Chap_5_Solutions_Odd

Chap_5_Solutions_Odd - Chapter 5: Answers to Questions and...

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Chapter 5: Answers to Questions and Problems 1. a. When K = 16 and L = 16 , ( 29 ( 29 0.75 0.25 16 16 16 Q = = . Thus, AP L = Q/L = 16/16 = 1. When K = 16 and L = 81 , ( 29 ( 29 ( 29 ( 29 0.75 0.25 16 81 8 3 24 Q = = = . Thus, AP L = 24/81 = 8/27 . b. The marginal product of labor is ( 29 3 4 2 L MP L - = . When L = 16 , ( 29 3 4 2 16 1/ 4 L MP - = = . When L = 81 , ( 29 3 4 2 81 2 / 27 L MP - = = . Thus, as the number of units of labor hired increases, the marginal product of labor decreases ( 29 ( 29 16 1/ 4 2 / 27 81 L L MP MP = = , holding the level of capital fixed. c. We must equate the value marginal product of labor equal to the wage and solve for L. Here, ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3/4 3/ 4 $100 2 200 L L VMP P MP L L - - = = = . Setting this equal to the wage of $25 gives ( 29 3/ 4 200 25 L - = . Solving for L , the optimal quantity of labor is L = 16. 2. 3. The law of diminishing returns is the decline in marginal productivity experienced when input usage increases, holding all other inputs constant. In contrast, the law of diminishing marginal rate of technical substitution is the rate at which a firm can substitute among different inputs while maintaining the same level of output. 4.
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This note was uploaded on 12/03/2011 for the course MANEC 387 taught by Professor Crawford,l during the Fall '08 term at BYU.

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Chap_5_Solutions_Odd - Chapter 5: Answers to Questions and...

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