Publisher Summary The extensive structure of modern trade theory has been built on a foundation of several extreme assumptions, including that of low and even dimensionality. This chapter is concerned with Heckscher–Ohlin theory of international trade in higher dimensions. This theory, in its standard two-commodity, two-factor version has dominated international trade theory for over 30 years. But this dominance has long been made uneasy by a widespread suspicion that world commerce does not accord well with the theoretical structure. There are two particular areas of concern. The first stems from the fact that the largest part of world trade involves the exchange of roughly similar products among similar economies, whereas the factor endowment theory, and comparative cost theory, generally teaches to look to international dissimilarities for the causes of trade. A large part of this actual trade is classified as intraindustry even with significant disaggregation. Thus probing its causes requires a high degree of disaggregation—that is, the explicit consideration of a large number of goods. The second area of concern stems from the Leontief Paradox. The sensitivity to higher dimensions of the basic propositions of the modern theory of international trade is the key issue for the practical relevance of the logical structure that has dominated trade theory in the past 30 years.

Chapter 3 Higher dimensional issues in trade theory

This paper examines various theorems of trade and general equilibrium in a generalized framework involving arbitrary numbers of goods and factors. It develops structural relations among the changes in outputs, commodity prices, factor rewards, and factor endowments. By finding a way of inverting a bordered matrix with a singular Hessian, the paper derives explicit expressions for the following matrices: the Stolper-Samuelson matrix; the Rybczynski matrix; the matrix which measures the effect of a change in factor endowments upon factor rewards at constant commodity prices; and the matrix which measures the effect of a change in commodity prices upon outputs at constant factor endowments. Various properties of these matrices are used to obtain, among other results, the reciprocity relations and general results on factor-price equalization. The paper also ey.amines the problem of indeterminacy in production when the number of commodities exceeds the rank of the input-coefficient matrix and presents the correct specifications of the supply functions of outputs. Finally a new theorem on the degree of flatness of the production transformation surface is derived.

Some theorems of trade and general equilibrium with many goods and factors

Students of international economics have absorbed the factor price equalization (FPE) theorem over recent decades. It may be time to reconsider that factor prices would likely converge outside the context of the formal Heckscher-Ohlin-Lerner Samuelson model. This paper reviews the theoretical evolution of FPE and the empirical evidence regarding the influence of trade on the international pattern of factor prices.

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Factor Price Equalization: Theory and Evidence

Factor price equalization and the factor proportions theorem when commodities outnumber factors: the case with intensity reversals(1)

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Higher d imensional issues in trade t heory

In a recent article in this journal, Professor H. G. Johnson has been able to show that an earlier finding by Dr. Land that factor prices may diverge with trade violates a consistency condition relating the changes in production resulting from the introduction of free trade and the requirement of full employment of fixed factor supplies.2 In his paper, Professor Johnson is also concerned with the question considered by Land of whether increasing the number of commodities increases or reduces the probability of factor price equalization. He concludes that "contrary to Dr. Land's general position the larger the number of goods relative to the number of factors the more likely is free trade to lead to factor price equalization" (p. 288). This Note contends that both Johnson's and Land's arguments on this latter question are not valid. Following Land and Johnson, a two-factor (capital, K, and labour, L), three commodity (X, Yand Z) and two-country (I and II) model is used. It is assumed that the production functions fulfil the strong Samuelson factor-intensity assumption, i.e., X, Y and Z are characterized by decreasing capital-to-labour input ratios for all factor price ratios (price of labour in terms of capital). Johnson's argument is illustrated in Figure 1, which corresponds to Figure 2 in his paper. Neglecting for the moment commodity Y, the possibility of factor price equalization may be defined for the two-good case. "The upper part of the diagram shows the technological relationship between the capital-labour ratios in the two industries and the factor-price ratio .. .; the lower part shows the technological relationship between the factor-price ratio and the relative price (cost) of Z in terms of X, for arbitrarily chosen units of Z and X, the price of Z rising as the relative price of labour rises because Z is labour-intensive relative to X" (p. 283). With fixed factor endowments, the capital-labour endowment ratios in the two countries determine a range of factor prices consistent with production of X and Z. For country I, this range is wlw3 and for country II it is w2w4. If the factor endowment ratios of the two countries are close enough so that there is a range of overlap in the feasible factor prices as in Figure 1, then there is a possibility of factor price equalization. If free trade leads to a

Trent J. Bertrand

Papers

On Factor Price Equalization When Commodities Outnumber Factors: A Note