I tried to work through a proof of “free trade makes the pie no smaller,” and it seems like it only works if you’re considering one good. I reasoned thusly: 1

I tried to work through a proof of “free trade makes the pie no smaller,” and it seems like it only works if you’re considering one good. I reasoned thusly: 1. Country A can produce good X at price p_a < price p_b the price at which domestic X is available in B. 2. No deadweight trade loss, so X is available at p_a in B 3. Thus for the same quantity n of X, B has a surplus of n(p_b - p_a). 4. But domestic producers of X have lost income, and if there isn’t something else for them to do, the total shrinkage in B’s economy may exceed the surplus (I haven’t worked out this term but it should be pretty easy), thus leaving B worse off. Factor in deadweight losses and free trade definitely could leave B worse off, by forcing some of its economy to be unproductive.