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Non‐smooth monotonicity constraints in optimal control problems: Some economic applications
Author(s) -
Ruiz del Portal X.
Publication year - 2010
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.948
Subject(s) - smoothness , monotonic function , monopoly , piecewise , mathematical economics , variable (mathematics) , mathematical optimization , control variable , optimal control , control (management) , function (biology) , economics , state variable , incentive , mathematics , computer science , microeconomics , mathematical analysis , statistics , physics , management , evolutionary biology , biology , thermodynamics
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. Copyright © 2010 John Wiley & Sons, Ltd.