# PS6 - capital curve(the production function for a fixed...

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UCLA Economics 11 – Fall 2009 Professor Mazzocco Problem Set 6 Due by November 12 before 9:00am in the box located outside room 2221E 1) Suppose that a firm’s production function is given by: Q= K + L [ ] α where α is a given parameter. a) Find the marginal product of capital and labor. b) Find the average product of capital and labor. c) Does this production function have increasing, constant or decreasing returns to scale? Explain. d) Find the Ratio of Technical Substitution 2) Suppose the production function for widgets is given by: Q=f(K,L)=KL–0.8K 2 0.2L 2 a) Suppose L=10 (is fixed), derive an expression for and graph the total product of
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Unformatted text preview: capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? c) Again, assuming L=10, derive an expression for and graph the MP K curve. At what level of capital input does MP K =0? d) Does this production function exhibit constant, increasing or decreasing returns to scale? For the curious student: http://demonstrations.wolfram.com/ConstantElasticityOfSubstitutionProduction/...
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## This note was uploaded on 04/19/2010 for the course ECON Econ 11 taught by Professor Mcdevitt during the Fall '07 term at UCLA.

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