Variable returns to scale, urban unemployment and welfare: comment.

• Author: Yabuuchi, Shigemi
• Position: Comment on Hamid Beladi's article in Southern Economic Journal, p. 412, October 1988

1. Introduction

   Recently, Beladi [1] explored the question of gains from trade in the presence of urban unemployment and variable returns to scale (hereafter VRS).(1) That is, using a sector-specific minimum wage model, he examined the welfare implications of free trade with those of export-promoting policies and import-substituting policies in the context of VRS. His main results are that "for a small open economy, the import-substituting policies are suboptimal when compared to free trade and the export-promoting policies are superior to free trade if elasticity of returns to scale of the agricultural sector (exportable good) is larger than or equal to that of the manufacturing sector (importable good). However, if the elasticity of returns to scale of the manufacturing sector is larger than that of the agricultural sector, then the import-substituting policies seem preferable to the export-promoting policies [1, 42]."

   However, he treated the variable which captures scale economies ([g.sub.j])as exogenous in the analysis of the positive aspects of the model presented in his appendix. Therefore, the existence of VRS has not been taken into account in the essential manner at all in the derivation of the effects of various policies on the outputs, the urban unemployment ratio and so on. It is easily seen that solutions of the matrix of his appendix are nothing but those corresponding to the case of constant returns to scale.

   Then, in this note, we pursue the analysis of gains from trade in the presence of urban unemployment and VRS as Beladi exactly intended to do. We focus our attention to the case of wage subsidy for manufacturing (as an import-substituting policy) and wage subsidy for agriculture (as an export-promoting policy) for simplicity. The effect of the other policies will be discussed similarly.

2. The Model and Assumptions

   Following Panagariya and Succar [6] and Beladi [1], we deploy the neoclassical version of the Harris-Todaro model by Corden and Findlay [2] incorporating VRS such as: There are two commodities, [X.sub.a] (agricultural output) and [X.sub.m] (manufacturing output), respectively produced in rural and urban sectors, using two factors of production, labor (L) and capital (K). Capital is fully utilized, but labor is fully employed only in the rural sector, where the real wage rate ([w.sub.a]) is flexible. In the urban sector where the real wage rate ([w.sub.m]) is rigid, there may be unemployment. Factors are perfectly mobile between sectors within an economy but perfectly immobile among economies. Each commodity has a different factor intensity which is non-reversible among commodities. Factor endowments are also assumed to be inelastically supplied.

   The production function may be written as (1) [Mathematical Expression Omitted]...