The law of one price across borders. Big Mac index logic and long-run exchange rates.
Warming up the engine…
Purchasing power parity: in the long run, exchange rates move to equalize the price of the same basket of goods across countries, so currencies of high-inflation countries depreciate.
S = P_home / P_foreign ; %ΔS ≈ π_home − π_foreign
If a basket costs twice as much in Australia as in the US at the current exchange rate, there is profit in buying American and selling Australian, and that arbitrage pressure pushes the exchange rate toward parity. It works well over decades and for big inflation gaps (the Big Mac index is the famous demo), poorly month to month, because much of what we buy is not tradeable.
Use the relative form for questions: the currency of the country with HIGHER inflation depreciates by roughly the inflation differential. Cite non-tradeables as the main reason PPP fails short-run.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Also in Trade & Open Economy
Equilibrium at P 40, e 40.
Equilibrium: P* = 40.0, e* = 40.0
Current equations
The same basket of goods should cost the same everywhere once you convert currencies, if it didn't, you could buy cheap and sell dear. So countries that inflate faster see their currencies fall to compensate.