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

Journal of Optimization Theory and Applications, Vol. 23, pp. 245-275, October 1977

31 Pages Posted: 11 Mar 2008 Last revised: 29 Apr 2014

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Timothy W. Mcguire

Management Science Associates, Inc.

Date Written: November 1, 1971

Abstract

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.

Keywords: Human capital, optimal control, retarded control problems, labor training, economics, maximum principle

JEL Classification: C61, J24, I28

Suggested Citation

Sethi, Suresh and Mcguire, Timothy W., Optimal Skill Mix: An Application of the Maximum Principle for Systems with Retarded Controls (November 1, 1971). Journal of Optimization Theory and Applications, Vol. 23, pp. 245-275, October 1977, Available at SSRN: https://ssrn.com/abstract=1101098

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Timothy W. Mcguire

Management Science Associates, Inc. ( email )

6565 Penn Avenue
Pittsburgh, PA 15206
United States

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