Using Coffee to Explain Purchasing Power Parity and the Law of One Price

In a previous Open Vault blog post, Jack Fuller explained the role that exchange rates would play on your trip from the U.S. to Switzerland. In the hypothetical example given, you landed at an airport in Switzerland and found that a coffee there would cost you only 2 Swiss francs but 2.27 U.S. dollars. The example assumed an exchange rate where one dollar was equal to 0.88 francs, or one franc was equal to $1.14.

Here, I’m going to change the story just slightly to explore the ways in which exchange rates are more complicated than you may have thought. What you might expect a price to be after adjusting for the exchange rate is related to concepts called the law of one price and purchasing power parity.

The Law of One Price: An Example

The law of one price (LOP) says that identical goods should have the same price (after adjusting for exchange rates) in any market, so long as there are no barriers to trade, transaction costs or other market frictions.

What does that mean for my coffee purchasing example?

Say you start your trip in New York City—Times Square, specifically. You have an early morning flight to Zurich, so you leave your hotel and walk to the nearest Starbucks on West 43rd Street and Sixth Avenue. It’s autumn, and you order a venti pumpkin spice latte with only one shot of espresso. It costs $7.65 before tax.

Some time later, you land in Zurich. You take a train from the airport to Zurich Hauptbahnhof, a train station in the center of the city, and go to the Starbucks there. You again order a venti pumpkin spice latte with only one shot of espresso. It costs approximately 11 Swiss francs when tax is excluded. Once you get back to your hotel, you calculate what you paid in U.S. dollars, assuming the franc-dollar exchange rate is now 0.86 francs per dollar, or 1.16 dollars per franc. That means in Zurich you paid $12.76 for the same drink that cost you only $7.65 in Manhattan. In other words, a Swiss pumpkin spice latte costs the same as 1.67 American pumpkin spice lattes.

You may have expected that even though the price of the drink in francs was higher, accounting for the exchange rate would reveal that one Swiss coffee is worth one American coffee. If this were the case, we would be able to compare the prices of the coffees from the two stores to figure out what the exchange rate should be. In my example, the LOP implied exchange rate in terms of Swiss francs per U.S. dollar would be calculated as the price of the Zurich coffee divided by the price of the New York coffee:

11.00 Swiss francs ÷ 7.65 U.S. dollars = 1.44 francs per dollar

But this is wildly different from the actual spot exchange rate—the market exchange rate for an immediate transaction—used earlier (0.86 francs per dollar). To be exact, a dollar can get you 0.58 francs less than we would expect based on the LOP! We might also say that the Swiss franc is currently overvalued—it is more expensive than it should be—relative to the U.S. dollar. Conversely, the U.S. dollar is undervalued relative to the franc.

But isn’t a latte in Zurich the same as a latte in New York? Wouldn’t the LOP suggest their prices should be the same?

Not quite. The latte in my example isn’t a great candidate for the LOP because it’s not something that can be easily traded, and the ability to trade without barriers is necessary for the LOP to work. While there’s a large global market for coffee beans, the same can’t be said for the latte itself. Imagine how difficult it would be to ship a cup of coffee from Switzerland to the United States (without it spilling or getting cold).

Extending the Law of One Price to Purchasing Power Parity

So how does purchasing power parity (PPP) factor into this? PPP is the extension of the LOP from a single good to a broad collection of goods and services that economists use to track inflation. This collection is referred to as a consumption basket, and it is supposed to represent what consumers typically spend their money on each year. The idea here is that even though exchange rates might not follow the LOP for all individual goods and services, they might more closely follow what PPP would predict according to a group of goods and services. But, as it turns out, spot exchange rates often differ from both LOP and PPP implied exchange rates.

However, this doesn’t mean that PPP is completely disconnected from currency markets. While the PPP implied exchange rates and the spot exchange rates are often very different, they do tend to move in the same direction over the long run. Below is a FRED chart that shows the spot Swiss franc/U.S. dollar exchange rate (in red) and the PPP implied exchange rate using the consumer price indexes (CPI) for both Switzerland and the U.S. (in blue). The CPI represents the price level in each country for a consumption basket. Using the CPI to calculate PPP is then like using the prices of many goods and services in both countries rather than using the price of only one good. For ease of comparison, the two lines are equal to 100 in the first quarter of 1971.

NOTES: Consumer price index data via Organization for Economic Cooperation and Development’s Main Economic Indicators complete database, accessed Jan. 3, 2025. Copyright, 2016, OECD. Reprinted with permission.

While the spot rate has been volatile, the underlying multidecade trend has been broadly the same for each rate. You can see that for most of the 1970s, both rates declined fairly quickly but have fallen more gradually in the time since. The case is similar for the U.S. dollar to British pound spot and PPP implied exchange rates, and others.

What Drives These Exchange Rates?

The previous Open Vault blog post cited a few reasons why spot exchange rates change over time. These factors, like demand for foreign securities, the terms of trade or changes in countries’ economic stability, can ultimately push demand for currencies in different directions.

As most exchange rates are set by supply and demand for currencies, these fluctuations in demand change market prices. These reasons also explain some of the difference between spot rates and PPP implied rates more broadly. Other reasons, such as the fact that some items or services can’t be traded across borders and that different countries have different income levels, also play a role in the persistent differences, as mentioned in an August 2022 FRED blog post suggested by Ugo Panizza.

There’s a lot that goes into determining exchange rates and understanding differences in prices of goods and services across countries. But even though the coffee may be relatively more expensive in Switzerland than in the U.S., you may still want that pick-me-up after your flight.