Elluminate10-20-11

Elluminate10-20-11 - Elluminate 11 - Direct Estimation of...

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Unformatted text preview: Elluminate 11 - Direct Estimation of the Cost Function: The CES Production Function Charles B. Moss ( University of Florida ) October 25, 2011 This manuscript derives the dual cost function for the constant elasticity of substitution (CES) production function. This derivation starts with the most basic form of the maximization problem min x i X i x i w i s . t .Y = f ( x ) (1) focusing our attention on the four input CES production function min x 1 ,x 2 ,x 3 ,x 4 w 1 x 1 + w 2 x 2 + w 3 x 3 + w 4 x 4 s . t .Y = 1 1 x - 1 1 + 1 2 x - 1 2 + 1 3 x - 1 3 + 1 4 x - 1 4 - 1 . (2) Forming the Lagrangian L = w 1 x 1 + w 2 x 2 + w 3 x 3 + w 4 x 4 + Y- 1 1 x - 1 1 + 1 2 x - 1 2 + 1 3 x - 1 3 + 1 4 x - 1 4 - 1 ! . (3) The first-order conditions for the Lagrangian are then L x i = w i- 1 i - 1 x - 1 - 1 i - 1 1 1 x - 1 1 + 1 2 x - 1 2 + 1 3 x...
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This note was uploaded on 11/08/2011 for the course AEB 6184 taught by Professor Staff during the Spring '09 term at University of Florida.

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Elluminate10-20-11 - Elluminate 11 - Direct Estimation of...

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