Although the United States can make either product more efficiently it has a comparative advantage in food, and Mexico has a comparative advantage in clothing.
Without free trade 2 units of food will be worth 1 unit of clothing in the United States. In Mexico 4 units of food will be worth 3 units of clothing. So the exchange rate of food to clothing in the U.S. will be 2:1, or 6:3, in the US and 4:3 in Mexico.
Next lets assume the traders set a compromise exchange rate of 5:3, or 5 units of food for 3 units of clothing. Before free trade if someone in the U.S. had 60 units of food they could exchange that for 30 units of clothing. With free trade they could exchange the 60 units of food for 36 units of clothing. Before free trade if someone in Mexico had 60 units of clothing they could exchange that for 80 units of food. With free trade they could exchange the 60 units of clothing for 100 units of clothing. The trader will be taking in food from the U.S. and clothing from Mexico, allowing for supply and demand for both products and no shortages or surpluses of either.
The net effect will be that the price of clothing will drop in the U.S. from 2 days labor to 5/3 of a day, and the price of food will drop in Mexico from 3 days labor to 2.4 days.
Yes, there will be a temporary loss of clothing jobs in the U.S. and farming jobs in Mexico but with a movement in the labor force into more farming in the U.S. and more clothing in Mexico everybody will be able to enjoy a higher standard of living.
For more information please read the chapter 'International Trade and the Theory of Comparative Advantage' in Economics by Paul J. Samuelson which is seems to invariably be the textbook of choice for freshmen in economics.
Michael Shackleford, A.S.A., March 9, 1999