How to Calculate Purchasing Power Parity

Imagine that a car costs $50,000 in the United States, and an identical car costs the equivalent $60,000 USD in Canada. Assuming the transport and shipping costs were free, then someone could buy the car in the U.S. and sell it in Canada, making a so-called arbitrage profit of $10,000 per car – a very lucrative business. This is the basis for purchasing power parity. PPP suggests that in the long term, exchange rates will develop to wipe out arbitrage profits, so the car will cost the same in all countries.

Imagine your friend has fulfilled his dream and works as a chef in the U.K. His monthly salary is £4,000. In the U.K. one loaf of bread (hypothetically) costs £1, so your friend can afford 4,000 loaves each month.

On this side of the pond, you also work as a chef and earn $6,000 a month. Comparing the two incomes, and with an exchange rate of 1.3 dollars to the pound, you would earn £4,615.38 GBP a month. You could say that you're richer than your friend because you have more British pounds a month in your bank account.

Unfortunately, bread is more expensive in the U.S. Assuming (hypothetically) that bread costs $2 per loaf here, then you can only afford 3,000 loaves with your income. You're technically richer because you earn more salary, but you have less purchasing power because your salary does not stretch as far as your friend's.

Purchasing power parity or PPP describes the situation in which two currencies have the same purchasing power, so it would cost you exactly the same amount of money to buy the same product in both countries. With PPP, the British loaf and the American loaf would be exactly the same price once you'd converted the currency.

PPP is based on the idea that the price of two identical goods should equalize between two countries in the long term since people can shop around for the best price. In other words, a car buyer in Canada could hop over the border and purchase the car he wants for $50,000 USD in the U.S., saving $10,000. The ability to comparison shop, even across borders, means that prices will eventually level out and everyone's purchasing power winds up being exactly the same no matter where they are in the world.

In economics, absolute PPP is based on a principle known as the law of one price. This states that if two or more countries produce an identical product, then the price of the product should be the same, no matter which country produces it.

Let's look at a simple example. Suppose the price of a loaf in the U.S. is indeed $2. In the U.K., the price of an identical loaf is £1. If the law of one price holds, then the purchasing power of the British pound and the American dollar should be the same. Here, the PPP exchange rate formula to find the exchange rate between the two currencies, reveals the absolute purchasing power parity. It's simply a matter of calculating the ratio between the two prices:

E = P1/P2

Where:

E = Exchange rate
P1 = Cost of the good in Currency 1
P2 = Cost of the good in Currency 2

E = 2/1 = 2

In other words, an exchange rate of USD $2/GBP would equalize the price of bread according to PPP theory.

You could also write this calculation in reverse, using GBP as the first currency. The result is the same:

E = P1/P2
E = 1/2
E = GBP £**0.5/USD.**

This is simply the reciprocal rate of USD $2/GBP.

Absolute PPP is not a very dynamic concept as it only calculates the exchange rate at the present time. On a global scale, economists are more interested in how exchange rates might move in the future. Specifically, they want to know whether currencies are going to appreciate or depreciate and what impact this will have on the cost of living.

To find out how currency values are going to behave in the future, you would have to switch over the relative version of PPP. This is an incredibly challenging calculation that adjusts PPP for inflation. Relative PPP is not something that regular folk tend to get involved with as it's mostly used to figure out PPPs for entire economies. This allows economists to compare the economic output of multiple nations over a given time frame.

When you read a list of the world's largest economies, then relative PPP will have been used to compare the gross domestic product of the listed nations. Economists use PPP in this context as most nations will not use the U.S. dollar as a measure of their economic output. Re-calculating the GDP using PPP means you can compare each country's GDP as if it were being priced in the United States.

In 2017, for instance, China produced 127 trillion yuan's worth of goods. This is equivalent to $19 trillion USD if a currency exchange rate of, say, 6.68 ¥/$ is applied. If the exchange rate changed to 7.06 ¥/$ as it stands in December 2019, then the output would be $17.99 trillion USD. When you don't apply PPP, then a country's GDP will change when its exchange rate changes. After running a PPP calculation, the CIA World Factbook calculated China's 2017 GDP at just over $23 trillion – much larger than the unadjusted figure.

What you're essentially doing here is figuring out how much things would cost overseas if there were no exchange rates and everyone used the U.S. dollar – which is the same as calculating what anything would cost if it was sold right here in the United States. Add all these goods and services together and you get a country's PPP-adjusted GDP.

Different countries have different standards of living, and PPP can help to understand this. It can also help compare the economic output of different countries and adjust GDP. However, it's important to understand that PPP is an economic theory rather than anything observed in practice. It makes a lot of assumptions about things that don't happen in real life, such as no transport costs for shipping your car from the U.S. to Canada, and no trade barriers, taxes and import quotas.

That's just not true in the real world. Most countries enter into trade agreements that raise or lower prices through trade tariffs, so there isn't a level playing field. Transportation costs are very real and prohibitive. In reality, there are many barriers that prevent costs from equalizing, which seriously limits the theory.