Lecture 03-2005 - Substituting One Input for Another in...

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Unformatted text preview: Substituting One Input for Another in Production Lecture III Elasticity of Scale and Law of Variable Proportions We continue to develop the economics of production through a ray from the origin. Last lecture, we developed the notion of returns to scale by looking at changes in production along a ray from the origin 1 x 2 x 1 x λ 2 x λ Following the definition of this ray, we defined the elasticity of scale: ( 29 ( 29 1 ln ln f x λ λ ε λ = & = ( 29 ( 29 1 1 1 ln ln n n i i i i i f x f x x y λ λ ε λ = = = & & = = Building on these definitions, we next define the ray average product as where λ is a strictly positive scalar. In addition, we define the ray marginal product ( 29 f x RAP λ λ = ( 29 ( 29 1 n i i i f x f x x x λ λ λ = = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 n i i i f z x f x x z x f z x z x z x f x x x λ λ λ λ λ λ = = & & & = = ( 29 ( 29 2 2 1 1 n n i j j i i j f x f x x x x x λ λ λ = = = 1 x 2 x y 1 x 2 x ( 29 1 2 , f x x λ λ y x λ ( 29 y f x λ =...
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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 03-2005 - Substituting One Input for Another in...

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