Assume that two countries (Home and Foreign) each produce two goods (corn and wheat) under constant cost production. Home produces 0.5 ton of corn or 1 ton of wheat with a day of labor. Foreign produces 1 ton of corn and 0.5 ton of wheat. Without trade (in autarky), Home's daily production is 20 tons of wheat and 10 tons of corn. At which international price will Home's gains from trade be largest?

1/2 ton of wheat per ton of corn

Explanation:

Home produces 0.5 ton of corn or 1 ton of wheat with a day of labor:

Opportunity cost of producing a ton of corn = (1 ÷ 0.5)

                                                                         =  2 tons of wheat

Opportunity cost of producing a ton of Wheat = (0.5 ÷ 1)

                                                                             =  0.5 tons of corn

Foreign produces 1 ton of corn and 0.5 ton of wheat:

Opportunity cost of producing a ton of corn = (0.5 ÷ 1)

                                                                         =  0.5 tons of wheat

Opportunity cost of producing a ton of Wheat = (1 ÷ 0.5)

                                                                             =  2 tons of corn

Therefore,

Foreign has a comparative advantage in producing corn because of lower opportunity cost and Home has a comparative advantage in producing wheat.

So, home country will be importing corn from foreign. Hence, if the international price will be 0.5 tons of wheat per ton of corn then the home country will get the largest gains from the trade because it is willing to sacrifice 2 tons of wheat for a ton of corn.