Non-smooth monotonicity constraints in optimal control problems: Some economic applications

This paper presents a theorem on necessary conditions for optimal control problems containing monotonicity constraints that bear on a joint function of the control variable, the state variable, and the time. These constraints are often found, under continuity and piecewise smoothness assumptions for the endogenous variables of the problem, in various economic fields that include monopoly regulation, non-uniform pricing, implicit contracts, and optimal taxation. After applying our theorem to a general incentive provision model, we show its usefulness in relaxing the standard continuity and smoothness assumptions, for the case of two screening problems among those that have received more attention in the literature.