Weak concavity properties of indirect utility functions in multisector optimal growth models


  • This work was supported by French National Research Agency Grant (ANR-08-BLAN-0245-01). I would like to thank J. Blot, P. Cartigny, J.P. Drugeon, J.M. Grandmont, P. Michel, L. Montrucchio, K. Nishimura and an anonymours referee for helpful discussions and comments which greatly improved the exposition of the paper.


Studies of optimal growth in a multisector framework are generally addressed in reduced-form models. These are defined by an indirect utility function which summarizes the consumers’ preferences and the technologies. Weak concavity assumptions of the indirect utility function allow one to prove differentiability of optimal solutions and stability of the steady state. This paper shows that if the consumption good production function is concave-inline image, and the instantaneous utility function is concave-inline image, then the indirect utility function is weakly concave, and its curvature coefficients are bounded from above by a function of inline image and inline image.