The theory of comparative advantage is about the best uses to which America can put its productive resources, what economists call "factors of production." We have certain cards in hand, so to speak, the other players have certain cards, and the theory tells us the best way to play the hand we've been dealt. Or more precisely, it tells us to let the free market play our hand for us, so market forces can drive all our factors to their best uses in our economy.
Unfortunately, this relies upon the impossibility of these same market forces driving these factors right out of our economy. If that happens, all bets are off about driving these factors to their most productive use in our economy. Their most productive use may well be in another country, and if they are internationally mobile, then free trade will cause them to migrate there.
This will benefit the world economy as a whole, and the nation they migrate to, but it will not necessarily benefit us.
This problem applies to all factors of production, but the crux of the problem is capital. Capital mobility replaces comparative advantage, which applies when capital is forced to choose between alternative uses within a single national economy, with absolute advantage. And absolute advantage contains no guarantees whatsoever about the results being good for both trading partners.
Capital immobility doesn't have to be absolute, but it has to be significant and as it melts away, trade shifts from a guarantee of win-win relations to a possibility of win-lose relations.
David Ricardo, the British economist who invented the theory of comparative advantage in 1817, actually knew about this problem perfectly well, and wrote about it in his book on the subject. So there's no excuse for modern economists to ignore it.
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