How to Find the Range of Acceptable Terms of Trade
Acceptable terms of trade lie strictly between the two countries' opportunity costs of the traded good, so each side does better than producing it at home.
The Terms of Trade Range formula
Calculator
Enter each country's maximum corn and steel to get the lower and upper bound of workable terms of trade.
Corn produced if Country A makes nothing else.
A proposed price for 1 steel, checked against the range below.
Trade helps both sides only strictly between 2 and 4 corn per steel; at either bound one country gains nothing.
- Lower bound for 1 steel
- 2 corn
- Upper bound for 1 steel
- 4 corn
- Country A opportunity cost of 1 steel
- 4 corn
- Country B opportunity cost of 1 steel
- 2 corn
- Steel exporter
- Country B
- Range for 1 corn
- 0.25 to 0.5 steel
- Rate to test verdict
- Both countries accept
The steel exporter's own cost. Anything at or below this and it would rather make steel itself.
The steel importer's own cost. Anything at or above this and it would rather make steel itself.
Whichever country gives up less corn per steel has the comparative advantage in steel.
The same range read the other way: take the reciprocal of each bound and swap the order.
A rate of 3 corn per steel sits inside the range.
How to calculate Terms of Trade Range, step by step
- 1Compute both opportunity costs of the same good. Express the cost of 1 unit of that good in units of the other good, once for each country.
- 2Set the two bounds. The exporter's opportunity cost is the lower bound and the importer's opportunity cost is the upper bound.
- 3Write the range with both bounds. State it as lower cost < price of 1 unit < higher cost, using strict inequalities so neither country merely breaks even.
- 4Invert the ratio for the other good. Terms for the second good are the reciprocals of these bounds, so flip both numbers and swap which one is smaller.
Worked example: Terms of Trade Range
Country A can produce 200 corn or 50 steel, so its opportunity cost of 1 steel = 200 ÷ 50 = 4 corn. Country B can produce 120 corn or 60 steel, so its cost of 1 steel = 120 ÷ 60 = 2 corn. B has the comparative advantage in steel, and acceptable terms lie between the two costs: 2 corn < 1 steel < 4 corn. A rate of 3 corn per steel works, while 5 corn per steel is refused by A and 1.5 corn per steel is refused by B.
Terms of Trade Range questions
Why must the terms fall strictly between the two costs?
At or beyond its own opportunity cost a country gains nothing, because it could produce the good at home for the same or less. Only rates inside the range make both sides better off.
How do you state the range for the other good?
Take the reciprocal of each bound and swap the order. If 1 steel trades for between 2 and 4 corn, then 1 corn trades for between 0.25 and 0.5 steel.
Which country gains more inside the range?
The closer the agreed rate sits to a country's own opportunity cost, the smaller that country's gain. A rate near the middle of the range splits the gains fairly evenly.
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