Inference from Outcomes in the Market for Lemons
Nenad Kos
(University Bocconi)
“Inference from Outcomes in the Market for Lemons”
Abstract: This paper studies inference from equilibrium outcomes in a market for lemons. The model is a posted-price adverse-selection environment: a monopsonist offers a price to a continuum of sellers, each of whom privately observes the quality of her good, which affects the buyer’s value, and decides whether to trade. We ask what an analyst who knows players’ preferences can infer about the latent quality distribution, surplus, and welfare from observing an equilibrium price and, possibly, the quantity traded. The key observation is that the price is a revealed choice: if the buyer optimally posted the observed price, then every alternative price must have yielded weakly lower payoff, generating equilibrium inequalities that restrict the unobserved distribution. We characterize the boundaries of the set of distributions consistent with a price–quantity pair, or with a price alone, through extremal distributions obtained from binding optimality constraints. These bounds imply sharp ranges for producer surplus, consumer surplus, total welfare, and deadweight loss. The analysis shows that sparse market data can have nontrivial welfare content once the equilibrium logic of the lemons model is imposed. In the private-values benchmark, the problem reduces to standard monopoly pricing and admits a simple stochastic-dominance characterization.