On the minimum degree of returns to scale in sunspot models of the business cycle

Bennett and Farmer (J. Econ. Theory 93 (2000) 118) claim that the degree of increasing returns to scale required for indeterminacy in a single sector growth model can be lowered by allowing for preferences that are non-separable in consumption and leisure. In this paper I show that the example they give violates concavity. In a more general setup, which does not impose specific functional forms on utility, I prove that there are no concave utility functions compatible with indeterminacy if the elasticity of scale is lower than the inverse of the labor share in production.