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Conditional Factor Demands and Positive Output Effects: A Necessary and Sufficient Condition

Author

Listed:
  • Pierre Ouellette
  • Stephane Vigeant

    (LEM - Lille économie management - UMR 9221 - UA - Université d'Artois - UCL - Université catholique de Lille - Université de Lille - CNRS - Centre National de la Recherche Scientifique)

Abstract

The duality between cost and production functions has been thoroughly studied and is well-known. A given set of assumptions on the technology implies a set of restrictions on the Jacobian of the cost function and on a subset of its Hessian matrix. The vector of second derivatives of the cost function with respect to the input prices and the output has not been fully characterized, however. In this note, we present a necessary and sufficient condition to ensure that the components of this vector are all strictly positive. That is, we specify the condition for all conditional demand functions to be simultaneously increasing in output. This condition is interpreted as a strengthening of the quasiconcavity of the production function.

Suggested Citation

  • Pierre Ouellette & Stephane Vigeant, 2017. "Conditional Factor Demands and Positive Output Effects: A Necessary and Sufficient Condition," Post-Print hal-02988112, HAL.
    • Handle: RePEc:hal:journl:hal-02988112
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    References listed on IDEAS

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    1. Alarie, Yves & Bronsard, Camille & Ouellette, Pierre, 1990. "Preferences and normal goods: A necessary and sufficient condition," Journal of Economic Theory, Elsevier, vol. 51(2), pages 423-430, August.
    2. Leroux, Alain, 1987. "Preferences and normal goods: A sufficient condition," Journal of Economic Theory, Elsevier, vol. 43(1), pages 192-199, October.
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    JEL classification:

    • D2 - Microeconomics - - Production and Organizations

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