Can consumption spillovers be a source of equilibrium indeterminacy?

Resumo

In the framework of a one-sector exogenous growth model we show that consumption externalities are not a source of equilibrium indeterminacy when the labor supply is inelastic, whereas they are under endogenous labor supply. In particular, when the marginal rate of substitution between own consumption and the others' consumption is constant along the equilibrium path, the equilibrium may exhibit indeterminacy when the following two conditions are simultaneously satisfied: (i) both consumption and production externalities are present and (ii) the elasticity of the labor demand is larger than the elasticity of the Frisch labor supply. In contrast, when the marginal rate of substitution is not constant, the equilibrium may exhibit indeterminacy even if the previous two conditions are not met. In this case, the equilibrium can exhibit indeterminacy even if production externalities are absent. We also show that these results do not apply to an endogenous growth model, where indeterminacy may arise only when condition (ii) is met.