Continuous Markov equilibria with quasi-geometric discounting

We prove that the standard quasi-geometric discounting model used in dynamic consumer theory and political economics does not possess continuous Markov perfect equilibria (MPE) if there is a strictly positive lower bound on wealth. We also show that, at points of discontinuity, the decision maker strictly prefers lotteries over the next period’s assets. We then extend the standard model to have lotteries and establish the existence of an MPE with continuous decision rules. The models with and without lotteries are numerically compared, and it is shown that the model with lotteries behaves more in accord with economic intuition.