Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme
Theorem

Envelope Theorem

Game Theory

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.

Facts
Statement
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 1
Classification
Statement Form
Identity or Equation 1
Connections

Has Statement Form

Equation, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Envelope theorem - Wikipedia
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 Branch: Optimization, Lead sentence
    operties of the value function of a parameterized optimization problem.
View the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.