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Duality Theory for Variable Costs in Joint Production

Author

Listed:
  • Jeffrey LaFrance
  • Rulon Pope

    (School of Economic Sciences, Washington State University)

Abstract

Duality methods for incomplete systems of consumer demand equations are adapted to the dual structure of variable cost functions in joint production. This allows the identification of necessary and sufficient restrictions on technology and cost so that the conditional factor demands can be written as functions of input prices, fixed inputs, and cost. These are observable when the variable inputs are chosen and committed to production, hence the identified restrictions allow ex ante conditional demands to be studied using observable data. This class of production technologies is consistent with all von Neumann-Morgenstern utility functions when ex post production is uncertain.

Suggested Citation

  • Jeffrey LaFrance & Rulon Pope, 2008. "Duality Theory for Variable Costs in Joint Production," Working Papers 2009-02, School of Economic Sciences, Washington State University.
    • Handle: RePEc:wsu:wpaper:lafrance-4
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    File URL: http://faculty.ses.wsu.edu/WorkingPapers/LaFrance/WP2009-02-LP_DTiJP.pdf
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    References listed on IDEAS

    as
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    2. Jay T. Akridge & Thomas W. Hertel, 1986. "Multiproduct Cost Relationships for Retail Fertilizer Plants," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 68(4), pages 928-938.
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    5. Larry G. Epstein, 1982. "Integrability of Incomplete Systems of Demand Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(3), pages 411-425.
    6. Jeffrey T. LaFrance, 1990. "Incomplete Demand Systems And Semilogarithmic Demand Models," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 34(2), pages 118-131, August.
    7. Lau, Lawrence J, 1972. "Profit Functions of Technologies with Multiple Inputs and Outputs," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 281-289, August.
    8. LaFrance, Jeffrey T., 2004. "Integrability of the linear approximate almost ideal demand system," Economics Letters, Elsevier, vol. 84(3), pages 297-303, September.
    9. Jeffrey T. LaFrance & W. Michael Hanemann, 1989. "The Dual Structure of Incomplete Demand Systems," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 71(2), pages 262-274.
    10. Chambers,Robert G. & Quiggin,John, 2000. "Uncertainty, Production, Choice, and Agency," Cambridge Books, Cambridge University Press, number 9780521785235, January.
    11. Blackorby, Charles & Primont, Daniel & Robert Russell, R., 1977. "Dual price and quantity aggregation," Journal of Economic Theory, Elsevier, vol. 14(1), pages 130-148, February.
    12. Lopez, Ramon E, 1985. "Structural Implications of a Class of Flexible Functional Forms for Profit Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 593-601, October.
    13. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    14. Pope, Rulon D. & Just, Richard E., 1996. "Empirical implementation of ex ante cost functions," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 231-249.
    15. Hall, Robert E, 1973. "The Specification of Technology with Several Kinds of Output," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 878-892, July-Aug..
    16. LaFrance, Jeffrey T., 1985. "Linear demand functions in theory and practice," Journal of Economic Theory, Elsevier, vol. 37(1), pages 147-166, October.
    17. C. Richard Shumway, 1983. "Supply, Demand, and Technology in a Multiproduct Industry: Texas Field Crops," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 65(4), pages 748-760.
    18. Hausman, Jerry A, 1981. "Exact Consumer's Surplus and Deadweight Loss," American Economic Review, American Economic Association, vol. 71(4), pages 662-676, September.
    19. Rulon D. Pope & Jean-Paul Chavas, 1994. "Cost Functions Under Production Uncertainty," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 76(2), pages 196-204.
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    Cited by:

    1. Santeramo, Fabio Gaetano, 2014. "On the Estimation of Supply and Demand Elasticities of Agricultural Commodites," MPRA Paper 56126, University Library of Munich, Germany.
    2. Jeffrey LaFrance & Rulon Pope & Jesse Tack, 2011. "Risk Response in Agriculture," NBER Chapters, in: The Intended and Unintended Effects of US Agricultural and Biotechnology Policies, pages 143-186, National Bureau of Economic Research, Inc.
    3. Thomas, N., 2021. "Alternative Crop Management Methods to Increase Crop Productivity and Farmer Utility," 2021 Conference, August 17-31, 2021, Virtual 315042, International Association of Agricultural Economists.
    4. Adélaïde Fadhuile & Stéphane Lemarié & Alain Pirotte, 2016. "Disaggregating the Demand for Pesticides: Does it Matter?," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 64(2), pages 223-252, June.
    5. Jesse Tack & Rulon Pope & Jeffrey LaFrance & Timothy Graciano & Scott Colby, 2012. "Intertemporal Risk Management in Agriculture," Monash Economics Working Papers 16-12, Monash University, Department of Economics.
    6. Jesse Tack & Rulon Pope & Jeffrey LaFrance & Ricardo Cavazos, 2012. "Flexible Specification and Robust Estimation of Input Demand Systems," Monash Economics Working Papers 48-12, Monash University, Department of Economics.
    7. Jesse B. Tack & Rulon D. Pope & Jeffrey T. LaFrance & Ricardo H. Cavazos, 2015. "Modelling an aggregate agricultural panel with application to US farm input demands," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 42(3), pages 371-396.
    8. Raushan Bokusheva & Lajos Baráth, 2024. "State‐contingent production technology formulation: Identifying states of nature using reduced‐form econometric models of crop yield," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(2), pages 805-827, March.
    9. Eldon V. Ball & Ricardo Cavazos & Jeffrey T. LaFrance & Rulon Pope & Jesse Tack, 2010. "Aggregation and Arbitrage in Joint Production," Monash Economics Working Papers archive-22, Monash University, Department of Economics.

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    More about this item

    Keywords

    Joint production; variable cost; duality theory;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • D2 - Microeconomics - - Production and Organizations
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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