Differentiability of the Value Function without Interiority Assumptions Articles uri icon

publication date

  • September 2009

start page

  • 1948

end page

  • 1964

issue

  • 5

volume

  • 144

international standard serial number (ISSN)

  • 0022-0531

electronic international standard serial number (EISSN)

  • 1095-7235

abstract

  • 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.