11 2015.06.19.
Title: Comment on Suzuki’s rebuttal of Batra and Casas By Yoshiaki Nakada, Division of Natural Resource Economics, Graduate school of Agriculture, Kyoto University, Kita-Shirakawa-Oiwake-cho, Sakyo, Kyoto, Japan E-Mail: [email protected],
Abstract: Batra and Casas (1976) claimed that ‘a strong Rybczynski result’ arises in the three-factor two-good general equilibrium trade model. In subsequent comments, Suzuki (1983) contended that this could not be the case. Among his comments, Suzuki found that the set of three equations holds for the Allen-partial elasticity of substitution under the assumption of perfect complementarity, and he applied these to his analysis. In the following, I demonstrate that these are impossible, hence his dissenting proof is not plausible. Keywords: three-factor two-good model; Rybczynski result; perfect complementarity; Allen-partial elasticity of substitution; general equilibrium. 1.
Introduction In a rebuttal to the article by Batra and Casas (1976) on functional relations in a three-factor two-good neoclassical model, Suzuki (1983) provided a dissenting proof. In a review of this rebuttal, I find that Suzuki made an error in his proof which renders it implausible. Batra and Casas (1976) were looking at the relation between outputs and factor endowments, which can be found in Theorem 6 (p34). According to Suzuki, they contended that ‘if commodity 1 is relatively capital intensive and commodity 2 is relatively labor intensive, an increase in the supply of labor increases the output of commodity 2 and reduces the output of commodity 1.’ In presenting his proof, Suzuki argues that, ‘their conclusion is not true […] The argument is developed in terms of their notations in a model in which capital and land are perfectly complementary to each other in the production of each commodity.’ Suzuki found that the set of three equations holds for the Allen-partial elasticity of substitution (hereinafter, AES) under the assumption of perfect complementarity. On this, see eq. (1) shown below. In applying this to his analysis, he tried to show that, in contrast to Batra and Casas, ‘a strong Rybczynski result’ (to use Thompson’s terminology, 1985, p617) does not hold in case of perfect complementarity. This rebuttal was subsequently confirmed by Jones and Easton (1983, p67) and Thompson (1985). In a summary of the article, Thompson (1985, p617) suggests that, ‘Batra and Casas (1976) claim a strong Rybczynski result [which holds for a two-factor, two-good model] stated in terms of extreme factors is also found in the three-factor model. Suzuki (1983) and Jones and Easton (1983) point out, as is done here, that a strong Rybczynski result is not necessary.’ In this paper, I return to Suzuki’s original rebuttal, finding that elements of his disproof are questionable. 2.