Optimal Skill Mix : An Application of the Maximum Principle for Systems with Retarded Controls

In this paper, we analyze the optimal skill mix in a model with two kinds of imperfectly substitutable labor, skilled and unskilled. The population is characterized by a distribution of innate abilities, and individuals are trained according to optimal rules or market rules (with imperfect expectations); the length of each individual's training period depends upon his innate ability. The market and optimal rules are characterized and compared, and corrective policies are investigated. This model represents a major advance over earlier models, which are based on the following assumptions: (a) either unskilled and skilled labor are perfectly substitutable or training is a necessary condition for employment; (b) individuals are innately identical; (c) in most cases, training occurs either instantaneously or with fixed lag. PDF Version: Sethi, S. P. and T. W. McGuire, "Optimal Skill-Mix: An Application of the Maximum Principle for Systems with Continuous Lags," W. P. # 46-71-2, GSIA, Carnegie-Mellon University, November 1971