How to Calculate Comparative Advantage (Opportunity Cost)

Which way round to divide

Almost every lost mark on this topic comes from dividing the wrong way, and the reason is that the rule genuinely flips depending on what the table gives you.

An output table says how much a producer can make. The US line reading 100 wheat or 50 cloth means giving up all wheat production buys 50 cloth, so one cloth costs 100 ÷ 50 = 2 wheat. You divide the other good by the good you are pricing.

An input table says how much of a resource each unit takes. If the US needs 2 hours per wheat and 4 hours per cloth, one cloth costs 4 ÷ 2 = 2 wheat, the same answer reached by dividing the good you are pricing by the other good. The two tables describe the same economy, so a correct method returns the same number from either. If yours does not, you have applied the output rule to an input table.

A sanity check that catches it every time: a producer's two opportunity costs must be reciprocals. The US pays 2 wheat for a cloth, so it must pay ½ cloth for a wheat. If your pair does not multiply to 1, one of them is upside down.

Where the trade price has to sit

Finding who specialises in what is only half the question. The follow-up asks which exchange rates both sides would actually accept, and the answer is any rate strictly between the two opportunity costs.

Using the same numbers, cloth costs the US 2 wheat to make and Mexico 1 wheat. So a cloth has to trade for more than 1 wheat, or Mexico would rather make its own, and less than 2 wheat, or the US would rather make its own. Anything between 1 and 2 wheat per cloth works.

Pick 1.5 wheat per cloth and check both sides gain. The US hands over 1.5 wheat for a cloth that would have cost it 2 wheat to produce, saving half a wheat. Mexico hands over a cloth and receives 1.5 wheat, which it would have had to give up 1.5 cloth to produce for itself, saving half a cloth. Both are better off, which is the whole claim the model makes.

Absolute advantage is a distraction, on purpose

Questions are written so that one country is better at everything, because the interesting result is that trade still pays. In the table above the US makes more wheat and more cloth than Mexico with the same resources, so it holds the absolute advantage in both. It still gains from buying cloth from Mexico.

The reason is that absolute advantage compares producers, while opportunity cost compares what each producer gives up. A country cannot have the lower opportunity cost in both goods, because the two costs are reciprocals: being cheaper at one necessarily makes you dearer at the other. So there is always something for each side to specialise in, however far apart their productivity is.

If a question ever appears to give one producer the comparative advantage in both goods, recheck the arithmetic. The result is impossible, not surprising.