Ch07app Textbook Answers

Ch07app Textbook Answers - Chapter7Appendix,Questions14.

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Chapter 7 Appendix, Questions 1-4. 1.  Of the following production functions, which exhibit increasing, constant, or decreasing  returns to scale? a. F(K, L) = K L b. F(K, L) = 10K + 5L c. F(K, L) = (KL) .5 Returns to scale refer to the relationship between output and proportional increases in  all inputs.  This is represented in the following manner (with  λ > 0) : F( λ K λ L ) >  λ F( K, L ) implies increasing returns to scale; F( λ K λ L ) =  λ F( K, L ) implies constant returns to scale; and F( λ K λ L ) <  λ F( K, L ) implies decreasing returns to scale. a.  Applying this to F( K, L ) =  K 2 L , F( λ K λ L ) = ( λ K ) ( λ L ) =  λ 3 K 2 L  =  λ 3 F( K, L ). This is greater than  λ F( K, L ); therefore, this production function exhibits increasing  returns to scale. b.  Applying the same technique to F( K, L ) = 10 K  + 5 L , F( λ K λ L ) = 10 λ K  + 5 λ L  =  λ F( K, L ). This production function exhibits constant returns to scale. c.  Applying the same technique to F( K,   L ) = ( KL ) .5 , F( λ K λ L ) = ( λ K   λ L ) .5  = ( λ 2 ) .5  ( KL ) .5  =  λ ( KL ) .5  =  λ F( K, L ). This production function exhibits constant returns to scale. 2.  The production function for a product is given by q = 100KL.  If the price of capital is  $120 per day and the price of labor $30 per day, what is the minimum cost of producing  1000 units of output? The cost-minimizing combination of capital and labor is the one where MRTS MP MP w r L K = = . The marginal product of labor is   K L q 100 = .   The marginal product of capital is  L K q 100 = .  Therefore, the marginal rate of technical substitution is 100 100 K L K L = . To   determine   the   optimal   capital-labor   ratio   set   the   marginal   rate   of   technical 
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This note was uploaded on 12/12/2009 for the course ECON 2296 taught by Professor Gray during the Spring '09 term at Langara.

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Ch07app Textbook Answers - Chapter7Appendix,Questions14.

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