Price uncertainty and the labor managed firm: comment.

• Author: Kahana, Nava
• Position: Comment on articles by E. Kwan Choi and Eli Feinerman and by Shoji Haruna, Southern Economic Journal, pp. 43 and 518, 1991 and 1993

1. Introduction

   Muzondo [4] and Paroush and Kahana [5] were the first to investigate the behavior of a labor managed firm (LMF) under price uncertainty. The main conclusion of these studies is that in the short run, when labor alone is a variable input, the risk-averse LMF produces more under output price uncertainty than under complete information.

   Recently, Choi and Feinerman [1] and Haruna [2] attempt to extend Paroush and Kahana's results to the long run when capital also becomes a variable input.

   The purpose of this note is twofold. First, it points out a few mistakes in Choi and Feinerman, and second, it shows that all their results as well as those of Haruna are either identical to Kahana and Paroush's findings [3], or can be obtained as special cases. The study by Kahana and Paroush [3, 26], published in the Eastern Economic Journal about a decade ago, can be summarized by the following proposition: "All the results that hold for the short run can be readily generalized to the long run provided that labor and capital are competing inputs or that the product produced by the cooperative is an important user of labor."

   Apparently being unaware of this publication, the studies by Choi and Feinerman [1] and Haruna [2] recently appeared in the Southern Economic Journal. It seems that the distance between the South and the East is difficult to bridge.

2. The Model and Comparison of Results

   In the following we adopt the notations used in Choi and Feinerman [1]. Consider an LMF which produces Q by a neoclassical production function Q = F(K, L) where K and L are capital and labor inputs respectively. The LMF is assumed to maximize EU(w) with respect to K and L where w = (pQ - rK)/L is the income per member, p is the random unit price of Q, and r is the rental rate of K. The utility function U is assumed to exhibit risk aversion, i.e., U[prime] [greater than] 0, U[double prime] [less than] 0.

   Denote by [K.sup.a], [L.sup.a], [Q.sup.a] the optimal solutions of the above problem where [Q.sup.a] = F([K.sup.a], [L.sup.a]) and denote by [K.sup.n], [L.sup.n] and [Q.sup.n] the corresponding optimal values in the case where p is certain and equal to [Mathematical Expression Omitted]. Proposition 1(i) in Choi and Feinerman [1, 49] is identical to Theorem 1 in Kahana and Paroush [3, 24]. In Choi and Feinerman's Proposition 1(ii) L should be substituted by K the latter being an inferior input and then one can find that 1(ii) is a special case of Theorem 2...