The aim of this paper is to examine whether the development of waste recycling activities can be a source of economic fluctuations. We assume that the recycling sector has four fundamental characteristics. (i) The production factors are restricted by the production of the last period. (ii) These production factors are waste for which the price determination is noncompetitive. (iii) The sector produces a recycled good, which is a perfect substitute for the primary good. (iv) It reduces the waste stream. We consider the simplest economy, with an infinitely lived agent and a life-cycle hypothesis for the goods. We show that the equilibrium is unique and is always determinate. In spite of the lack of indeterminacy, however, our economy can display cyclical behavior, depending on some usual conditions on parameters. Namely, the steady state may undergo a flip bifurcation or a Hopf bifurcation.