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Further Implications of Distortion in the Factor Market

Yair Mundlak

Abstract

The mini-general-equilibrium model of a two-factor, two-product economy with production functions homogeneous of the first degree provides verifiable propositions for a great many subjects in economics. The data for empirical verification, however, may not, and usually do not, meet the underlying assumptions. In this paper the effects of differences in the wage-rental ratios between the two sectors are traced. Let $q$ be the wage-rental ratio in sector $j$; the paper deals with distortions of the kind $q_{1} = \gamma q_{2}$. The admissible values for $q_{1}$ and $q_{2}$ are derived as functions of $\gamma$ and the overall capital-labor ratio ($k$). Theorem 1 states the values of @c for which the sign of the difference in capital intensities is (i) preserved and (ii) reversed. Next we establish conditions under which the sign of the difference in factor shares is (i) in line with that of no distortion, (ii) reversed, (iii) a combination of (i) and (ii). Such conditions depend not only on $\gamma$ and $k$ but also on the elasticities of substitution (ES) in the two sectors. Theorem 2 summarizes the discussion on this subject. The proofs of the proposition leading to Theorems 1 and 2 are illustrated graphically. In order to analyze the effect on the sign of the supply function in this economy, the ES of products with respect to their prices is expressed in terms of the parameter of the individual production functions. The expression shows clearly the augmentation effect observed by Johnson [$\textbf{1}$] (i.e., in the absence of distortion, the ES between products is larger than those which exist between factors). Finally, Theorem 3 states conditions under which the supply function is increasing, declining, perfectly elastic, or a combination of these.