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


  • Pawel Dziewulski

    (University of Sussex)

  • John K.-H. Quah

    (John Hopkins Univeristy)


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

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    References listed on IDEAS

    1. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    2. Garud N. Iyengar, 2005. "Robust Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 257-280, May.
    3. 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.
    4. Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    5. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    6. 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.
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    Cited by:

    1. 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


    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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