Journal of Intmnmional Economics 24 (1986) 275-297. Noxq~h.H~ TRADE EXPENDITUP~ ~.~NCTIONS AND THE GAE~S F~O~ T ~ P3. LLOYD U~,.~vers~y ~ Mdbom'me, Me/bomb, V~m'~ A ~ r ~ A.G. SCHWEINBERGER* Am~am Nmio~al U~y, Cambenva,ACT 2601. Aus~r~ geared August 1985, ~q~ed version l ~ i v e d AWil 1987 This paigr developt a numher of eoncell~ of trade etpeaditure fuactio~ for an in~tio~l|y trading emaomy with many ~ which di~ in tast~ and factor endowments. These ~ are then apjdied to the aaay~is of pins from trade in ~ emnemks with and without f~remmenUd interventio~o We paeralise and extend a number of proposi~ mnceming sufficient, and necessary and sufficient conditions for individual bouseboMs and Igroups of households to ~ from tt~a,, in economies which are subje~__,to trade taxes and subsidies. The subjegt-matter of the present paper is one oi the oldest and most central topics in trade theory - the analysis of gains from trade in mu|tihousehold economies with and without 8o-ernmental intervcntion. In order to analyse these issues we develop concepts which we call trade expenditure functions. A ~rade expenditure function can be defined ~or an individual household, a group of households, a country, or a number of countries. Essentially it relates the net cost of "produmng" a given utility level or utility vector of households to parameters ~ch as technology, factor endowments, tastes, given distortions, etc. We were not the ~rst to invent ~rade expenditure function. It appears that trade e~penditure functions have been derived independently by a number of economists. ~ We have extended *We are grateful to an ~.mknown referee and to Richard Briber for conunen~s. Any r~maining 'Wan (1965) stated the fun~on in terms of the mazimum bahn~ of payments surplus and called it the "maximum bonus: Chipman (1970) derived it as the envelope function which is dual to the direct trade utility function and cal|e~ it the 'n~nirdum income function'. Woodland {1982, p. 170) defined a 'net revenue' function, and Bhagwati, Brecher and Hatta {1983) defined an 'overspending function' in the same manner as our economyowide trade expe~di~ur© function of definition OH). AI| of t h ~ derivations are apparent|y independent and we were not aware of ~,-, '~'~ we first de~ved our economy-wide trade e~penditure function. ~'~22-1996/88/$3.50 © 1988, Elsevier Science Publishers B.V. (North-Holland)