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Production optimization for a monopolist who does not set prices

Published online by Cambridge University Press:  17 April 2009

L.J. Armour ,
D.J. Gates  and
J.A. Rickard
L.J. Armour
Affiliation:
Department of Mathematics, Footscray Institute of Technology, Footscray, Victoria;
D.J. Gates
Affiliation:
Commonwealth Scientific and Industrial Research Organization, Division of Mathematics and Statistics, Canberra, ACT;
J.A. Rickard
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
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Abstract

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Consider a monopolistic firm selling each business period's production at the end of that period at a price determined by the buyers, and wishing to determine the production for which business period profit is maximal. In this paper we announce the results of our investigations into what happens when the firm employs a certain algorithm (based on linear approximations to its average contribution profit function) in an attempt to determine this optimal production. Our results are as follows: firstly, for many apparently feasible average contribution profit functions the algorithm generates production sequences globally convergent to the optimal production, the convergence being linear with convergence ratio dependent on the average contribution profit function; secondly, in certain cases a lower bound for the initial rate of convergence of the algorithm can be obtained. Proofs are for the most part given only in outline, and will be published in full later.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 3 , December 1977 , pp. 351 - 361
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Armour, L.J., Gates, D.J. and Rickard, J.A., “A convergent optimization algorithm with application to the monopolistic firm”, submitted.Google Scholar
[2]Gates, D.J. and Rickard, J.A., “Pareto optimum by independent trials”, Bull. Austral. Math. Soc. 12 (1975), 259–265.CrossRefGoogle Scholar
[3]Gates, D.J., Rickard, J.A., and Wilson, D.J., “A convergent adjustment process for firms in competition”, Econometrica (to appear).Google Scholar
[4]Luenberger, David G., Introduction to linear and nonlinear programming (Addison-Wesley, Reading, Massachusetts; Menlo Park, California; London; Don Mills, Ontario; 1973).Google Scholar