Two producers can each draw a PPC and measure their own opportunity costs (Opportunity Cost Along the PPC). Comparing those costs, as Unit Rates compares prices per item, tells us who should make what.
Key idea
A producer has an absolute advantage in a good if it can make more of it with the same resources (or the same amount with fewer). A producer has a comparative advantage in a good if its opportunity cost of making it is lower. Unless two producers have identical opportunity costs, each has a comparative advantage in something.
Why it works
Why must each have a comparative advantage in something? Opportunity costs come in reciprocal pairs. If Ana gives up $\tfrac{1}{2}$ shirt per loaf, then a shirt costs her 2 loaves. If Ben gives up 1 shirt per loaf, a shirt costs him 1 loaf. Ana's loaf is cheaper, so Ben's shirt must be: when one cost is lower, its reciprocal is higher. Being faster at everything (absolute advantage) can't change that.
Worked example: An output table
In a day Ana can bake 6 loaves of bread or sew 3 shirts; Ben can bake 4 loaves or sew 4 shirts. Who has the absolute advantage in each good, and who has the comparative advantage?
- Absolute advantage: Ana makes more bread (6 > 4); Ben makes more shirts (4 > 3).
- Ana's cost of a loaf: $\dfrac{3 \text{ shirts}}{6 \text{ loaves}} = \dfrac{1}{2}$ shirt. Ben's: $\dfrac{4}{4} = 1$ shirt. Ana's is lower, so Ana has the comparative advantage in bread.
- Ana's cost of a shirt: $\dfrac{6}{3} = 2$ loaves. Ben's: $\dfrac{4}{4} = 1$ loaf. Ben has the comparative advantage in shirts.
Answer: Ana: bread (both absolute and comparative). Ben: shirts (both).
Worked example: An input table: hours per unit
Country X needs 2 hours of labor per bushel of corn and 6 hours per bike. Country Y needs 4 hours per bushel and 8 hours per bike. Who has the comparative advantage in bikes?
- Here smaller numbers are better: fewer hours per unit. X has the absolute advantage in both goods.
- In X, 6 hours spent on one bike could have made $6 \div 2 = 3$ bushels: a bike costs 3 bushels.
- In Y, 8 hours on one bike could have made $8 \div 4 = 2$ bushels: a bike costs 2 bushels.
- Y gives up less corn per bike, so Y has the comparative advantage in bikes (and X in corn).
Answer: Country Y.
Common mistake
Confusing the two kinds of advantage, and treating the bigger number as better in an input table. In the second example X is faster at both goods, yet Y has the comparative advantage in bikes. Check: in an input table, first ask "how many of the other good could these same hours have made?" Then compare those opportunity costs; the lower one wins.