Differentiability of the value function without interiority assumptions

• 成果类型: Article
• 署名作者: Pablo Rincon-Zapatero, Juan; Santos, Manuel S.
• 署名单位: Universidad Carlos III de Madrid; University of Miami
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2009.02.006
• 发表日期: 2009
• 页码: 1948-1964
• 关键词: Constrained optimization; Value and policy functions; differentiability; Envelope theorem; Shadow price

摘要

This paper studies first-order differentiability properties of the value function in concave dynamic programs. Motivated by economic considerations, we dispense with commonly imposed interiority assumptions. We suppose that the correspondence of feasible choices varies with the vector of state variables, and we allow the optimal solution to belong to the boundary of this correspondence. Under minimal assumptions we prove that the value function is continuously differentiable. We then discuss this result in the context of some economic models, and focus on some examples in which our assumptions are not met and the value function is not differentiable. (C) 2009 Elsevier Inc. All rights reserved.