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


  • Axel PIERRU

    (Center for economics and management, IFP School)


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, tins 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).

Suggested Citation

  • Axel PIERRU, 2007. "Short-run and long-run marginal costs of joint products in linear programming," Discussion Papers (REL - Recherches Economiques de Louvain) 2007022, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  • Handle: RePEc:ctl:louvre:2007022

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    References listed on IDEAS

    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Dennis Anderson, 1972. "Models for Determining Least-Cost Investments in Electricity Supply," Bell Journal of Economics, The RAND Corporation, vol. 3(1), pages 267-299, Spring.
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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. Massol, O., 2011. "A cost function for the natural gas transmission industry: further considerations," Working Papers 11/03, Department of Economics, City University London.
    3. 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.

    More about this item


    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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