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Supermodular Correspondences

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  • John Quah

Abstract

Supermodular functions are widely used in economics to model complementarity. For example, a firm's production function is supermodular if the marginal productivity of each factor increases with the usage of other factors. This in turn guarantees that when the price of a factor falls, the firm's demand for all factors increase. We generalise the notion of supermodular functions so the concept is also applicable to correspondences. Supermodular correspondences arise naturally in a variety of settings. To illustrate the use of the concept and our results, we apply them to study, amongst other things, the optimising behaviour of firms producing multiple output goods and of agents with ambiguity aversion.

Suggested Citation

  • John Quah, 2016. "Supermodular Correspondences," Economics Series Working Papers 795, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:795
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    References listed on IDEAS

    as
    1. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    2. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2014. "A constructive study of Markov equilibria in stochastic games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 815-840.
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    5. Rabah Amir, 2002. "Complementarity and Diagonal Dominance in Discounted Stochastic Games," Annals of Operations Research, Springer, vol. 114(1), pages 39-56, August.
    6. Milgrom, Paul & Roberts, John, 1990. "The Economics of Modern Manufacturing: Technology, Strategy, and Organization," American Economic Review, American Economic Association, vol. 80(3), pages 511-528, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    supermodular correspondence; monotone comparative statics; multi- output production; ambiguity aversion;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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