Which theorem says free trade equalizes factor prices under specific assumptions?

The theorem saying that free trade can equalize factor prices under specific assumptions is the factor price equalization theorem.

Associated with Paul A. Samuelson's 1948 work, the theorem is a major result of the Heckscher–Ohlin model. In its standard two-country, two-good, two-factor setting, countries use the same technology, face free trade in goods, produce both goods, and operate under competitive conditions. If trade equalizes the prices of goods, those common output prices can also equalize the returns paid to labor and capital.

The striking implication is that workers and capital do not need to move between countries for their factor prices to converge. Trade in goods can indirectly transmit the economic effects of each country's abundant or scarce resources. Wages are the most familiar example, although the theorem concerns identical factors more generally.

The result is a conditional theoretical benchmark, not a universal prediction. Transport costs, tariffs, different technologies, incomplete specialization, skill differences, and other real-world frictions can prevent equalization. Rybczynski's theorem instead concerns how factor supplies affect output quantities, making it a related but distinct trade result.