Indeterminacy and endogenous fluctuations with arbitrarily small externalities

In this paper we study the occurrence of local indeterminacy, endogenous fl uctuations, and bifurcations in a simple non-monetary 2-period overlapping generations economy (in which people do not consume when young) with capita l-labor substitution, elastic labor supply, and productive externalities. W e show that, in contrast with the local dynamics generated by many one-sect or models of capital accumulation studied in the current literature, local indeterminacy and, therefore, stationary stochastic equilibria driven by se lf-fulfilling beliefs (sunspots), as well as Multiple stationary equilibria , are pervasive phenomena when the elasticity of input substitution is larg e and when the size of externalities is arbitrarily, small. We also demonst rate that, when externalities are arbitrarily small, the Cobb-Douglas produ ction function, often used for its analytical tractability in many models, is structurally unstable: it is always associated with uniqueness of the st eady-state, but any small perturbation of the elasticity of input substitut ion leads to the existence of two stationary equilibria, which may be close to each other, with the consequence that the dynamics may be qualitatively very different from those originated in the unit elasticity case. (C) 2001 Academic Press.