Terms of Trade and the Gains from Trade

Before trading, each country is stuck consuming only what it makes, limited by its own opportunity cost of shifting between two goods. Comparative advantage tells each country which good to specialize in: the one with the lower opportunity cost. Once both countries specialize and produce more total output between them than they would producing a mix of both goods themselves, there's more to go around. Trade is how that extra output actually reaches each country's households.

The terms of trade decide how that gain gets split. Pick a trading ratio strictly between the two countries' opportunity costs, and both sides end up on the winning end of the trade compared to producing alone. Each country gives up less of its good than its own opportunity cost would demand, and gets more of the other good than it could make for itself. That's why gains from trade aren't zero-sum: one country consuming more doesn't force the other to consume less, because the total available to trade is larger than what either country could produce alone.

This connects directly to production possibilities frontiers: specialization moves each country to a single point on its own frontier, and trade lets both countries consume at a point beyond that frontier, something autarky never allows. The next question is always which exact ratio gets chosen, since any point in the shared range works, but real trades settle somewhere based on bargaining power and demand.