Compute comparative advantage

Lower opportunity cost, not greater output, decides specialization.

Suppose Harbor can make 12 fish or 6 units of grain per day, while Prairie can make 8 fish or 8 grain. Harbor gives up 6/12=0.5 grain per fish. Prairie gives up 8/8=1 grain per fish. Harbor therefore has comparative advantage in fish. For grain, use reciprocals: Harbor gives up 2 fish per grain while Prairie gives up 1, so Prairie has comparative advantage in grain.

Comparative advantage is a comparison of ratios within each producer. First calculate what one producer sacrifices to gain a unit of a good. Then compare that same unit across producers. Do not compare Harbor’s fish output directly with Prairie’s grain output. Those are different goods and do not state opportunity cost. A clean table labels every ratio with “for each.”

The lower entry in each column identifies comparative advantage: Harbor for fish and Prairie for grain. Within a two-good model, the opportunity costs are reciprocals. This produces a useful audit. If Harbor’s cost of a fish is 0.5 grain, its cost of a grain must be 2 fish. If your second calculation gives 0.5 fish, you repeated the first ratio instead of reversing it.

Harbor also has absolute advantage in fish because it can produce more fish with the same daily resources. Prairie has absolute advantage in grain. Absolute advantage can be split this neatly, but it need not be. One producer may have absolute advantage in both goods. Comparative advantage must still divide when opportunity costs differ.

For output tables, absolute advantage means the larger maximum output with the same resources. For input tables, such as labor hours required per unit, absolute advantage means the smaller input requirement. This change in direction is another common trap. Comparative advantage always follows lower opportunity cost, but the numbers supplied may require different first steps.

A productivity advantage in everything

Ada can write 12 reports or design 6 graphics. Bo can write 4 reports or design 4 graphics. Ada has absolute advantage in both. Ada’s cost of a report is 0.5 graphic. Bo’s is 1 graphic, so Ada has comparative advantage in reports. Bo’s cost of a graphic is 1 report versus Ada’s 2, so Bo has comparative advantage in graphics.

Comparative advantage depends on relative productivity, not on being “bad” at a task. Bo specializes in graphics because his disadvantage is smaller there. Each graphic costs him one forgone report, while it costs Ada two. Assigning Ada to reports and Bo toward graphics uses their time where its opportunity cost is lower, which can increase combined output.

When resources are divisible, specialization can be partial. When preferences require both goods or opportunity costs change as production expands, a producer need not move to a corner. Introductory constant-cost tables usually support clear specialization, but the reason is still lower opportunity cost rather than a rule that every producer must abandon one good entirely.

Finish by checking units and pairing. If one producer has comparative advantage in both goods, an arithmetic error has occurred unless opportunity costs are equal, in which case neither has a strict comparative advantage. With two producers and two goods, lower cost in one good implies higher reciprocal cost in the other.