Assignment12-2010 - AEB 6571 Econometric Methods I...

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AEB 6571 Econometric Methods I Assignment 12 - 2010 Charles B. Moss November 24, 2010 1. As I develop in AEB 6184 Production Economics a cost function which is concave in input prices and convex in output levels can be derived assuming cost minimizing behavior. Given this cost function, we can derive the input demand equations by taking the derivative of the cost function with respect to input prices (by Shephard’s Lemma). Hence, we can specify a quadratic cost function c ( w, y ) = α 0 + α w + 1 2 w Aw + β y + 1 2 y By + y Γ w (1) where w is the vector of input prices, y is a vector of output prices, and α 0 , α , A , β , B , and Γ are estimated parameters. The input demand equations can then be specified assuming three inputs and three outputs as x 1 = α 1 + A 11 w 1 + A 12 w 2 + A 13 w 3 + Γ 11 y 1 + Γ 12 y 2 + Γ 13 y 3 + 1 x 2 = α 2 + A 12 w 1 + A 22 w 2 + A 23 w 3 + Γ 21 y 1 + Γ 22 y 2 + Γ 23 y 3 + 2 x 3 = α 3 + A 13 w 1 + A 23 w 2 + A 33 w 3 + Γ 31 y 1 + Γ 32 y 2 + Γ 33 y 3 + 3 . (2) Note that the symmetry of the cost function has already been imposed under Young’s theorem. In addition, the third equation is singular (take AEB 6184 for more information).
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