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Optimal skill mix: An application of the maximum principle for systems with retarded controls

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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.

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Authors and Affiliations

  1. Faculty of Management Studies, University of Toronto, Toronto, Ontario, Canada

    S. P. Sethi (Associate Professor of Management Science)

  2. Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania

    T. W. McGuire (Professor of Economics and Statistics)

Authors
  1. S. P. Sethi
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  2. T. W. McGuire
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Additional information

communicated by J. V. Breakwell

Earlier versions of this paper were delivered at the IFAC/IFORS International Conference on Dynamic Modelling of National Economies held in Coventry, England. A Guest Lecture was delivered by the first author to the 14th Biennial Seminar of the Canadian Mathematical Congress on Optimal Control Theory and its Applications held in London, Ontario, 1973. The authors acknowledge with appreciation support from a National Science Foundation Grant in Economics to Carnegie-Mellon University; in addition, the second author was supported by a Ford Foundation Faculty Research Fellowship during the academic year 1970–71. The authors are indebted to D. Cass, R. E. Lucas, and G. L. Thompson for valuable comments on an earlier draft, although all remaining errors of commission and omission are ours.

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Sethi, S.P., McGuire, T.W. Optimal skill mix: An application of the maximum principle for systems with retarded controls. J Optim Theory Appl 23, 245–275 (1977). https://doi.org/10.1007/BF00933051

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