Lecture04-2011

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

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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

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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 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

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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 w 1 α β 1 = x 1 α β 1 x 1 ( p Y , w 1 , w 2 ) = p 1 1 α β Y w 1 α 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 w 1 α 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. Moss Some Simple Production Mechanics: Lecture IV

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