Elluminate10-20-11

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

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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 = α 1 σ 1 x σ- 1 σ 1 + α 1 σ 2 x σ- 1 σ 2 + α 1 σ 3 x σ- 1 σ 3 + α 1 σ 4 x σ- 1 σ 4 σ σ- 1 . (2) Forming the Lagrangian L = w 1 x 1 + w 2 x 2 + w 3 x 3 + w 4 x 4 + λ Y- α 1 σ 1 x σ- 1 σ 1 + α 1 σ 2 x σ- 1 σ 2 + α 1 σ 3 x σ- 1 σ 3 + α 1 σ 4 x σ- 1 σ 4 σ σ- 1 ! . (3) The first-order conditions for the Lagrangian are then ∂L ∂x i = w i- λα 1 σ i σ- 1 σ x σ- 1 σ- 1 i σ σ- 1 α 1 σ 1 x σ- 1 σ 1 + α 1 σ 2 x σ- 1 σ 2 + α 1 σ 3 x σ...
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Elluminate10-20-11 - Elluminate 11 Direct Estimation of the...

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