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Non-Constant Discounting in Continuous Time

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  • Karp, Larry

Abstract

This note derives the dynamic programming equation (DPE) to a differentiable Markov Perfect equilibrium in a problem with non-constant discounting and general functional forms. We begin with a discrete stage model and take the limit as the length of the stage goes to 0 to obtain the DPE corresponding to the continuous time problem. We characterize the multiplicity of equilibria under non-constant discounting and discuss the relation between a given equilibrium of that model and the unique equilibrium of a related problem with constant discounting. We calculate the bounds of the set of candidate steady states and we Pareto rank the equilibria.

Suggested Citation

  • Karp, Larry, 2004. "Non-Constant Discounting in Continuous Time," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7pr05084, Department of Agricultural & Resource Economics, UC Berkeley.
    • Handle: RePEc:cdl:agrebk:qt7pr05084
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