Intertemporal utility with heterogeneous goods and constant elasticity of substitution

Abstract

We characterize intertemporal utility functions over heterogeneous goods that feature (i) a constant elasticity of substitution between goods at each point in time and (ii) a constant intertemporal elasticity of substitution for at least one of the goods. We find that a standard, stationary intertemporal utility function is consistent with these two properties if and only if it either is of the intertemporal constant elasticity of substitution (ICES) form, that is, if all elasticities of substitution are identical, or if the instantaneous utility function is Cobb–Douglas. We also characterize the families of stationary intertemporal utility functions that feature either (i) or (ii), but not the respective other property.