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.
Weak concavity properties of indirect utility functions in multisector optimal growth models
Version of Record online: 21 FEB 2012
International Journal of Economic Theory
Special Issue: The Legacy of Lionel W. McKenzie: Special Issue 1
Volume 8, Issue 1, pages 13–26, March 2012
How to Cite
Venditti, A. (2012), Weak concavity properties of indirect utility functions in multisector optimal growth models. International Journal of Economic Theory, 8: 13–26. doi: 10.1111/j.1742-7363.2011.00171.x
- Issue online: 21 FEB 2012
- Version of Record online: 21 FEB 2012
- Accepted 5 May 2011
- indirect utility function;
- social production function;
- multisector optimal growth model;
- weak concavity
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-, and the instantaneous utility function is concave-, then the indirect utility function is weakly concave, and its curvature coefficients are bounded from above by a function of and .