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 in a general class of economies with multidimensional action spaces and uncountable state spaces. Under standard complementarity assumptions on preferences, aswell as a mild geometric condition on transition probabilities, we prove existence of timeconsistent solutions in Markovian policies, and provide conditions for the existence of continuous and monotone equilibria. We present applications of our methods to habit formation models, environmental policies, and models of consumption under borrowing constraints, and hence show how our methods extend the results obtained by Harris and Laibson (Econometrica 69:935-957, 2001) to a broad class of dynamic economies. We also present a simple successive approximation scheme for computing extremal equilibrium, and provide some results on the existence of monotone equilibrium comparative statics in the model's deep parameters.