Summary: This paper explores the distinction between nonatomicity and thick markets as the source of perfect competition. The focus of the paper is the construction of a model of an imperfectly competitive economy with a nonatomic continuum of traders and a continuum of differentiated commodities, for which Walrasian equilibria exist. The failure of perfect competition in this instance can be identified in two ways: individuals can affect prices and the core is strictly larger than the set of Walrasian allocations. By contrast, it is shown that, when markets are physically or economically thick (or both), then individuals cannot typically affect prices and the core always coincides with the set of Walrasian allocations.