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A generalization of monotone comparative statics

Author

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  • Koji Shirai

    (Waseda University, Graduate School of Economics)

Abstract

In this paper, we generalize the lattice theoretical comparative statics by Li Calzi and Veinott, and Milgrom and Shannon. While their theorem is constructed on lattices, particularly on partially ordered sets, we do not require the antisymmetry on a binary relation defined on the set. On the basis of this result, we can deal with the comparative statics of constrained optimization problems, including the cases with nonlinear constraints, in a very intuitive, but considerably general fashion. Specifically, we can extend the "value order methods" proposed by Antoniadou and Mirman and Ruble in the context of consumer problems with linear constraints. It is also worth noting that our results on the value order can be applicable for any comparative criterion as long as it is a complete preorder on the domain of the objective function.

Suggested Citation

  • Koji Shirai, 2008. "A generalization of monotone comparative statics," Economics Bulletin, AccessEcon, vol. 3(39), pages 1-9.
    • Handle: RePEc:ebl:ecbull:eb-08c00009
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    References listed on IDEAS

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    1. Leonard J. Mirman & Richard Ruble, 2008. "Lattice Theory and the Consumer's Problem," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 301-314, May.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    4. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    5. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    6. Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods 0509001, University Library of Munich, Germany.
    7. Elena Antoniadou, 2007. "Comparative Statics for the Consumer Problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 189-203, April.
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    Cited by:

    1. Koji Shirai, 2009. "A generalization of monotone comparative statics: Correction," Economics Bulletin, AccessEcon, vol. 29(1), pages 116-121.

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    More about this item

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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