This paper presents a model of dynamic price duopoly with short-term price inertia. A perturbation of consumer behavior, specifying that a consumer may purchase from the higher priced seller with positive probability, endows each duopolist with an arbitrarily small degree of monopoly power. It is shown that the slightest degree of asymmetry between the firms with respect to this monopoly power unambiguously identifies a firm which appropriates almost all the surplus from those consumers over whom the firms compete. This outcome is the unique Pareto dominant equilibrium if firms are restricted to state dependent strategies.