How much trade does the transfer paradox require?

Samuelson (1947) stated that a regular equilibrium exhibits the transfer paradox if and only if it is unstable. Gale (1974) and many in the early 1980’s debunked this equivalence by adding extra countries, reaching an anti consensus. We reinterpret Samuelson’s result as identifying the threshold, i.e. the minimum level of trade beyond which the transfer paradox appears. This reinterpretation generalizes fully to finitely many countries and commodities, and reaffirms the anti consensus quantitatively. A by-product is an explicit general example of Donsimoni and Polemarchakis (1994), that whatever the equilibrium prices and incomes, the welfare impact of a transfer is made arbitrary by some compatible economy.