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Optimal and Market Control in a Dynamic Economic System with Endogenous Heterogeneous Labor

In most control theoretic analyses of optimum economic growth the fraction of output allocated to investment is the control. The few models treating labor training assume innately identical individuals and a fixed amount of training for employability. We extend these models by assuming a CES production function of both skilled and unskilled labor (abstracting from capital) and a continuous distribution of innate ability. This results in a continuous lag optimal control problem for which the theory is still incomplete with regard to existence. [Analysis assuming existence is carried out in a separate paper.] In this paper we develop a discrete model with a finite number of training classes as state variables. The control solution is obtained by the Discrete Maximum Principle and is generally different from the market solution, assuming static expectations about future relative wages, except when the production function is linear. There exists, in general, a unique stationary optimal control not greater than the Golden Rule but equivalent to the market stationary control under certain circumstances. There also exists a stably controllable tax-subsidy system that induces dynamically optimal market behavior. PDF version: McGuire, T. W. and S. P. Sethi, "Optimal Economic Dynamics with Heterogeneous Labor by the Discrete Maximum Principle," Management Sciences Research Report #260, Carnegie-Mellon University, November 1971.