Lecture4_ MathIV - Lecture4 LastMathLecture...

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Lecture 4 Last Math Lecture Econ 101A: Microeconomic Theory UC Berkeley Spring 2011 Prof. Cristian Santesteban
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Topics Finish Lagrangian Formulation for Equality Constraints Meaning of the Multiplier Second Order Conditions Envelope Theorem for Constrained Optimization Lagrangian Formulation for Inequality Constraints
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Equality Constraints Consider the simplest problem–two variables and one equality constraint. max x,y f(x,y) s.t. h(x,y) = a Rewrite in the Lagrangian formulation: max x,y L = f(x,y) – λ (h(x,y)–a) FOCs with respect to λ , x, and y.
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Example
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Example
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Meaning of Multiplier The Lagrange multiplier measures the sensitivity of the optimal value of the objective function to changes in the right hand side of the constraint. As a result, it provides a natural measure of value for scarce resources in economic maximization problems.
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Meaning of Multiplier Consider the simplest problem–two variables and one equality constraint. Max
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This note was uploaded on 01/21/2012 for the course ECON 101a taught by Professor Staff during the Spring '08 term at University of California, Berkeley.

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Lecture4_ MathIV - Lecture4 LastMathLecture...

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