Regularity and Stability of Equilibria in an Overlapping Generations Model with Exogenous Growth Preliminary Draft

In an exogenous-growth economy with overlapping generations (OG) we analyse local stability of the balanced growth equilibria with respect to perturbations of consumption endowments, thought of as the “monetised” value of a government policy to individuals. We show that perturbed economies have a unique equilibium in the neighbourhood, that the equilibrium allocation expressed in terms of efficient labour units is Fréchet differentiable in L∞ with derivatives given by kernels, and that the equilibrium is stable in the sense that if perturbations converge to 0 at ±∞, the corresponding equilibria converge back to the unperturbed equilibrium at ±∞. As a corollary this implies a proof of non-vacuity of the main result in Mertens and Rubinchik (2006). Date: February 5, 2009. 2000 Mathematics Subject Classification. 91B14, 91B62 J.E.L. Classification numbers. D50, H43.