The marginal value of management using stochastic control

Abstract

This paper considers the problem of valuing the managerial factor input to the firm. It focuses on the value of the professional manager in terms of his control of the economic activities of the firm. This includes the monitoring and decision-making aspects of management when the firm's opportunity set is given. The analysis assumes competitive firms with Cobb-Douglas production functions and fixed capital. Prices, wages, and the value of the market portfolio are described by a system of Ito stochastic differential equations. The primary focus of the model is the determination of marginal managerial value, and its relationship to the parameters of the production, wage, and price processes. The value of managerial control is shown to be an increasing function of the correlation of wages with the aggregate real consumption process and the standard deviation of the growth rate of wages, and a decreasing function of the correlations of wages and output prices and output prices and the market factor (and their standard deviations). Furthermore, the paper demonstrates the difficulty of embedding the managerial input into the production process in a manner consistent with traditional returns to scale concepts.