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...

We propose a new welfare criterion that allows us to rank alternative financial market structures in the presence of belief heterogeneity. We analyze economies with complete and incomplete financial markets and/or restricted trading possibilities in the form of borrowing limits or transaction...