(1/a_LC)(P_C/P_W)>1/a_LW or P_C/P_W>a_LC/a_LW. But we just saw that in international equilibrium, if neither country produces both goods, we must have P_C/P_W>a_LC/a_LW. This shows that home can produce wine more efficiently by making cheese and trading it than by producing wine directly for itself. Similarly, foreign can produce cheese more efficiently by making wine and trading it. This is one way of seeing that both countries gain.
Another way to see the mutual gains from trade is to examine how trade affects each country’s possibilities for consumption. In the absence of trade, consumption possibilities are the same as production possibilities. Once trade is allowed, however, each economy can consume a different mix of cheese and wine from the mix it produces. Home’s consumption possibilities are indicated by the colored line TF in figure 2-4a, while foreign’s consumption possibilities are indicated by T*F* in figure 2-4b. in each case trade has enlarged the range of choice, and therefore it must make residents of each country better off.