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Lecture04-2011

# Lecture04-2011 - Outline Single Product Primal Optimization...

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Unformatted text preview: Outline Single Product Primal Optimization Multiproduct Primal Functions Assignment Some Simple Production Mechanics: Lecture IV Charles B. Moss September 2, 2011 Charles B. Moss Some Simple Production Mechanics: Lecture IV Outline Single Product Primal Optimization Multiproduct Primal Functions Assignment Single Product Primal Optimization Supply Curve Profit Function Cost Function Multiproduct Primal Functions Assignment Charles B. Moss Some Simple Production Mechanics: Lecture IV Outline Single Product Primal Optimization Multiproduct Primal Functions Assignment Supply Curve Profit Function Cost Function Single Product Primal Optimization I Profit Maximization max x 1 , x 2 π = p Y x α 1 x β 2- w 1 x 1- w 2 x 2 ∂π ∂ x 1 = p Y α Y x 1- w 1 = 0 ∂π ∂ x 2 = p Y β Y x 2- w 2 = 0 ⇒ x 2 = w 1 w 2 β α x 1 (1) Charles B. Moss Some Simple Production Mechanics: Lecture IV Outline Single Product Primal Optimization Multiproduct Primal Functions Assignment Supply Curve Profit Function Cost Function p Y α Y x 1- w 1 = 0 ⇒ p Y x α- 1 1 x β 2- w 1 = 0 p Y α w 1 w 2 β α x 1 β = w 1 p Y α w 1 w 2 β β α β x α + β- 1 1 = w 1 p Y β w 2 β h w 1 α i β- 1 = x 1- α- β 1 ⇒ x * 1 ( p Y , w 1 , w 2 ) = p 1 1- α- β Y h w 1 α i 1- β 1- α- β β w 2 β 1- α- β (2) Charles B. Moss Some Simple Production Mechanics: Lecture IV Outline Single Product Primal Optimization Multiproduct Primal Functions Assignment Supply Curve Profit Function Cost Function x 2 = w 1 w 2 β α " p 1 1- α- β Y w 1 α β- 1 1- α- β β w 2 β 1- α- β # = p 1 1- α- β Y h w 1 α i 1+ β- 1 1- α- β β w 2 1+ β 1- α- β 1 + β- 1 1- α- β = 1- α- β + β- 1 1- α- β =- α 1- α- β 1 + β 1- α- β = 1- α- β + β 1- α- β = 1- α 1- α- β ⇒ x * 2 ( p Y , w 1 , w 2 ) = p 1 1- α- β Y α w 1 α 1- α- β w 2 β α- 1 1- α- β (3) Charles B. MossCharles B....
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Lecture04-2011 - Outline Single Product Primal Optimization...

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