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he price of this good and lose from an increase in the prices of the other goods. Household 2 produces good 3 as well as good 2 in positive quantities and good 1 in a negative quantity. As θ22 dominates the other terms in the second column of θ, the value of the output of this good is larger than the income of household 2. The weak generalisation of the Stolper-Samuelson Theorem follows from Equation (12) and consequently the basic generalisation also follows. Allowing diversification of household ownership of factors opens up a much richer variety of possibilities. One can find a region of household diversification which yields the basic generalisation. The patterns of diversification in this region will suffice for the generalisation, irrespective of the household preferences.

First, for all sets of endowments in the zones marked (1), (2) and (3), the strong generalisation of the theorem holds. Since only one good is produced positively in each household, the value of the imputed output of this good exceeds its income and the household gains from an increase in the price of the good, irrespective of its preferences. For the other h h h two goods, γi < 0 and, therefore, (γi - φi ) < 0. (These endowments are such that the strong generalisation holds even though the Kemp-Wegge condition does not hold.) The basic generalisation holds for all sets of endowments such that each household produces one good in value greater than its total output (income). This holds for any technology as represented by a θ. Of course there are more than three households in an economy.

With many households, all that is required for a generalisation to hold is that there be one household in each of the stipulated zones or areas. These regions of factor ownership are sufficient for the theorem. With knowledge of the preferences of the households, there is a wider set of household distributions which is necessary and sufficient for the theorem. Even in the extreme case in which each household owns a fraction of the nation’s endowments, all households will have the same endowment point in the cone of diversification but the theorem will hold if there is sufficient diversity in preferences.

The theorem retrieves the spirit of the Stolper-Samuelson Theorem. It has not been stated previously to my knowledge. Cassing (1981) proved the row property for the restricted model with specialised factor ownership and nxn dimensions. If the numbers of households and goods and factors is n and every household owns only one factor and every factor is owned by one household, each household can be associated with a factor.

Hence, there must be at least one positive and one negative element in each row of the matrix. Lloyd and Schweinberger (1988, p. 281) stated the general form of the row property in the theorem, using the household trade expenditure function. The general proof of the row property derives from the use of a true index of utility rather than the Stolper-Samuelson criterion of real income change. In fact, it is the homogeneity property of the indirect utility function which produces the result that Cassing noted. This result is much more general than the special case of an nxn economy with undiversified households which Cassing considered. It applies to any household with a diversified factor ownership and it allows specific as well本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。