Time Consistent Markov Policies in Dynamic Economies with Quasi-Hyperbolic Consumers

We study the question of existence and computation of time-consistent Markov policies of quasi-hyperbolic consumers under a stochastic transition technology and borrowing constraints. Under standard assumptions on preferences, as well as a mild geometric condition on a transition probabilities, we prove existence of the greatest and the least time-consistent policies, and provide conditions for (Lipschitz) continuous and monotone equilibria. We show how our methods extend the results of Harris and Laibson (2001). We present a simple approximation scheme for extremal equilibrium, and provide some monotone equilibrium comparative statics results in the model's deep parameters