Regularity and stability of equilibria in an overlapping generations model with exogenous growth

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 e?cient labour units is Fréchet di?erentiable 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)