An Application of Integrability and Duality Theory to the Classical Transfer Problem in International Trade

Abstract

A classic problem in the theory of international trade, going back to John Stuart Mill (1844, pp. 41—3), is that of showing that if one country makes a unilateral transfer of funds to another, not only will it lose by the amount of the transfer, but it will also suffer a “secondary burden” of worsened terms of trade, i.e., lower prices of its exports relative to its imports. This is known as the “classical transfer problem.” Mill’s thesis was disputed by Ohlin (1928, 1929) but defended by Keynes (1929, 1930) in their debate on the effects of the German reparations payments to the Allied Powers after the First World War. In Samuelson’s (1952, 1954) classic treatment the idealization was used (as a way of taking account of transport costs) that commodities deteriorated en route from one country to another. In Chipman (1974) I replaced this by the idealization introduced by Taussig (1927) of nontraded goods, assuming traded goods to be tradable with zero transport costs. In Chipman (1989) I took up the particular case of constant costs in production (the basic assumption made by Mill), in a model in which each of the two countries produces an export good and a nontradable good with a single factor of production (say labor), but relies on imports for the remaining good. I used the concept of a “tradeutility function” developed in Chipman (1979, 1981), in which country k’s trade utility is defined as a function, U(z 1 , z k 2 ), of its “trades” (import quantity if positive, export quantity if negative), and the concept of country k’s tradedemand function z = ĥ(p1, p2, D ), expressed as a function of the the prices of the two tradables and of the deficit in its balance of payments on current account (this function being generated by maximization of the trade-utility ∗I wish to thank the referees for their detailed and helpful comments.