The paper studies equilibria for economies with imperfect competition and non-convex technologies. Following Negishi, firms maximise profits under downward-sloping perceived demand functions. Negishi’s assumptions, in particular the assumption of a single monopolistic competitor in each market, are relaxed. Existence of equilibria is obtained, under otherwise standard assumptions, for productions sets defined in each firm by the union of a convex technology and a technology subject to fixed costs. In the light of a counterexample, it is assumed that fixed factors are distinct from variable factors. Technically, the proof rests on pricing rules.