Optimal employment strategies of profit‐maximizing and labour‐managed firms

This paper deals with the problem of finding optimal hiring and firing policies for profit‐maximizing and labour‐managed firms whose objective is to maximize profits and net income per worker, respectively. Assuming a concave production function with labour force as a variable production factor, a non‐linear demand function, increasing marginal production costs, and convex costs of changing the labour force, we determine the optimal employment strategies by the maximum principle. By using phase portrait analysis, we prove that for a relatively small manpower stock the optimal policies of the profit‐maximizing firms are to increase its labour force over time such that the increase is largest in the beginning. However, for a ‘large’ initial stock, firing can be optimal at the beginning. For a labour‐managed firm, the same behaviour is shown to be optimal for the infinite‐time‐horizon problem only under additional assumptions. The joint analysis of profit‐maximizing and labour‐managed firms provides a possibility to compare the optimal stationary employment policies.