Lecture 21-2005 - Profit Functions Lecture XXI A Primal...

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Unformatted text preview: Profit Functions Lecture XXI A Primal Approach to the Profit Function • Taking as a starting point, the Cobb- Douglas form, we could formulate the profit function as: 1 2 1 1 2 2 1 1 1 2 1 1 2 1 1 2 2 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 2 1 1 1 1 2 max 1 y x y y y y y y p x x w x w x y p w x x x w w x x y x w w p w x x w p x x w w w w w w x p p x p α β β α β β β β α β α β α β α β π π α α β π β α β β α α β α β α--- +- +- +---- =-- ∂ =- = ∂ ⇒ = ⇒ = ∂ =- = ∂ ⇒ = ⇒ = ⇒ ⇒ = 1 1 1 2 1 w w α α α β α β α β β α- +- +-- ( 29 1 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 max , 1 y y y y y p y C w y w w p y w y w y w w w w p y y w w w w w w p y w w y w w β α α β α β α β α β β α α β α β α β β α α β α β α β α β π α β β α α β β α α β π α β β α-- + + +-- + +-- +-- + =- =-- =- + ∂ ⇒ =- + = ∂ + 1 1 1 2 1 1 2 1 2 y w w y p w w w w α β β α β α α β α β α β α β α β β α + +--- + +-- ⇒ = + • However, like our discussion regarding the cost function, we can bypass the primal form and derive the economic concepts of the dual profit function. Properties of the Profit Function • Properties of Π ( p , w ): – Π ( p , w ) ≥ 0; – If p 1 ≥ p 2 , then Π (...
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This note was uploaded on 07/15/2011 for the course AEB 6184 taught by Professor Staff during the Fall '09 term at University of Florida.

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Lecture 21-2005 - Profit Functions Lecture XXI A Primal...

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