Heterogeneous discounting in economic problems
Article first published online: 10 JAN 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Optimal Control Applications and Methods
Volume 33, Issue 1, pages 32–50, January/February 2012
How to Cite
Marín-Solano, J. and Patxot, C. (2012), Heterogeneous discounting in economic problems. Optim. Control Appl. Meth., 33: 32–50. doi: 10.1002/oca.975
- Issue published online: 13 JAN 2012
- Article first published online: 10 JAN 2011
- Manuscript Accepted: 22 OCT 2010
- Manuscript Revised: 17 OCT 2010
- Manuscript Received: 12 MAR 2010
- heterogeneous discounting;
- dynamic programming equation;
- time consistent solution
There is a growing literature considering deviations from standard discounting. In this paper, we analyze a continuous-time model in finite horizon in which the agent discounts the instantaneous utility function and the final function at constant but different instantaneous discount rates of time preference. Within this context we can model problems in which, when the time t approaches to the final time, the valuation of the final function increases compared with the previous valuations in a way that cannot be explained by using a constant or a variable discount rate. Despite its simplicity, the differential time preference suffices to obtain time-inconsistent results if standard optimal control theory is applied, for the same reason as in problems with non-constant discounting or hyperbolic preferences. We derive a dynamic programming equation whose solutions are time-consistent Markov equilibria. We solve a simple model and discuss some extensions of the model. Copyright © 2011 John Wiley & Sons, Ltd.