in the two countries, and that, so long as there are differences, there will always be opportunities for trade, even if one country can produce everything more cheaply than the other.
The modern theory of international trade has its roots in the work of David Ricardo. The central idea in Ricardo's theory, which is equally central to the modern theory, is that two countries can obtain mutual gains from trade, provided that they trade along the lines of "comparative advantage;" and that ideally a market system with profit-seeking enterprises will lead them to do so.
The theory of comparative advantage is a bit more subtle than it appears to be on the surface. It tells us that opportunities for mutual gains from trade arise from differences in the conditions of production in the two countries, and that, so long as there are differences, there will always be opportunities for trade, even if one country can produce everything more cheaply than the other.
The theory is a little more subtle than the words "trade according to comparative advantage" suggest, and the idea is best understood through a numerical example.
Productivity in Two Countries
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