Rigid monopoly prices

A consumer in the real world typically must visit (e.g. by phone) a monopolist to observe its price, even though the consumer may have correct expectations about that price. This causes monopoly prices to be higher and stickier than is predicted by the textbook model. If visiting costs are small, and consumers do not observe the firm's costs, then prices conform to the textbook model when costs are high but are downwardly rigid when costs drop below a threshold. Price flexibility increases as the fraction of ignorant consumers, who observe their idiosyncratic valuations of the product only after visiting the firm, increases. In a repeated game, a 'ratchet' equilibrium, in which price increases are permanent and price decreases temporary within a certain band, supports equilibria for which price is rigid on the equilibrium path but which Pareto dominate the fluctuating one-shot equilibrium. The ratchet equilibrium has the advantages that price is a continuous function of past prices near the equilibrium path and the price coordination problem is solved in a natural way: the equilibrium price is the lowest price that can be sustained by such a ratchet. This equilibrium price exceeds but is close to the average prediction of the textbook model. Additional results are derived for the case in which costs are fixed.