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Estimating the buyer's willingness to pay using Bayesian belief distribution with IFR

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  • Brusset, Xavier
  • Cattan-Jallet, Roxane

Abstract

In supply chain management, information about the downstream party's willingness to pay (wtp) for a service or a good sold by an upstream party may not be known to the latter. The seller has to make an educated guess for the price at which to offer a good or service. If the buyer refuses to buy, the seller can still turn to a third party and sell at a lower price or hold onto the good. We show that the seller has one interior profit maximizing price if his Bayesian belief about the buyer's wtp follows a distribution which has an increasing failure rate (IFR) in the sense of \cite{bar3}. We prove that the precision of information available to the supplier influences the rent distribution and how the downstream party might opportunistically mis-inform the upstream partner. We propose another reading of the single-price newsvendor problem in Lariviere and Porteus (2001), Ziya et al. (2004a,b), Paul (2006) or Lariviere (2006). Our approach applies to all types of mechanism design problems where a profit-maximizing party has to rely on Bayesian belief to palliate information asymmetry and has alternative sources of income or cost.

Suggested Citation

  • Brusset, Xavier & Cattan-Jallet, Roxane, 2009. "Estimating the buyer's willingness to pay using Bayesian belief distribution with IFR," MPRA Paper 22638, University Library of Munich, Germany, revised 10 May 2010.
  • Handle: RePEc:pra:mprapa:22638
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    References listed on IDEAS

    as
    1. Anand Paul, 2005. "A Note on Closure Properties of Failure Rate Distributions," Operations Research, INFORMS, vol. 53(4), pages 733-734, August.
    2. Martin A. Lariviere & Evan L. Porteus, 2001. "Selling to the Newsvendor: An Analysis of Price-Only Contracts," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 293-305, May.
    3. Oliver D. Hart & Jean Tirole, 1988. "Contract Renegotiation and Coasian Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(4), pages 509-540.
    4. Martin A. Lariviere, 2006. "A Note on Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 54(3), pages 602-604, June.
    5. Serhan Ziya & Hayriye Ayhan & Robert D. Foley, 2004. "Relationships Among Three Assumptions in Revenue Management," Operations Research, INFORMS, vol. 52(5), pages 804-809, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    supply chain optimization; Bayesian belief; mechanism design; increasing failure rate;
    All these keywords.

    JEL classification:

    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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