Why does comparative advantage benefit both trading countries?

Trade based on comparative advantage helps both countries for one reason: each country gets the good it imports for less than its own opportunity cost of making it. That works whenever three things hold. The two countries have different opportunity costs for the same good, each specializes in the good it makes at the lower opportunity cost, and the terms of trade settle strictly between the two countries' costs. Absolute advantage does not enter the argument, so a country that is less productive at everything still gains, and so does its more productive partner.

Here is an illustration with hypothetical numbers. Using all of its resources, Country X can produce 180 tons of rice or 60 bicycles, and Country Y can produce 40 tons of rice or 20 bicycles. X has the absolute advantage in both goods. Opportunity costs tell a different story. One bicycle costs X 180 divided by 60, or 3 tons of rice, but costs Y only 40 divided by 20, or 2 tons. So Y has the comparative advantage in bicycles, and X, whose rice costs one third of a bicycle per ton against Y's one half, has it in rice.

Specializing raises total output. Before trade, suppose X makes 120 tons of rice and 20 bicycles, and Y makes 20 tons of rice and 10 bicycles, for a world total of 140 tons and 30 bicycles. Now Y makes only bicycles, 20 of them, and X moves resources out of bicycles until it makes 10 bicycles and 150 tons of rice. The world still has 30 bicycles but now has 150 tons of rice, 10 tons more, because 10 bicycles are now built where each costs 2 tons of rice instead of 3.

The terms of trade decide who gets the extra rice. Any price between 2 and 3 tons of rice per bicycle works; take 2.5. Y sends X 10 bicycles and receives 25 tons of rice. Y ends with 10 bicycles and 25 tons, 5 tons more than the 20 it had before trade. X ends with 20 bicycles and 125 tons, 5 tons more than its 120. Each side wins on every unit traded: X pays 2.5 tons for a bicycle that would cost it 3 tons to make, and Y receives 2.5 tons for a bicycle that cost it only 2 tons to make. At a price of 3 tons or more X would gain nothing, and at 2 tons or less Y would gain nothing, which is why the price has to sit strictly between the two costs.

Both countries in this illustration now consume a bundle outside their own production possibilities curve, which is the consumption side of the same result; can a country consume beyond its PPC works through it with a separate example. The gains need not be equal: a price closer to 3 tons gives more of the gain to Y, and a price closer to 2 tons gives more to X. A gain for each country as a whole also does not mean every person gains, since workers and firms in the industry that shrinks can lose. Run your own numbers with the gains from trade calculator or the terms of trade range calculator, and see absolute vs comparative advantage for the distinction this answer depends on.