Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-20T13:19:05.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Short-run and long-run marginal costs of joint products in linear programming

Published online by Cambridge University Press:  17 August 2016

Axel Pierru
Axel Pierru*
Affiliation:
Center for economics and management, IFP School, IFP, 228-232 Avenue Napoléon Bonaparte, 92852 Rueil-Malmaison, France
Get access

Summary

In standard microeconomic theory, short-run and long-run marginal costs are equal for production equipment with adjusted capacity. When the production of joint products from interdependent equipment is modeled with a linear program, this equality is no longer verified. The short-run marginal cost then takes on a left-hand value and a right-hand value which generally differ from the long-run marginal cost. In this article, we demonstrate and interpret the relationship existing between long-run marginal cost and shortrun marginal costs for a given finished product. That relationship is simply expressed as a function of marginal capacity adjustments (determined in the long run) and marginal values of capacities (determined in the short run).

Résumé

Résumé

Dans la théorie microéconomique classique, coût marginal de court terme et coût marginal de long terme sont égaux pour un équipement à capacité adaptée. Lorsque l'on modélise par programmation linéaire la fabrication de produits liés à partir d'équipements interdépendants, cette égalité n'est plus vérifiée. Le coût marginal de court terme prend alors deux valeurs (à gauche et à droite) généralement différentes du coût marginal de long terme. Dans cet article, nous démontrons et interprétons la relation existant alors entre coût marginal de long terme et coûts marginaux de court terme d'un produit donné. Celle-ci s'exprime simplement en fonction des ajustements optimaux des capacités (déterminés à long terme) et des valorisations marginales des capacités (déterminées à court terme).

Keywords

Microeconomicsmarginal costlinear programmingD20C61microéconomiecoût marginalprogrammation linéaireD20C61
Type
Research Article
Information
Recherches Économiques de Louvain/ Louvain Economic Review , Volume 73 , Issue 2 , 2007 , pp. 153 - 171
Copyright
Copyright © Université catholique de Louvain, Institut de recherches économiques et sociales 2007 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The author is grateful to an anonymous referee and to Denis Babusiaux for helpful comments.

References

Anderson, D., (1972), Models for determining least-cost investments in electricity supply, Bell Journal of Economics and Management Science, 6, pp. 267–299.Google Scholar
Aucamp, D.C. and Steinberg, D. I. (1982), The computation of shadow prices in linear programming, Journal of the Operational Research Society, 33, pp. 557–565.Google Scholar
Boiteux, M., (1960), Peak-load pricing, The Journal of Business, 33, pp. 157–179.Google Scholar
Gal, T., (1986), Shadow prices and sensitivity analysis in linear programming under degeneracy, OR Spektrum, 8, pp. 59–71.Google Scholar
Greenberg, H. J., (1986), An analysis of degeneracy, Naval Research Logistics Quarterly, 33, pp. 635–655.Google Scholar
Milgrom, P. and Segal, I. (2002), Envelope theorems for arbitrary choice sets, Econometrica, 70, pp. 583–601.Google Scholar
Palmer, K.H., Boudwin, N.K. Patton, H.A. Rowland, A.J. Sammes, J.D. and Smith, D.M. (1984), A model-management framework for mathematical programming - An Exxon Monograph, New York, John Wiley & Sons.Google Scholar
Pierru, A. and Babusiaux, D. (2004), Breaking down a long-run marginal cost of an LP investment model into a marginal operating cost and a marginal equivalent investment cost, The Engineering Economist, 49, pp. 307–326.Google Scholar