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envelope theorem


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A theorem determining the effect of a differential change in a parameter on the outcome of a maximization problem. Formally, consider the problem of choosing x to maximize a function f(x; a), where a is a parameter. Denote the solution to this maximization by x(a) and define the maximum value function V(a) byV(a)=max{x}f(x;a)=f(x(a);a).The envelope theorem states thatso that the derivative of the value function is the partial derivative of the objective evaluated at the solution to the optimization.

V(a)=max{x}f(x;a)=f(x(a);a).

Subjects: Economics.


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