How to Calculate the Gains From Trade
Gains from trade equal consumption with trade minus production without trade: subtract each country's autarky bundle from its post-trade bundle.
The Gains From Trade formula
Calculator
Set each country's maximum output, its mix before trade and the traded quantities to see who gains what.
Output if Country A makes only wheat.
Output if Country A makes only cloth.
Its own mix before trade. The matching cloth comes from its straight-line PPC.
The two traded quantities set the terms of trade and split the gains.
Specializing adds 10 wheat, 10 cloth to what the two countries made alone, and the traded quantities decide how that total splits.
- Country A opportunity cost of 1 wheat
- 0.5 cloth
- Country B opportunity cost of 1 wheat
- 1 cloth
- Specialization
- A makes wheat, B makes cloth
- Country A gain from trade
- 4 wheat, 4 cloth
- Country B gain from trade
- 6 wheat, 6 cloth
- Verdict
- Both countries gain
Cloth given up for one more wheat, which is max cloth divided by max wheat.
Each country produces the good it gives up less of the other good to make.
Consumption after trade minus what Country A produced on its own.
Neither country consumes less of either good than it did before trade.
How to calculate Gains From Trade, step by step
- 1Find each producer's opportunity costs. For each good, divide the other good's output by this good's output to get the cost of one unit.
- 2Assign comparative advantage. Each country specializes in the good it can produce at the lower opportunity cost.
- 3Record the autarky bundle. Write down what each country produced and consumed on its own production possibilities curve before trade.
- 4Pick terms of trade between the two costs. Any exchange rate strictly between the two opportunity costs leaves both countries better off.
- 5Subtract to find the gain. Gains from trade = post-trade consumption − autarky production, calculated separately for each good and each country.
Worked example: Gains From Trade
Atlantis can make 100 wheat or 50 cloth; Borealis can make 60 wheat or 60 cloth. Atlantis gives up 0.5 cloth per wheat versus Borealis at 1 cloth, so Atlantis specializes in wheat (100) and Borealis in cloth (60). In autarky Atlantis produced 60 wheat and 20 cloth, Borealis 30 wheat and 30 cloth. Trading 36 wheat for 24 cloth (1 cloth = 1.5 wheat) leaves Atlantis with 64 wheat and 24 cloth, a gain of 4 wheat and 4 cloth, and Borealis with 36 wheat and 36 cloth, a gain of 6 wheat and 6 cloth.
Gains From Trade questions
Can both countries gain at the same time?
Yes. Trade is not zero sum: when each country specializes where its opportunity cost is lower, combined output rises and both can consume outside their own production possibilities curves.
What if the terms of trade fall outside both opportunity costs?
One country would end up worse off than producing the good itself, so it refuses to trade. Workable terms lie strictly between the two opportunity costs.
Does a country with an absolute advantage in both goods still gain?
Yes. Gains come from differences in opportunity cost, not from absolute output, so a country better at making both goods still gains by specializing where its relative cost is lowest.
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