Consider two countries (call them Country A and Country B) both of which grow corn and wheat. Country A has \(200\text{ farmers}\) that grow a total of \(1200\text{ bushels of wheat}\) a year (\(6\text{ bushels per farmer}\)), and \(300\text{ farmers}\) that grow a total of \(1200\text{ bushels of corn}\) a year (\(4\text{ bushels per farmer}\)).

Country B is much less efficient than Country A, and has \(600\text{ farmers}\) that grow a total of \(1200\text{ bushels of wheat}\) a year (\(2\text{ bushels per farmer}\)), and \(400\text{ farmers}\) that grow a total of \(1200\text{ bushels of corn}\) a year (\(3\text{ bushels per farmer}\)).

In summary:
Country A: \(200\text{ farmers}\) grow \(1200\text{ bushels of wheat}\) a year (\(6\text{ bushels of wheat per farmer}\))
\(300\text{ farmers}\) grow \(1200\text{ bushels of corn}\) a year (\(4\text{ bushels of corn per farmer}\))
Country B: \(600\text{ farmers}\) grow \(1200\text{ bushels of wheat}\) a year (\(2\text{ bushels of wheat per farmer}\))
\(400\text{ farmers}\) grow \(1200\text{ bushels of corn}\) a year (\(3\text{ bushels of corn per farmer}\))

Country A is clearly more efficient at growing both corn and wheat than Country B. The question is: Can these two countries reach a trade agreement that is beneficial to both sides?

Lets say that Country A decides to grow only wheat, and that Country B decides to grow only corn.

In Country A, the \(300\text{ farmers}\) that previously grew corn will now be growing wheat, making a total of \(500\text{ farmers}\) growing wheat. Since a farmer in Country A grows \(6\text{ bushels of wheat}\) a year, a total of \((6)(500)\) or \(3000\text{ bushels of wheat}\) will be grown in that country each year.

In Country B, the \(600\text{ farmers}\) that previously grew wheat will now be growing corn, making a total of \(1000\text{ farmers}\) growing corn. Since a farmer in Country B grows \(3\text{ bushels of corn}\) a year, a total of \((3)(1000)\) or \(3000\text{ bushels of corn}\) will be grown in that country each year.

Country A now has: \(1500\text{ bushels of wheat}\) (whereas before the trade it had \(1200\)), and
\(1500\text{ bushels of corn}\) (whereas before the trade it had \(1200\))

Country B now has: \(1500\text{ bushels of wheat}\) (whereas before the trade it had \(1200\)), and
\(1500\text{ bushels of corn}\) (whereas before the trade it had \(1200\))

In this case, the trade was clearly beneficial (mathematically speaking) to both countries even though one of the countries was more efficient at growing both wheat and corn than the other..

Is it possible to have a mutually beneficial trade agreement with the following productivity numbers?

Country A: \(200\text{ farmers}\) grow \(1200\text{ bushels of wheat}\) a year (\(6\text{ bushels of wheat per farmer}\))
\(300\text{ farmers}\) grow \(1200\text{ bushels of corn}\) a year (\(4\text{ bushels of corn per farmer}\))

Country B: \(300\text{ farmers}\) grow \(1200\text{ bushels of wheat}\) a year (\(4\text{ bushels of wheat per farmer}\))
\(400\text{ farmers}\) grow \(1200\text{ bushels of corn}\) a year (\(3\text{ bushels of corn per farmer}\))