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


  • Axel Pierru


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 short-run 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). JEL Classification: D20, C61

Suggested Citation

  • Axel Pierru, 2007. "Short-run and long-run marginal costs of joint products in linear programming," Recherches économiques de Louvain, De Boeck Université, vol. 73(2), pages 153-171.
  • Handle: RePEc:cai:reldbu:rel_732_0153

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    References listed on IDEAS

    1. Mongin, P., 1998. "Does Optimization Imply Rationality?," Papers 9817, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    2. Philippe Mongin, 2003. "L'axiomatisation et les théories économiques," Revue économique, Presses de Sciences-Po, vol. 54(1), pages 99-138.
    3. Machlup, Fritz, 1978. "Methodology of Economics and Other Social Sciences," Elsevier Monographs, Elsevier, edition 1, number 9780124645509 edited by Shell, Karl.
    4. Debreu, Gerard, 1993. "Existence of competitive equilibrium," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 15, pages 697-743 Elsevier.
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    Cited by:

    1. Pierru, Axel, 2010. "Allocating the CO2 emissions of an oil refinery with Aumann-Shapley prices: A reply," Energy Economics, Elsevier, vol. 32(3), pages 746-748, May.
    2. Tehrani Nejad Moghaddam, Alireza, 2010. "Allocating the CO2 emissions of an oil refinery with Aumann-Shapley prices: Comment," Energy Economics, Elsevier, vol. 32(1), pages 243-255, January.
    3. Massol, O., 2011. "A cost function for the natural gas transmission industry: further considerations," Working Papers 11/03, Department of Economics, City University London.

    More about this item


    microeconomics; marginal cost; linear programming;

    JEL classification:

    • D20 - Microeconomics - - Production and Organizations - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis


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