Competitive Markets with Imperfectly Discerning Consumers

We develop a market model in which products generate state-dependent potential hidden charges. Firms differ in their ability to realize this potential. Unlike firms, consumers do not observe the state. They try to infer hidden charges from market prices, using idiosyncratic subjective models. We show that an interior competitive equilibrium is uniquely given by what is formally a Bellman equation. We leverage this representation to characterize equilibrium headline prices, add-on charges and welfare. Market responses to shocks display patterns that are impossible under rational expectations. For example, equilibrium prices can be fully revealing and yet vary with consumers' private information.