Generalizing the Stolper–Samuelson Theorem: A Tale of Two Matrices

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.