A generalisation of the Stolper-Samuelson theorem with diversified households: A tale of two matrices

Abstract

Past attempts to generalise the Stolper-Samuelson Theorem have used a matrix of real income terms which is sufficient but not necessary to define a change in utility.In contrast, one can define a second matrix of terms which are necessary and sufficient for a change in indirect utility.Using this matrix, the paper presents an extension of the Stolper-Samuelson Theorem to a model of any dimension 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 how each household is affected by the changes in goods prices.The condition required is that there be sufficient diversity among households in their ownership of factors or preferences..

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