 In autarky, Home faces a production constraint of the form
from which it follows that Home's cloth consumption at the production possibilities frontier is

With free trade, Home produces cloth exclusively, an amount of which it exports in exchange for wine at the prevailing rate.Thus Home's overall consumption is now subject to the constraint
while its cloth consumption at the "consumption possibilities" frontier is given by

A symmetric argument holds for Foreign.Therefore, by trading and specializing in a good for which it has a comparative advantage, each country can expand its consumption possibilities.