On indeterminacy in one-sector models of the business cycle with factor-generated externalities

By relaxing the restrictions commonly imposed on the magnitude of capital externalities in one-sector models with Cobb-Douglas technology, we find that indeterminacy can arise in the following two cases: (i) the felicity function is separable in consumption and leisure and there are negative capital externalities; (ii) the felicity function is non-separable and the social elasticity of production with respect to capital is greater than one. In both cases indeterminacy happens when the aggregate labor-demand curve is downward-sloping. In addition, with Cobb-Douglas technology we show that the presence of income effects on the demand for leisure is a necessary condition for indeterminacy to occur, and that therefore for certain felicity functions characterized by the presence of no income effects indeterminacy can never occur regardless of the signs and magnitudes of capital and labor externalities.