We consider a standard overlapping generations (OLG) economy with a simple demographic structure where a new cohort of agents appears at each period and whose economic activity is extended over two successive periods, and finitely many firms may be active. The production possibilities are described by a sequence of production set-valued mappings and the main innovation comes from the fact that we allow for increasing returns to scale of more general type of non-convexities. To describe the behavior of the firms, we consider loss-free pricing rules, which cover the case of the average pricing rule, the competitive behavior when the firms have convex production sets, and the competitive behavior with quantity constraints à la Dehez–Drèze. We prove the existence of an equilibrium under assumptions, which are at the same level of generality than the ones for the existence in an exchange OLG economy.