Q.If inflation is higher in country A than in Country B, and the exchange rate between the two countries is fixed, what is likely to happen to the trade balance between the two countries?

When the exchange rate is fixed, nominal exchange rate movements cannot offset inflation differences. If inflation is higher in Country A than in Country B, the real exchange rate for Country A appreciates. The real exchange rate is defined as:

where $e_n$ is the fixed nominal exchange rate (units of A’s currency per unit of B’s currency), $P_A$ is the price level in A, and $P_B$ is the price level in B. With $e_n$ fixed and $P_A$ rising faster than $P_B$, the ratio $P_B / P_A$ falls, so $e_r$ falls — meaning Country A’s goods become relatively more expensive compared to Country B’s goods. …

The key here is the real exchange rate — the price of foreign goods relative to domestic goods, adjusted for inflation. Even when the nominal exchange rate is fixed (say, 1 unit of Country A’s currency always equals 1 unit of Country B’s currency), the real exchange rate can shift because of differences in price levels.

Think of it this way: the real exchange rate tells you how many baskets of foreign goods you can get for one basket of domestic goods. If Country A’s prices rise faster than Country B’s, then goods made in A become more expensive relative to goods made in B — even though the currency conversion rate hasn’t changed.

Here, if Country A is the domestic country and Country B is foreign, and the nominal rate is fixed, then a rise in $P_{\text{domestic}}$ (A’s inflation) lowers the real exchange rate. That means A’s goods are now more expensive relative to B’s goods.

What follows is straightforward:

• Exports from A to B fall — because A’s goods are pricier for B’s consumers.
• Imports from B to A rise — because B’s goods are cheaper for A’s consumers. …