therefore, in the long-run, it’s going to be expected to appreciate, and
therefore we might want to go ahead and buy Philippine pesos now and hold them, waiting for the price to rise, so we
can make some money off of currency appreciation.”
Anyway, the Big Mac Index is kind of a convenient way of incorporating purchasing power parity into a nice readable
journalistic form. Purchasing power parity refers to the relative cost of living in two countries, using the exchange rate
for the conversion. The Big Mac Index is just a simple form of that. When the Big Mac costs the same in the United
States as it does in Mexico, with given prices of Big Macs in the two countries and the going nominal exchange rate,
then we say we have purchasing power parity between the US and Mexico. On the other hand, when that equation is
not satisfied, then we can make predictions about whether the peso is expected to appreciate or depreciate in the
long-run. Purchasing power parity is a long-run target for the exchange rate. It’s where the exchange rate tends to go
with the arbitrage of goods and services over time. But at any given day, purchasing power parity is unlikely to be
satisfied, because the economy is moving toward that long-run equilibrium, although it never quite gets there.