On the convergence of optimal solutions in infinite horizon discrete time models

Abstract

We analyse the dynamic properties of a one-sector optimal growth model and then extend this analysis to the optimal growth model in which each generation cares about its own parent generation, its own consumption and the utility of its successor.

Keywords::

• stability theory
• difference equations
• optimality conditions
• uniqueness of solutions
• mathematical economics

AMS Subject Classification::

• 39A30
• 39A99
• 49K99
• 74G30
• 91B02

Acknowledgements

We thank anonymous referees for helpful comments on the earlier version of the paper and also Sadao Kanaya for the helpful discussion in the initial stage of the research.