A Maximum Principle for Control Problems with Monotonicity Constraints

Abstract

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 variable as a new control variable subject to a non-negativity constraint, the paper obtains the maximum principle without such an additional assumption. The result is useful for studying incentive problems with hidden characteristics when the type set is a continuum and preferences satisfy a single-crossing constraint.