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

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.