ch4notes - A Model of Production Production Function Y F (...

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A Model of Production Production Function 3 / 2 3 / 1 ) , ( L K A L K F Y = = Example: 18 9 2 3 / 2 ) 27 ( 3 / 1 ) 8 )( 1 ( 27 8 1 = × = = = = = Y L K A
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Production Table for 3 / 2 3 / 1 L K A Y = 1 = A L/K 0 1 2 3 4 5 6 7 8 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 0.00 0 1 0.00 0 1.00 0 1.26 0 1.44 2 1.58 7 1.71 0 1.81 7 1.91 3 2.00 0 2 0.00 0 1.58 7 2.00 0 2.28 9 2.52 0 2.71 4 2.88 4 3.03 7 3.17 5 3 0.00 0 2.08 0 2.62 1 3.00 0 3.30 2 3.55 7 3.78 0 3.97 9 4.16 0 4 0.00 0 2.52 0 3.17 5 3.63 4 4.00 0 4.30 9 4.57 9 4.82 0 5.04 0 5 0.00 2.92 3.68 4.21 4.64 5.00 5.31 5.59 5.84
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0 4 4 7 2 0 3 3 8 6 0.00 0 3.30 2 4.16 0 4.76 2 5.24 1 5.64 6 6.00 0 6.31 6 6.60 4 7 0.00 0 3.65 9 4.61 0 5.27 8 5.80 9 6.25 7 6.64 9 7.00 0 7.31 9 8 0.00 0 4.00 0 5.04 0 5.76 9 6.35 0 6.84 0 7.26 8 7.65 2 8.00 0
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Constant Returns to Scale ) , ( 3 / 2 ) ( 3 / 1 ) ( ) , ( L K hF hL hK A hL hK F = = Marginal Product of Labor 0 3 2 3 / 1 3 / 1 = - L K A L Y Declining Marginal Product of Labor 0 3 1 3 2 3 / 4 3 / 1 2 2 < - = - L K A L Y Marginal Product of Capital 0 3 1 3 / 2 3 / 2 = - L K A K Y Declining Marginal Product of Capital 0 3 2 3 1 3 / 2 3 / 5 2 2 < - = - L K A K Y
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Firms maximize profits 0 ) , ( 0 ) , ( ) , ( max , = - = Π = - = Π - - = Π w L L K F L r K L K F K wL rK L K F L K K Y K L A L K A K L K F MPK
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This note was uploaded on 07/17/2008 for the course ECON 502.02 taught by Professor Mccafferty during the Spring '08 term at Ohio State.

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ch4notes - A Model of Production Production Function Y F (...

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