ABSTRACT OF PAPER
Title: The Heckscher-Ohlin-Samuelson Model and the Cambridge Capital Controversies
Author: Kurose Kazuhiro, Yoshihara Naoki
The purpose of this paper is to survey the theoretical development of the Heckscher-Ohlin-Samuelson model. We are especially interested in how the neoclassical economics develops the model to prove the factor price equalisation theorem (FPET hereafter) in relation to the critiques of the Cambridge capital controversies. Samuelson's (1953) conjecture that the sufficient condition for the factor price equalisation is characterised by the Jacobian of cost functions is valid only in a two-sector model and is not in more general models. Therefore, many economists attempt to obtain the condition that generally holds, for example, Blackorby et al. (1993), Chipman (1969), Gale and Nikaido (1965), Mas-Colell (1979a, b), Nikaido (1972), and Kuga (1972). All previous attempts are based on the assumption that capital is a primary factor of production. In other words, they used models in which the principle of marginal productivity is valid. However, the primary lessen of the Cambridge capital controversies is that the principle of marginal productivity is not necessarily satisfied if capital consists of a bundle of heterogeneous and reproducible commodities. Garegnani (1970), Pasinetti (1966), Sraffa (1960), and others argue that the principle of marginal productivity is not generally valid; capital reversing and/or reswitching of techniques takes place in models with reproducible capital. The existence of reproducible capital is a focus in the field of international trade as well. Metcalfe and Steedman (1972, 1973) and Mainwaring (1984) assert that the FPET is not generally valid in models where reproducible capital is included. We demonstrate that, first, no capital-intensity reversal, which is the most basic premise of the FPET, is difficult to maintain in models where capital consists of reproducible commodities. It can be interpreted as the impossibility theorem of factor price equalisation in models with reproducible capital. Second, even though capital-intensity reversal does not take place, factor prices are not generally equalised if capital consists of reproducible commodities. This is shown through a numerical example of a vertically integrated model with two final commodities. Unlike Metcalfe and Steedman (1973), the numerical example is given by Leontief production techniques (i.e. physically input coefficient matrices and labour coefficient vectors). Third, although Burmeister (1978) is the most rigid neoclassical model with reproducible capital and characterises the conditions for the factor price equalisation, we show that the structure of the model is such that the `perverse' phenomena pointed out by the Cambridge capital controversies never take place. To be precise, Burmeister's model includes reproducible capital but it excludes many possible techniques by hypothesis. In this sense, the model is based on highly restrictive assumptions that are seldom satisfied in reality. The open question is, under what condition is the FPET valid in more general models with reproducible capital, and what is the likelihood of the condition being satisfied in reality? If the condition is unlikely to be satisfied, the foundations of the neoclassical international economics must be reconsidered.
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