## Abstract

We address intertemporal utility maximization under a general discount function that nests the exponential discounting and the quasi-hyperbolic discounting cases as particular specifications. Under the suggested framework, the representative agent adopts, at some initial date, an optimal behavior that shapes her consumption trajectory over time. This agent desires to take a constant discount rate to approach the optimization problem, but bounded rationality, under the form of a present bias, deviates the individual from the intended goal. As a result, decreasing impatience will end up dominating the agent’s behavior. The individual will not be aware of her own time inconsistency and, therefore, she will not revise her plans as time elapses, what makes the problem relatively simple to address from a computational point of view. The general discounting framework is used to approach a standard optimal growth model in discrete time. Transitional dynamics and stability properties of the corresponding dynamic setup are studied. An extension of the standard utility maximization model to the case of habit persistence is also considered.

## Keywords

Intertemporal preferences Exponential discounting Quasi-hyperbolic discounting Optimal growth Habit persistence Transitional dynamics## JEL Classification

C61 D91 O41## Notes

### Acknowledgments

We thank participants and organizers of the 6th Annual Meeting of the *Portuguese Economic Journal* and the comments of colleagues from the Business Research Unit of the Lisbon University Institute. We gratefully acknowledge, as well, the valuable and insightful comments of two anonymous referees. Alexandra Ferreira-Lopes and Orlando Gomes acknowledge financial support from PEst-OE/EGE/UI0315/2011. Alexandra Ferreira-Lopes and Tiago Neves Sequeira acknowledge support from FCT, Project PTDC/EGE-ECO/102238/2008.

## Supplementary material

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