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the price of good 1 or good 2. Since the factor endowments are fixed, income is proportional to the price of the owned factor. Assuming all goods are produced, there is a one-to-one mapping from goods prices to factor prices which is given by the zero profit conditions alone.

Moreover, the positive elements correspond to changes in the real incomes of the factors which are used intensively in the production of the good whose price has changed. This proves that, when the price of one good increases, the real income of the factor used intensively in the production of this good must increase and that of the other factor must decrease. There is, therefore, conflict between the factor owners. One group of factor owners would support the increase in the price of one good and the other would oppose it. When the number of goods and/or factors is greater than 2 and uneven, univalence breaks down. Attempts to generalise the theorem to higher dimensions, therefore, have been mainly confined to dimensions of nxn. It is usually assumed that there are no intermediate inputs. This can be relaxed to include intermediate usage of the produced outputs but pure intermediates can be admitted only if other produced commodities are omitted as this would otherwise upset the evenness of the model. But even this nxn case has proven extraordinarily difficult. In this case, let w = (w1,...,wn)t and p = (p1,...,pn)t be the column vectors of prices of factors and goods respectively.

A problem now is that there is no natural definition of factor intensity when the number of goods and factors is greater than 2. Hence, there is no natural way of characterising the sign matrix to represent generalisations of the Stolper-Samuelson Theorem. Three principal generalisations have been proposed.1 1. The “strong” generalisation: Each of the diagonal elements is positive (and greater than unity) and each of the off-diagonal elements is negative. 2. The “weak” generalisation: Each of the diagonal elements is positive (and greater than unity). 3. The “basic” generalisation: In every column and every row there is at least one element which is positive (and greater than unity) and at least one which is negative. The first two generalisations were proposed by Chipman (1969). The third was first considered by Meade (1968), Ethier (1974) and Jones and Scheinkman (1977).

Others have been proposed but they are less interesting. For example, Inada (1971) proposed a sign matrix in which the diagonal elements are negative and all the off-diagonal elements are positive but this is a mathematical curiosity.

Both the strong and the weak generalisations involve an association between goods and factors which is mutually exclusive and exhaustive. For every good, there is one and only one factor associated with this good such that the increase in the price of the good must increase the real income of the associated factor.

Hence, these generalisations preserve the identification of the particular factor which is associated with each good, as Stolper and Samuelson were able to do for the 2x2 case in terms of the factor intensities of the goods. By contrast, the third generalisation does not associate factors with goods. If it holds, it might not be possible to array the elements so that every column has a positive element on the diag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。