The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this...

This paper introduces a general method for computing equilibria with heteroge- neous agents and aggregate shocks that is particularly suitable for economies with private infor- mation. Instead of the cross-sectional distribution of agents across individual states, the method uses as a state...

I study the properties of optimal long-term contracts in an environment in which the agent.s type evolves stochastically over time. The model stylizes a buyer-seller relationship but the results apply quite naturally to many contractual situations including regulation and optimal...