Lecture4_ MathIV

# 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
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
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.
Meaning of Multiplier Consider the simplest problem–two variables and one equality constraint. Max

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Lecture4_ MathIV - Lecture4 LastMathLecture...

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