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A new approach to the envelope theorem

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  • Francesco Ruscitti

Abstract

We study the di¤erentiability of the value function of a constrained optimization problem. We consider the envelope-theorem framework of Milgrom and Segal (2002), and we accomplish two goals. We show how one can relax Milgrom and Segal’s assumption that the choice set does not vary with parameters. More importantly, we develop a new approach to proving the di¤erentiability of the value function. The key idea and main mathematical tool we employ in our approach are a novel feature in the literature dealing with the di¤erentiability of the value function.

Suggested Citation

  • Francesco Ruscitti, 2011. "A new approach to the envelope theorem," Departmental Working Papers of Economics - University 'Roma Tre' 0137, Department of Economics - University Roma Tre.
    • Handle: RePEc:rtr:wpaper:0137
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    More about this item

    Keywords

    value function; uniform convergence; differentiability; correspondences;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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