We have now seen that countries whose relative labor productivities differ across industries will specialize in the production of different goods. We next show that both countries derive gains from trade from this specialize. This mutual gain can be demonstrated in two alternative ways.
The first way to show that specialize and trade are beneficial is to think of trade as an indirect method of production. Home could produce wine directly, but trade with foreign allows it to produce wine by producing cheese and then trading the cheese for wine. This indirect method of producing a gallon of wine is a more efficient method than direct production. Consider two alternative ways of using an hour of labor. On one side, home could use the hour directly to produce 1/a_LW gallons of wine. Alternatively, home could use the international trade allows home and foreign to consume anywhere within the colored lines, which lie outside the countries’ production possibility frontiers.
Hour to produce 1/a_LC pounds of cheese. This cheese could then be traded for wine, with each pound trading for P_c/P_W gallons, so our original hour of labor yield (1/a_LC)(P_C/P_W) gallon of wine. This will be more wine than the hour could have produced directly as long as