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.