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Price Recall, Bertrand Paradox and Price Dispersion with Elastic Demand

This paper studies the consequence of an imprecise recall of the price by the consumers in the Bertrand price competition model for a homogeneous good. It is shown that firms can exploit this weakness and charge prices above the competitive price. This markup increases for rougher recall of the price. If firms have different production costs, those with higher costs are not driven out of the market. However they choose to have a higher price in equilibrium, therefore price dispersion arises. It is shown that firms behave on average as a monopolist with stricter demand and that price dispersion increases with the price recall errors. If bigger recall errors happen, then both consumers and firms on the aggregate level are worse off, for some parameter choices. Furthermore being given the irrational choice that some consumers make, there are situations where the protection of a monopolist against entrants is a welfare maximizing policy. The introduction of more firms in the market does not have a significant impact on the prices. Even though the presented model is static, it can be interpreted as a stage game of an infinitely repeated game where a Nash Equilibrium is played in every stage. The intuition is that consumers do not actually seek information before every purchase, but have a vague idea of the price they faced in previous purchases.