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