Envelope Theorem.s05

Envelope Theorem.s05 - The Envelope Theorem • The...

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Unformatted text preview: The Envelope Theorem • The envelope theorem concerns how the optimal value for a particular function changes when a parameter of the function changes • This is easiest to see by using an example The Envelope Theorem • Suppose that y is a function of x y = - x 2 + ax • For different values of a , this function represents a family of inverted parabolas • If a is assigned a value, then y becomes a function of x only and the value of x that maximizes y can be calculated The Envelope Theorem Value of a Value of x * Value of y * 1 1/2 1/4 2 1 1 3 3/2 9/4 4 2 4 5 5/2 25/4 6 3 9 Optimal Values of x and y for alternative values of a The Envelope Theorem 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 a y* As a increases, the maximal value for y ( y *) increases The relationship between a and y is quadratic The Envelope Theorem • Suppose we are interested in how y * changes as a changes • There are two ways we can do this – calculate the slope of y directly – hold x constant at its optimal value and calculate ∂ y / ∂ a directly The Envelope Theorem...
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This note was uploaded on 01/11/2012 for the course ECON 200 taught by Professor Riley during the Fall '10 term at UCLA.

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Envelope Theorem.s05 - The Envelope Theorem • The...

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