Non-Constant Discounting in Continuous Time

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.

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Publication Type:
Working or Discussion Paper
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Total Pages:
JEL Codes:
D83; L50
Series Statement:
CUDARE Working Paper 969

 Record created 2017-04-01, last modified 2018-01-22

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