Publication: Differentiability of the value function without interiority assumptions
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2007-03
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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 show that the value function is continuously differentiable. We then discuss this
result in the context of several economic models.
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Constrained optimization, Value and policy functions, Differentiability, Envelope theorem, Shadow price