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AEB 6184 – Mitscherlich-Baule Production Function and McFadden Cost Function

AEB 6184 – Mitscherlich-Baule Production Function and McFadden Cost Function. Elluminate - 13. Mitscherlich-Baule Production Function. Starting with the simulated cost surface for production

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AEB 6184 – Mitscherlich-Baule Production Function and McFadden Cost Function

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  1. AEB 6184 – Mitscherlich-Baule Production Function and McFadden Cost Function Elluminate - 13

  2. Mitscherlich-BauleProduction Function • Starting with the simulated cost surface for production • I generated 200 minimum cost solutions using numerical optimization for a vector of randomly drawn prices. • I also added a correlated error term.

  3. Normalized Quadratic Cost Function • Following our discussion from the class, I estimated the normalized quadratic cost function

  4. Normalized Quadratic Results

  5. Eigenvalues of A • The eigenvalues of A indicate that the cost function is concave in input prices. • In addition, the negative sign on the squared y indicates that the surface is convex in output levels.

  6. McFadden Cost Function • Diewert, W.E. and T.J. Wales. 1987. Flexible Forms and Global Curvature Conditions Econometrica 55(1), 43-68.

  7. Shephard’s Lemma • Taking the derivatives – Two cases • i=1 • i = 2,…

  8. Hessian Matrix • The Hessian matrix is then determined by the quadratic term • Concavity can be imposed by Lau’s method

  9. McFadden Estimates

  10. Concavity

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