We develop an envelope condition method (ECM) for dynamic programming problems -- a tractable alternative to expensive conventional value function iteration. ECM has two novel features: First, to reduce the cost, ECM replaces expensive backward iteration on Bellman equation with relatively cheap...

In a model with multiple Pareto-ranked equilibria we add trade in assets that pay based on the realization of a sunspot. Asset trading restricts the equilibrium set in a way that raises welfare by eliminating equilibria with a high likelihood of disasters. When the probability of a disaster is...

In a model with multiple Pareto-ranked equilibria we add trade in assets that pay based on the realization of a sunspot. Asset trading restricts the equilibrium set in a way that raises welfare by eliminating equilibria with a high likelihood of disasters. When the probability of a disaster is...

Two types of agents have diverse beliefs about the law of motion for an exogenous endowment. One type knows the true law of motion and the other learns about it via Bayes' theorem. Financial market structure affects the dynamics of the distribution of financial wealth. When markets are complete,...