On the Function Coefficient, Euler's Theorem, and Homogeneity in Production Theory

This paper makes three related points useful in teaching first-year graduate production theory. First, the local applicability of the classical function coefficient idea for short-run nonhomogeneous production technologies is shown for returns to scale, satisfaction of second-order and total conditions for profit maximization, and delineation of the economic region of production in factor space. Second, the general applicability of Euler's Theorem results to nonhomogeneous (variable-proportional-return) cases is developed. Lastly, it is shown that short-run, nonhomogeneous production/yield functions are fully consistent with long-run linear homogeneity.