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A New Theoretical Model for Depicting Profit Optimality

Published online by Cambridge University Press:  19 October 2009

A. Edward Spitz  and
André DeKorvin
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Extract

Each business firm has a large body of fundamental data that can be organized so that it can aid in graphically determining the firm's optimum profit. In this paper an attempt has been made to bring forth a method by which some choice of policy may be followed in order to select a particular profit curve. More precisely, a policy will be determined that leads to a given optimal profit curve. In this paper “optimal profit curve” will mean the profit curve that has been selected from a fixed set of possible profit curves. The purpose of the paper is to describe a method to determine the policy that will reduce the optimal curve. The method is based on a general form of the Riesz- Kakutani Representation Theorem, which states that a bounded linear operator from the space of continuous functions of one variable t where 0 ≤ t ≤ 1 to the space of continuous functions can be represented as an integral to a Gowurin measure.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 6 , Issue 4 , September 1971 , pp. 1117 - 1121
Copyright
Copyright © School of Business Administration, University of Washington 1971

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References

1 Several examples are as follows: Horowitz, Bertrand N., “Profit Responsibility in Soviet Enterprise,” The Journal of Business, XLI, No. 1, (January 1968), pp. 47–55Google Scholar; Starbuck, W. H. and Bass, F. M., “An Experimental Study of Risk-Taking and the Value of Information in a New Product Context,” The Journal of Business, XL, No. 2, (April 1967), pp. 155–165Google Scholar; Winters, Peter J., “Forecasting Sales by Exponentially Weighted Moving Averages,” Management Science, VI, No. 3, (April 1960), pp. 324–342Google Scholar; Kamerschen, David R., “The Determination of Profit Rates in Oligopolistic Industries,” The Journal of Business, XXXXII, No. 3, (July 1969), pp. 293–301Google Scholar; Smyth, D. J., Briscoe, G., and Samuels, J. M., “The Variability of Industry Profit Rates,” Applied Economics, I, No. 2, (May 1969), pp. 137–149.Google Scholar

2 For more information on bounded linear operators see Dunford, N. and Schwartz, J. T., Linear Operators, Vol. 1 (New York: Interscience Publishers, Inc., 1958).Google Scholar

3 Gowurin, M., “Uber die Stieltjesche Integration Abstrakter Funktionen,” Fund Math, XXVII, (1936), pp. 254–268.CrossRefGoogle Scholar

4 Tucker, D. H., “A Note on the Riesz Representative Theorem,” Proa. Amer. Math. Soc., XIV, (1963), pp. 354–358Google Scholar. For a more general statement see, Ukerka, D. J., “Generalized Stieltjes Integrals and a Strong Representation Theorem for Continuous Linear Maps on a Function Space,” Math. Annalen, CLXXXII, (August 1969), pp. 60–67.Google Scholar