We have considered a duopoly with perceived vertical differentiation, information disparity and optimistic consumers. When firms compete for informed and uninformed consumers, the former contribute to raise product quality, while equilibrium prices increase with optimistic misperception of the latter, in our first equilibrium. Brand premium includes a quality premium and a misperception rent. In our second equilibrium, informed consumers buy low-quality goods and minimum product differentiation without Bertrand competition occurs. The brand premium is just a misperception rent, however, an increase of the informed consumers share implies price re-balancing and rent reduction. Consumers externalities arise in both equilibria. Firms compete only for informed consumers within our third and fourth equilibrium, as uninformed ones are passive and represent a captive market. Uninformed consumers in one case are overoptimistic, they buy the high quality good and can be cheated in equilibrium. Uninformed consumers approach the real quality differential in the fourth equilibrium, and the model reduces to standard vertical differentiation with perfect information.
