Why parties gain from trade even when one is better at everything, opportunity cost does the work.
Warming up the engine…
A producer has comparative advantage in a good when they can make it at a lower opportunity cost than anyone else, even if they're worse at producing everything (absolute disadvantage).
Specialize where: opportunity cost of X = (units of Y forgone) / (units of X gained) is lowest
A lawyer who types faster than her assistant should still hire the assistant, every hour typing costs her an hour of legal fees. Trade lets everyone shift hours toward their cheapest-to-produce good, and total output rises without anyone working more.
Compute each producer's opportunity cost for BOTH goods first; the numbers must be reciprocals, so nobody can have comparative advantage in both.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at C 40, W 30.
Equilibrium: C* = 40.0, W* = 30.0
Current equations
Two producers, two frontiers. The steeper line gives up more wine for each unit of cloth, so cloth is expensive there. Each side should make the thing it gives up least to produce. That is comparative advantagecomparative advantageBeing able to produce something at a lower opportunity cost than others, the true basis for trade., and it holds even when one side is better at everything.