Lecture 24-2005

Lecture 24-2005 - Factor Bias Technical Change and Valuing...

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Factor Bias, Technical Change, and Valuing Research Lecture XXIV

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Mathematical Model of Technical Change If we start from the quadratic production function specified as assuming an output price of p and input prices of w 1 and w 2 for inputs x 1 and x 2 , respectively, the derived demands for each input can be expressed as ( 29 ( 29 1 2 0 1 1 2 2 2 2 11 1 12 1 2 22 2 , 1 2 2 f x x a a x a x A x A x x A x = + + + + +
( 29 ( 29 ( 29 ( 29 * 12 2 22 1 22 1 12 2 1 1 2 2 11 22 12 * 12 1 11 2 12 1 11 2 2 1 2 2 11 22 12 , , , , A a p A a p A w A w x p w w p A A A A a p A a p A w A w x p w w p A A A - + - = - - - + = -

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In order to analyze the possible effect of technological change, we hypothesize an input augmenting technical change similar to the general form of technological innovation introduced by Hayami and Ruttan.
Specifically, we introduce two functions where γ 1 (Ψ) and γ 2 (Ψ) are augmentation factors and Ψ is a technological change ( 29 ( 29 * 1 1 1 * 2 2 2 x x x x = γ ψ = γ ψ

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Hence, γ 1 (Ψ), γ 2 (Ψ)≥1 for any Ψ. Thus, technological change increases the output created by each unit of input. Integrating these increases into the forgoing production framework, the derived demands for each input becomes:
( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 * 1 1 2 12 2 1 2 22 1 1 2 22 2 1 12 1 2 2 2 11 22 12 1 2 * 2 1 2 12 1 1 2 11 2 1 2 12 2 1 22 1 2 2 11 22 12 1 2 , , , , , , x p w w A a p A a p A w A w p A A A x p w w A a p A a p A w A w p A A A ψ = γ ψ γ ψ - γ ψ γ ψ + γ ψ - γ ψ - γ ψ γ ψ ψ = γ ψ γ ψ - γ ψ γ ψ - γ ψ + γ ψ - γ ψ γ ψ

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In order to simplify our discussion, we assume that the new technology does not affect the effectiveness of x 2 , or
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Lecture 24-2005 - Factor Bias Technical Change and Valuing...

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