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

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  • Axel Pierru

Abstract

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

    as
    1. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    2. Christophe Barret & Philippe Chollet, 1990. "Canadian Gas Exports : Modeling a Market in Disequilibrium," Working Papers hal-02432570, HAL.
    3. Harvey J. Greenberg, 1986. "An analysis of degeneracy," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(4), pages 635-655, November.
    4. 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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    Citations

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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. repec:cty:dpaper:10.1080/0013791x.2011.573615 is not listed on IDEAS
    3. Olivier Massol, 2011. "A Cost Function for the Natural Gas Transmission Industry: Further Considerations," The Engineering Economist, Taylor & Francis Journals, vol. 56(2), pages 95-122.
    4. 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.
    5. Massol, O., 2011. "A cost function for the natural gas transmission industry: further considerations," Working Papers 1464, Department of Economics, City University London.

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    More about this item

    Keywords

    microeconomics; marginal cost; linear programming;
    All these keywords.

    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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