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Extending The Scope Of Monotone Comparative Statics Results

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  • Anne-Christine Barthel

    (Department of Economics, The University of Kansas)

Abstract

Generally we can distinguish between two types of comparative statics problems that have been approached with lattice programming methods. The first type of problem considers the change of the optimal solution to a maximization problem as the objective function changes, the other type the change due to a change in the constraint set. Comparative statics theorems have been developed for both cases under cardinal and ordinal assumptions in the literature; Quah (2007) expanded existing work by making it applicable to optimization problems with a new, weaker order on the constraint sets. The idea of this paper is to extend the existing comparative statics results to an even broader class of constrained optimization problems. We combine the two previously mentioned types of maximization problems and apply the existing comparative statics theorems to cases with changes in both the objective function and non-lattice constraint sets. Examples and applications from a variety of areas in economics, such as consumer theory, producer theory and environmental economics, are provided as well.

Suggested Citation

  • Anne-Christine Barthel, 2013. "Extending The Scope Of Monotone Comparative Statics Results," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201305, University of Kansas, Department of Economics, revised May 2013.
    • Handle: RePEc:kan:wpaper:201305
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    References listed on IDEAS

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    1. Harbaugh, William T, 1998. "The Prestige Motive for Making Charitable Transfers," American Economic Review, American Economic Association, vol. 88(2), pages 277-282, May.
    2. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    3. William J. Baumol & Wallace E. Oates, 1971. "The Use of Standards and Prices for Protection of the Environment," Palgrave Macmillan Books, in: Peter Bohm & Allen V. Kneese (ed.), The Economics of Environment, pages 53-65, Palgrave Macmillan.
    4. Zhang, Zibin & Qiu, Cheng & Wetzstein, Michael, 2010. "Blend-wall economics: Relaxing US ethanol regulations can lead to increased use of fossil fuels," Energy Policy, Elsevier, vol. 38(7), pages 3426-3430, July.
    5. Bruneau, Joel F., 2004. "A note on permits, standards, and technological innovation," Journal of Environmental Economics and Management, Elsevier, vol. 48(3), pages 1192-1199, November.
    6. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    8. Milgrom, Paul & Roberts, John, 1996. "The LeChatelier Principle," American Economic Review, American Economic Association, vol. 86(1), pages 173-179, March.
    9. William S. Reece & Russell S. Sobel, 2000. "Diagrammatic Approach to Capacity-Constrained Price Discrimination," Southern Economic Journal, John Wiley & Sons, vol. 66(4), pages 1001-1008, April.
    10. Peter P. Belobaba, 1989. "OR Practice—Application of a Probabilistic Decision Model to Airline Seat Inventory Control," Operations Research, INFORMS, vol. 37(2), pages 183-197, April.
    11. Don Patinkin, 1947. "Multiple-Plant Firms, Cartels, and Imperfect Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 61(2), pages 173-205.
    12. Nicholas Z. Muller & Robert Mendelsohn, 2009. "Efficient Pollution Regulation: Getting the Prices Right," American Economic Review, American Economic Association, vol. 99(5), pages 1714-1739, December.
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    More about this item

    Keywords

    Lattices; comparative statics; supermodularity; Single Crossing Property; consumer problem; LeChatelier principle;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • Q58 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environmental Economics: Government Policy

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