Doesn't the principle of comparative advantage assume a dynamic model in which absolute advantage changes?

For example, suppose I make brooms more cheaply than anyone in north america (I have an absolute advantage). Suppose further than I can meet quantity demanded in the continent. Surely it cannot matter that a mexican broom maker has a comparative advantage. He simply won't be able to sell any if I have an absolute advantage. If I understand correclty, theory will predict that wages will rise in other industries (where US has comparative advantage), and I will have to raise wages to keep my employees until I lose my absolute advantage. At that point my mexican rival will be able to take over the broom market. But this assumes that I do in fact lose my absolute advantage. Comparative advantage alone doesn't meant that my mexican rival can compete. Do I understand this correctly?

Answer:
No. It assumes there is an demand for what is produced, however. Supply shifts out in both countries and the quantity demanded increases. I wouldn't call this 'dynamic'.

If the Mexican has a comparative advantage in broom making, that means there is something else you can make better. The Mexican makes brooms because you can grow apples even more than making brooms. You will have more brooms and apples if you grow apples and he makes brooms.

Now it could be that the production functions change so that as one person begins making brooms he suddenly has a comparative advantage in growing apples, then things will start to switch and go back and forth like a chaotic system with multiple equilibrium. But it is generally assumed that the production functions do not behave this way and are regular, smooth and convex .

Another area of dynamism which I think is more important
are incomes and employment. As one side looses its industry it looses human capital and experience more or less for good. It also may experience temporary layoffs and experience a reduction in output. This also may change the scale of production and comparative advantage.

There are other arguments against free trade and comparative advantage which I don't have time to go into now.
An absolute advantage does not exist in international trade. Only comparative advantage matters. To use the example in the previous answer, both the apple and the broom industry in the US may be more efficient and lower cost than in Mexico. With free trade and flexible exchange rates, however, exchange rates will adjust so that it is cheaper for the US to import brooms from Mexico and cheaper for Mexico to import apples from the US. The exchange rate will adjust so that imported brooms are cheaper than domestic brooms no matter how efficient and low cost the domestic broom industry may be.
What comparative advantage says is that when you have a comparative advantage in computers and mexico has a comparative advantage in brooms it would be better for you to build computers and mexico to build brooms teh reason for this is that its cheaper for you to buy brooms and computers if that happens. For example if without trade teh US produces 100 computers and 500 brooms and mexico produces 50 computers and 400 brooms when the US needs to sacrifice 1/5th of a computer for 1 broom and mexico needs to sacrifice 0.125 of a computer for a broom (this is basic comparative advantage). Now what will happen is that the US will specialise in computers making 180 computers and mexico will specialise in brooms making 406.25 brooms. Now we see that when a broom used to cost the US a fifth of a computer it only costs them 0.125 so comparative advantage means you will trade with these countries because its cheaper for you to import these goods rather than construct them domestically.

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