Purchasing Power Parity

A burger costs $5.50 in Chicago and £4.20 in London. Convert the pound price at the prevailing exchange rate and, if it comes out well above or below $5.50, something looks off — either the burger is genuinely cheaper to make in one country, or the pound is mispriced against the dollar. Purchasing power parity (PPP) takes that intuition seriously as a theory of exchange rates: over the long run, currencies should adjust so that the same basket of goods costs the same amount everywhere once you convert to a common currency.

The relationship

$$S = \frac{P_{domestic}}{P_{foreign}}$$

In words: the exchange rate (units of domestic currency per unit of foreign currency) should equal the ratio of the price levels in the two countries — how much more, or less, things cost at home versus abroad. A country with persistently higher inflation than its trading partners should see its currency depreciate over time by roughly that inflation gap, keeping the relative cost of goods unchanged even as the nominal prices in each currency drift apart. This version — inflation differentials driving gradual currency drift — is called relative PPP, and it holds up far better in the data than the absolute, "prices should be literally equal" version above.

Worked example

The Economist's Big Mac index prices the same burger in different countries. Say a Big Mac costs $5.69 in the US and ¥450 in Japan, with spot USD/JPY at 150. PPP-implied fair value is $450 / 5.69 = 79.1$ yen per dollar — far below the actual rate of 150. That gap says the yen is roughly 47% "undervalued" against the dollar by burger prices: $\frac{150 - 79.1}{150} \approx 47\%$. A naive trader betting the yen must strengthen back toward 79 could easily be wrong for a decade, because labor costs, rents, tariffs, and the fact that Big Macs aren't tradeable goods (nobody ships a burger across the Pacific to arbitrage the price gap) keep the actual rate anchored to very different forces than a strict cost-of-goods comparison.

What this means in practice

Economists use PPP-implied rates as a long-run reference point — the "fair value" a currency should drift toward over a decade — and central banks use it loosely to judge whether a currency is dangerously over- or under-valued. Short-term traders mostly ignore it: interest-rate differentials, capital flows, and risk sentiment dominate exchange rates over any horizon shorter than several years, which is exactly why PPP deviations can persist for so long without being arbitraged away.