# A Stochastic Theory of the Generalized Cobb-Douglas Production Function

Conference paper

## Abstract

Factor substitution relations and returns to scale found in empirical studies of production functions are modeled in a way that is fully integrated with technological change and process innovation. The model is based on the Pareto boundary of random *n*-tuples, which is a rectangular hyperbola, asymptotic to the axes, whose parameter depends on the amount of sampling (search) activity. Conversion from probability fractiles to natural units of measurement of the factors give the Cobb-Douglas factor substitution relations. The influence of inputs on outputs is somewhat different because an upper bound on output cannot be assumed.

## Keywords

Production Function Natural Unit Rectangular Hyperbola Contract Production Progress Function
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© Springer-Verlag New York, Inc. 1989