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Unformatted text preview: way, we know that . ____________________________________________________________________ ______________________________ 7 Cobb-Douglas Long Run Cost Minimization Problem Having seen how to setup, solve and apply the envelope theorem to the general long run CMP we now consider long run CMPs for specific production functions, starting with the Cobb-Douglas production function where tells us the “returns to scale”. For example, here are some estimates of US manufacturing sectors CobbDouglas production parameters10: Returns to Scale (RTS) Tobacco Products 0.18 0.33 0.51 Food and Kindred Products 0.43 0.48 0.91 Transportation equipment 0.44 0.48 0.92 Apparel and other textiles 0.70 0.31 1.01 (see note below) Furniture and fixtures 0.62 0.40 1.02 Electronics and electric equipment 0.49 0.53 1.02 Paper and allied products 0.44 0.65 1.09 Petroleum and coal products 0.30 0.88 1.18 Primary metal 0.51 0.73 1.24 Note: Margin of error is In this case Decreasing Returns to Scale Increasing Returns to Scale may be considered to be “constant returns to scale” Suppose a company uses and as essential and “imperfect substitute” inputs to produce output according to a CobbDouglas production function. Its long run CMP is: { } { } [ ⏟ Note that labor and capital are essential...
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This document was uploaded on 01/19/2014.

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