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Comparative statics with linear objectives: normal demand, monotone marginal costs, and ranking multi-prior beliefs

Author

Listed:
  • Pawel Dziewulski

    (University of Sussex)

  • John K.-H. Quah

    (John Hopkins Univeristy)

Abstract

We formulate a set order on constraint sets C ? Rl which guarantee that argmin {?(x) : x ?C} increases in the product order as C increases in the set order, for all linear functions ?: Rl ?R. Using this result, we characterize the utility/production functions that lead to normal demand; we also show that this very same class of production functions have marginal costs that increase with factor prices. In the context of decision-making under uncertainty, our new set order leads to natural generalizations of first order stochastic dominance in multi-prior models.

Suggested Citation

  • Pawel Dziewulski & John K.-H. Quah, 2021. "Comparative statics with linear objectives: normal demand, monotone marginal costs, and ranking multi-prior beliefs," Working Paper Series 0121, Department of Economics, University of Sussex Business School.
    • Handle: RePEc:sus:susewp:0121
    as

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    File URL: https://www.sussex.ac.uk/business-school/documents/wps-01-2021.pdf
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    References listed on IDEAS

    as
    1. Mark Huggett, 2003. "When Are Comparative Dynamics Monotone?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(1), pages 1-11, January.
    2. , & ,, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    3. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    4. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    5. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    6. Garud N. Iyengar, 2005. "Robust Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 257-280, May.
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    Cited by:

    1. Takashi Ui, 2023. "Strategic Ambiguity in Global Games," Papers 2303.12263, arXiv.org, revised Nov 2024.
    2. Takashi Ui, 2021. "Strategic Ambiguity in Global Games," Working Papers on Central Bank Communication 032, University of Tokyo, Graduate School of Economics.

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    More about this item

    Keywords

    parallelogram property; increasing differences; ambiguity; first order stochastic dominance; normal demand; marginal costs;
    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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