101A_lec16 - Economics 101A (Lecture 16) Stefano DellaVigna...

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Economics 101A (Lecture 16) Stefano DellaVigna March 17, 2009
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Outline 1. Cost Minimization: Example 2. Cost Curves and Supply Function 3. One-step Pro f t Maximization
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1 Cost Minimization: Example Continue example above: y = f ( L, K )= AK α L β Cost minimization: min wL + rK s.t.AK α L β = y Solutions: Optimal amount of labor: L ( r, w, y μ y A 1 α + β Ã w r α β ! α α + β Optimal amount of capital: K ( w r α β μ y A 1 α + β Ã w r α β ! α α + β = = μ y A 1 α + β Ã w r α β ! β α + β
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Check various comparative statics: ∂L /∂A < 0 (technological progress and unem- ployment) /∂y > 0 (more workers needed to produce more output) /∂w < 0 ,∂L /∂r > 0 (substitute away from more expensive inputs) Parallel comparative statics for K
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Cost function c ( w, r, y )= wL ( r, w, y )+ rK ( = μ y A 1 α + β w ³ w r α β ´ α α + β + + r ³ w r α β ´ β α + β De f ne B := w ³ w r α β ´ α α + β + r ³ w r α β ´ β α + β Cost-minimizing output choice: max py B μ y A 1 α + β
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First order condition: p 1 α + β B A μ y A 1 (
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This note was uploaded on 09/05/2009 for the course ECON 101a taught by Professor Staff during the Spring '08 term at University of California, Berkeley.

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101A_lec16 - Economics 101A (Lecture 16) Stefano DellaVigna...

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