The Envelope Theorem: Numerical Examples
The Envelope Theorem: Numerical Examples
The envelope theorem is used to solve maximization problems in the fields of microeconomics and finance. It is a fundamental result in the calculus of variations and is therefore often used in large deviations research.
We verify that the envelope theorem holds for the log-likelihood function when the underlying data are generated from a normal distribution. The evidence that the theorem is true is that the top and bottom pictures in the Demonstration are identical.