The envelope theorem is a result in mathematics and economics describing how the value of a parameterized optimization problem changes as its parameters change. It shows that, at an optimum, the effect of a small change in a parameter on the value function can be computed by treating the optimal choice as fixed, because the indirect effect of the parameter change on the optimal choice contributes nothing to first order, which makes the theorem a standard tool for comparative statics in economic models.
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Statementthe envelope theorem shows that, in a certain sense, changes in the optimizer of the objective do not contribute to the change in the objective function 1 Classification
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Source Envelope theorem - Wikipedia
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Source Wolfram MathWorld: Envelope Theorem
Source Wolfram MathWorld: Envelope Theorem
Sources
1. Envelope theorem - Wikipedia
Introduction
the envelope theorem shows that, in a certain sense, changes in the optimizer of the objective do not contribute to the change in the objective function
In Group: Economic Theory, Lead section
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem.
In Branch: Optimization, Lead sentence
operties of the value function of a parameterized optimization problem.
View the Source2. Wolfram MathWorld: Envelope Theorem
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Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898.
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