Economics Letters 6 (1980) 153- 156 North-Holland Publishing Company 153 THE RECIPROCITY THEOREM IN A MODEL WITH VARIABLE FACTOR SUPPLY Stephen T. EASTON * Simon Fraser University, Burnaby, B.C. V5A IS, Canada University of Rochester, Rochester, NY 14627, USA Received 2 February 1981 The reciprocity theorem is extended to include variable factor supply in a specific factor model. The reciprocity relationships were originally developed by Samuelson (1953) and describe the duality that exists between the Stolper- Samuelson by Rybczynski theorems. More generally they provide the link between the response of a commodity output to a change in the endowment of a particular factor, and the response of that factor’s rental to a change in the commodity’s price under a wide variety of assumptions about tech- nology, numbers of goods and numbers of factors. ’ Formally these relationships may be written as ax,/av, = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA aRi/ap,, where x, and pj are the output and price of commodity j, and V, and R, are the endowment and rental of factor i. The reciprocity relationships are normally developed with given endowments of factors. In this note I discuss the reciprocity relationships appropriate to a model in which one * I am indebted to Ronald W. Jones for many helpful discussions of these issues. ’ Proofs of this relationship under very general conditions may be found, for example, in Samuelson (1953), Kemp (1976) or Jones and Scheinkman (1977). The relationships appear most explicitly in trade theoretic discussions of foreign investment. See Jones (1967) or Kemp (1966). Kemp and Ethier [in Kemp (1976, ch. 7)] develop a particularly broad interpretation of reciprocity. 0165-1765/81/0000-0000/$02.50 0 North-Holland