Stability and limit cycles in competitive equilibria subject to adjustment costs and dynamic spillovers

Abstract This paper derives conditions for Hopf bifurcations in a general class of competitive equilibria where individual actions (i) lead to a dynamic spillover or an externality that is found e.g. in environmental economics and in the endogenous growth literature and (ii) these actions can be only sluggishly adjusted. It turns out that only one and particularly simple to check condition allows for a Hopf bifurcation (in both instances of perfect foresight and myopic expectations): growth of the spillover at the steady state. In fact, this condition ensures the existence of a bifurcation if the adjustment costs are sufficiently convex.

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