chap005s

chap005s - Chapter 5 Answers to Questions and Problems 1 a...

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Managerial Economics and Business Strategy, 5e Page 1 Chapter 5: Answers to Questions and Problems 1. a. When K = 16 and L = 16 , () () 0.75 0.25 16 16 16 Q = = . Thus, AP L = Q/L = 16/16 = 1. When K = 16 and L = 81 , ( ) ( ) () () 0.75 0.25 16 81 8 3 24 Q = == . Thus, AP L = 24/81 = 8/27 . b. The marginal product of labor is 34 2 L MP L = . When L = 16 , 216 1 /4 L MP . When L = 81 , 281 2 /27 L MP . Thus, as the number of units of labor hired increases, the marginal product of labor decreases ( ) 16 1/ 4 2 / 27 81 LL 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, ( ) 3/4 \$100 2 200 VMP P MP L L −− = . Setting this equal to the wage of \$25 gives 200 25 L = . Solving for L , the optimal quantity of labor is L = 16. 2. See Table 5-1. (1) (2) (3) (4) (5) (6) (7) Capital Labor Output Marginal Product of Average Value Marginal KL Q MP K AP K L VMP K 02 00 - - - - - - 12 0 5 0 5 0 5 0 2 . 5 0 1 0 0 2 20 150 100 75 7.50 200 3 300 15 4 400 5 450 50 90 22.50 6 475 25 79.17 23.75 7 0 67.86 0 82 0 4 5 0 - 2 5 56.25 -50 9 44.44 -100 10 30 -200 11 -150 13.64 -300 Table 5-1 a. Labor is the fixed input while capital is the variable input. b. Fixed costs are 20(\$15) = \$300. c. To produce 475 units in the least-cost manner requires 6 units of capital, which cost \$75 each. Thus, variable costs are (\$75)(6) = \$450. d. Using the VMP K = r rule, K = 5 maximizes profits. e. The maximum profits are \$2(450) \$15(20) \$75(5) \$225 −= .

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Page 2 Michael R. Baye f. There are increasing marginal returns when K is between 0 and 3. g. There are decreasing marginal returns when K is between 3 and 11. h. There are negative marginal returns when K is greater than 7. 3. The law of diminishing marginal 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 a property of a production function stating that as less of one input is used, increasing amounts of another input must be employed to produce the same level of output. 4. a. FC = 50 b. () () () () 23 10 25 10 30 10 5 10 \$8,250 VC =+ += . c. () () ( ) ( ) 300 , 8 \$ 10 5 10 30 10 25 50 10 3 2 = + + + = C . d. () 5 \$ 10 50 \$ 10 = = AFC .
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chap005s - Chapter 5 Answers to Questions and Problems 1 a...

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