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 efficient labour units is FrÃ©chet differentiable in L? with derivatives given by kernels, and that the equilibrium is stable in the sense that if perturbations converge to 0 at Â±?, the corresponding equilibria converge back to the unperturbed equilibrium at Â±?. As a corollary this implies a proof of non-vacuity of the main result in Mertens and Rubinchik (2006).
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