Terms of Trade & the Output–Input Trap

You’ll be able to

Compute opportunity cost correctly from both output and input tables
Determine the range of mutually beneficial terms of trade
Explain why absolute advantage does not determine the gains from trade

The ratio inverts between the two table types

In an output problem the table shows how much each party can produce, and opportunity cost is other good ÷ own good. In an input problem the table shows hours or workers required per unit, and opportunity cost is own ÷ other. The mnemonic that survives exam pressure is O-O-O: Output, Other over Own. Applying the wrong one produces a fully reasoned wrong answer, which is why this appears every year.

Opportunity cost by table type

OUTPUT: cost of one unit = other / own · INPUT: cost of one unit = own / other

Sanity check: on an output table, whoever is good at making a good should have a LOW opportunity cost for it. If not, you inverted.

Absolute advantage is irrelevant

Absolute advantage is producing more with the same resources; comparative advantage is producing at lower opportunity cost. Only the second determines specialization. A party can hold an absolute advantage in everything and still gain from trade, because comparative advantage compares ratios — if one ratio is lower, the other must be higher. Nobody can hold a comparative advantage in both goods.

The terms of trade split the gains

Specialization creates a surplus; the terms of trade decide who gets it. A trade benefits both only when the exchange rate lies strictly between the two opportunity costs. If A gives up 2 shirts per hat and B gives up 5, any price between 2 and 5 shirts per hat works. At exactly 2, A is indifferent and gains nothing; outside the range, one party prefers self-sufficiency.

Worked example

A worker needs 3 hours per chair and 6 hours per table; another needs 2 hours per chair and 8 hours per table. Find each one's comparative advantage and the acceptable terms for one table.

1.This is an INPUT table, so opportunity cost = own ÷ other.
2.Worker 1: one table costs 6/3 = 2 chairs. Worker 2: one table costs 8/2 = 4 chairs.
3.Worker 1 gives up fewer chairs per table, so Worker 1 has the comparative advantage in tables.
4.Worker 2 therefore has it in chairs: one chair costs 2/8 = 0.25 tables against Worker 1's 3/6 = 0.5.
5.Acceptable terms for a table lie strictly between 2 and 4 chairs.

Answer: Worker 1 specializes in tables, Worker 2 in chairs, with terms between 2 and 4 chairs per table. Note that Worker 2 is faster at chairs and slower at tables in absolute hours — the ratios are what settle it.

Watch out

Normalize per unit of the good you are pricing. "The opportunity cost of a table" is 2 chairs, not 6 hours and not 6 chairs. Dividing by the wrong quantity is the second most common error after inverting the ratio.

Checkpoint

A table shows Country Z can produce 60 units of X or 15 units of Y with all its resources. Its opportunity cost of one Y is:

Checkpoint

Party P gives up 3 units of A per unit of B; Party Q gives up 7. Which terms would both accept?

Checkpoint

A firm can produce both of two goods more cheaply than a rival in absolute terms. Specialization and trade:

On the exam

Write both opportunity costs in a labeled two-row table before answering, with units ("1 table = 2 chairs"). The calculation is scored separately from the conclusion, so a correct table earns credit even if you then name the wrong party.

Answer the 3 checkpoints as you read.