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quare sub-matrix excluding the row for the non-specific factor, this has the pattern of the strong generalisation. In effect, factor specificity is a form of association between the factor and the good. As with the Kemp-Wegge condition in the 3x3 model, it generates the pattern of the strong generalisation for these inputs and it identifies the input which gains when each price is increased. But the row relating to the non-specific factor has neither an element greater than unity nor an element less than zero. Ruffin and Jones (1977) referred to the absence of an element greater than unity in this row as the “Neoclassical ambiguity”. Thus, again, the main sticking point in the basic generalisation is the property that the row have an element greater than unity.

Using a different real income criterion from Stolper-Samuelson and earlier writers, Cassing (1981) re-examined the case of nxn dimensions. He established the row property of the basic generalisation which Jones and Scheinkman could not establish. He did so without restricting the technology. This is an important but generally neglected paper. His criterion of real income change is employed below. All of these results have assumed that all households own only one factor. Plainly, we want a proposition relating real income changes to price changes which holds much more generally. We now consider the possibility of extending the theorem for a much more general model.

Consider a small open economy. There are any number of goods (n) and factors (m) and households (H). Factors are fixed in supply but may be specific or non-specific.

The weak generalisation holds, for a square matrix, if and only if all elements on the diagonal are strictly positive. The basic generalisation holds for a matrix of any dimensions if and only if there is a strictly positive and a strictly negative element in each row and column. The matrix in Equation (7) differs from the Generalised Stolper-Samuelson matrix in Equation (5) in terms of the criterion of a change in real income and in the diversification of the income of households. It permits any pattern of diversification. The analysis of the Theorem with diversified household ownership requires additional new concepts on the supply side of the model. These concepts are the generalised household income function and the imputed outputs of the household. Household income is the income from the factors which the household owns, Ih = wvht where vht is the column vector of factors owned by the household, the transpose of vh. Utilising w = w(p,v), the household income function is Ih = w(p,v)vht = gh(p,v,vh) These functions are homogeneous of degree +1 in p. The outputs imputed to a household, denoted by ~ y h, may be calculated in the same manner as outputs are determined for the national economy. (The concept of the imputed output of the household has been used by Lloyd and Schweinberger (1988, 1997).) Each household owns a given endowment of factors which will be fully employed. The household is assumed to possess the same technologies of producing each good as the nations’ firms.

That is, the imputed output of good i by household h is the weighted sum of the inputs supplied by this household to the firms of the economy. The weights are the marginal effects of the change in the aggregate supply of this input on the aggregate econo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。