A Model of Quality Uncertainty with a Continuum of Quality Levels

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.