Internal habit formation and optimality.

Abstract

Carroll et al. [7] establish that in a model with internal habits, an increase in economic growth may cause a positive change in savings. The optimality of this result has been recently questioned by several contributions in the literature which have observed that the parametrization used in [7] implies a utility function not jointly concave in consumption and habits. In this short paper, we revisit this issue: firstly we explain that it can be solved only through advanced techniques in Dynamic Programming and then we prove, using them, how the candidate optimal control found in [7] is indeed the unique optimal control.