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as nonspecific factors and intermediate inputs. The column property has not been proven before. Thus, it turns out that it is the row property which holds generally, not the column property. This is the opposite of the conclusion of Ethier (1974) and Jones and Scheinkman (1977) for the case of households which are completely undiversified in terms of the factor ownership and using the Stolper-Samuelson criterion of real income change. The contrast between these results and those of earlier generalisations of the StolperSamuelson Theorem is the contrast between the two matrices in Equations (5) and (7). Equation (7) permits any pattern of diversification in factor ownership, uses the necessary and sufficient criterion for a utility change and is unrestricted in terms of the dimensions of the model . The only restrictions which rule out a part of the gains from international trade is that the number of goods which are consumed is fixed and there are no economies of scale, unlike the models of Krugman, Helpman and others in which this number is endogenous and there are economies of scale. Even here, we can note that the consumers in the Krugman-Helpman models are identical in terms of their preferences (see, for example Helpman and Krugman (1985, especially chapter 9.5)). Again it is this lack of diversity which accounts for the result that all households may gain from trade, not the presence of economies of scale and product varieties.

In deriving the Stolper-Samuelson-type theorem above and the conditions for the strong and weak generalisations, the concept of the imputed outputs of a household is an expeditious method of extending the column property of the matrix of household changes in real income. However, the crucial step in the extension of the both the row and column properties of the Stolper-Samuelson theorem is the use of the true index of utility change. This provides a criterion which is necessary and sufficient for a price index to increase or decrease the real income of a household. The Stolper-Samuelson criterion was weaker and sufficient for the simple 2x2 Heckscher-Ohlin model.

Stolper and Samuelson (1941) stated: “The vast majority of writers take it as axiomatic that a calculation of effects upon real income must take into consideration the behaviour of prices of commodities entering the consumer’s budget.”

They saw But their criterion which removed the index number problem as a great advantage.the criterion was quite inadequate for more general models. It was too strict a test of real income change. Ironically, progress has been made in completing the row and column properties of a general version of the Theorem only by putting the consumption effect back into the criterion.

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