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# crs - Production Function Average and Marginal Products...

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Production Function, Average and Marginal Products, Returns to Scale, Change of Variables Production Function: links inputs to amont of output. Assume we have 2 inputs: Labor (L) and Capital (K), and we use Y for output . Then we write: Y = F (L , K) , where F ( ) is the production Function . We make a number of assumptions about this function. Examples: (1) Y = L . K (2) Y = L + K (3) Y = L . K 1/3 1/3 (4) Y = L . K 1/2 1/2 Average Product and Marginal Product of a Particular Input Labor : Average Product of Labor (APL): Y/ L Marginal Product of Labor (MPL): changes in Y / Changes in L (for small changes) = partial derivative of F(L, K) with respect to L. Capital : Average Product of Capital (APK): Y/ K Marginal Product of Capital (MPK): changes in Y/ Changes in K (for small changes) = partial derivative of F(L, K) with respect to K Returns to Scale: Percentage of change in Y when we change all inputs in the same proportion. Increasing Returns to Scale (IRS) : % change in Y > % change in L = % change in K Constant Returns to Scale (CRS) : % change in Y = % change in L = % change in K

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crs - Production Function Average and Marginal Products...

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