Generalizing the Stolper–Samuelson Theorem: A Tale of Two Matrices Peter Lloyd* Abstract Past attempts to generalize the Stolper–Samuelson theorem have used a matrix of real income terms which are sufficient but not necessary to define a change in utility. One can define a second matrix of terms which are necessary and sufficient for a change in indirect utility. Using this matrix, the paper extends the Stolper–Samuelson theorem to a model of any dimensions and to households which have diversified ownership of factors. The theorem states that there is a positive and a negative element in every row and every column of the matrix showing household responses to changes in goods prices. 1. Introduction Even after its Golden Jubilee in 1991, there is still doubt about the generality of the Stolper–Samuelson theorem (Deardorff and Stern, 1994). This is unfortunate. The theorem is one of the few comparative statics propositions in general equilibrium theory and it is the foundation of political economy models of tariffs and other taxes and government interventions. The importance of the theorem derives from its key message; goods price changes necessarily create conflict between households owning different factors. This paper considers a general model of an economy with constant returns to scale. The introduction of diversification in households’ ownership of factors changes the relationships between prices and real incomes fundamentally. Nevertheless, a general- ization of the Stolper–Samuelson theorem that holds much more widely than earlier versions can be obtained. The paper begins with a brief history of attempts to generalize the original Stolper–Samuelson theorem. The outcome is rather dismal. These extensions apply to models in which the households are completely specialized in their ownership of factors, as in the original theorem, and they require quite severe restrictions on the technology when they do hold. All of these generalizations are special cases of one generalized Stolper–Samuelson matrix. Then the paper presents the generalization of the Stolper–Samuelson theorem. This uses a second matrix defined in terms of real income effects which are both necessary and sufficient for a change in welfare. This criterion of real income was introduced by Cassing (1981). It can be extended to models of any dimensions beyond 2 ¥ 2 and to diversified household ownership of factors. These results are interpreted in terms of a household’s excess demand vector, using the notion of the imputed output vector of households. Some examples are given. The paper ends with some concluding remarks. Review of International Economics, 8(4), 597–613, 2000 © Blackwell Publishers Ltd 2000, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA *Lloyd: University of Melbourne, Parkville, Vic. 3052, Australia. Tel: 61 3 93448015; Fax: 61 3 9349 2397; E-mail: p.lloyd@ecomfac.unimelb.edu.au. I would like to acknowledge the comments of Alan Deardorff, Rod Falvey, Murray Kemp, and Viktor Zolotenko on an earlier draft of the paper, and the comments of a referee.