This paper examines a reputation-based mechanism that sustains the provision of high quality in the presence of competition among providers, where the incentive for high-quality production comes from a reputation premium: firms with higher reputations charge higher prices. The way we model the market highlights the fact that prices are not solely determined from consumers' willingness to pay as in the monopolistic setting studied in the previous literature. In effect, equilibrium prices are determined endogenously, from the interaction of the distribution of consumers' valuations for high quality and the distribution of firms' reputations—the demand and the supply sides of the market, respectively. This paper shows that: (i) there is a steady-state distribution of reputations, a result that allows the study of a stationary equilibrium; (ii) there are parameter configurations for which the existence of a high-quality equilibrium is guaranteed, and where the incentives for high quality production in the repeated game depend on the shape of the price function; and (iii) the Walrasian-equilibrium price function depends on the shape of the steady-state distribution of reputations, and the assignment of consumers to firms with different reputation levels in such an equilibrium is positively assortative if quality is a normal good.