Price bubbles in markets with inattentive consumers and imperfectly informed firms

We study a model of price competition in a homogeneous good market where consumers may be fully rational or inattentive to small price differences. At the beginning, firms are pricing at marginal cost, and receive a stochastic signal concerning consumers' rationality. They then compete for two periods, observing the market outcome at the end of the first. We characterize an equilibrium in which, when consumers are effectively inattentive (and at least one firm receives the correct signal), the market price jumps to the monopoly level by the second period. This is achieved after a first period in which the informed firms (those that received the correct signal) raise their prices just a little: through this mild price increase, these firms forward their signal to the uninformed firms, and they do so in a credible way, as this makes the actual consumers' status common knowledge. Our model adds insights on the dynamics through which firms may be able to exploit consumers' inattention to prices.