A Model of Quality Uncertainty with a Continuum of Quality Levels

Christopher Gertz (Center for Mathematical Economics, Bielefeld University) offers A Model of Quality Uncertainty with a Continuum of Quality Levels.

ABSTRACT: This work takes a closer look on the predominant assumption in usual lemon market models of having finitely many or even only two different levels of quality. We model a situation which is close to the classical monopolistic setting but admits an interval of possible quality values. Additionally, to make the model interesting, the consumer receives a signal which is correlated to the quality level and is her private information. We introduce a new concept for the consumer reaction to the received information, encompassing rationality but also allowing for a certain degree of imperfection. We find that there is always a strictly positive price-quality relation in equilibrium but the classical adverse selection effects are not observed. In contrast, low quality levels do not make any sales. After applying a refinement to these equilibria, we show that when the additional signal is very precise, more low quality levels are ! excluded from the market. In the limit of perfect information, the market breaks down, a behavior completely opposed to the original perfect information case. These different and quite extreme results compared to the classical lemon market case should serve as a warning to have a closer look at the assumption of having finitely many quality levels.