The Competitive Firm with Uncertainty in the Rate of Labor Turnover

Abstract

The adoption of more sophisticated production techniques usually requires firms to increase their expenditures on worker training and to pay greater attention to the costs of labor turnover. Economists are beginning to explicitly incorporate both training expenditures and the rate of labor turnover into the theory of the firm. At the same time, they are extending the theory of the firm to cases in which the firm faces uncertainty in its environment; for example, uncertainty in the price of output, the prices of inputs, or the quantity of output that a given input mix will yield. This paper seeks to extend both of these areas of research by first introducing uncertainty in the rate of labor turnover and then examining the consequences of this new form of uncertainty for optimal training expenditures, the optimal wage, and the optimal level of output at the firm. The paper assumes that the firm can increase output by providing workers with more training and can discourage turnover by paying workers a higher wage. The quantities of labor and capital that the firm employs are held constant throughout the analysis. It is found that the introduction of uncertainty in the rate of labor turnover results in lower optimal expenditures for both training and wages. The reduction in training also reduces the level of output per worker at the firm. Comparative static analysis of ceteris paribus changes in the mean and variance of the labor turnover rate are also performed. An increase in the mean of the turnover rate, with the variance held constant, reduces the wage and the amount of training provided. Also, an increase in the variance of the turnover rate, with the mean held constant, reduces the wage and the amount of training provided. A number of authors have considered models of the competitive firm in which the firm must determine its output level in the presence of uncertainty. Sandmo [13], Batra and Ullah [2], Hartman [7], Ishii [9], Ingene and Yu [8], Flacco [5], and many others consider the behavior of the competitive firm facing uncertainty in its output price. Blair [3], Ratti and Ullah [12], Stewart [15], Perrakis [11], MacMinn and Holtman [10], and many others consider cases in which the firm faces uncertainty in its technology or factor prices. In all of these models, it is assumed that the firm must make its input and output decisions before the uncertainty is resolved, without ex