A firm's production function is Q=70L06 K03. Its marginal product of labor is thus MP =...

 

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A firm's production function is Q=70L06 K03. Its marginal product of labor is thus MP = 42L-0.4 K0.3 and its marginal product of capital is MPK = 21L0.6 K-0.7 a. What returns to scale does this production function exhibit: constant, increasing, or decreasing? Show mathematically. b. Suppose the wage rate is $12 and the rental rate for capital is $48. Show that the firm is not minimizing cost when it employs 40 workers (L) per day and 15 machines (K) per day. c. How should this firm adjust its use of capital and labor to minimize the cost? You do not need to solve for an actual amount of each. Just indicate the direction of change of each assuming it stays on the same isoquant. Briefly explain your answer. A firm's production function is Q=70L06 K03. Its marginal product of labor is thus MP = 42L-0.4 K0.3 and its marginal product of capital is MPK = 21L0.6 K-0.7 a. What returns to scale does this production function exhibit: constant, increasing, or decreasing? Show mathematically. b. Suppose the wage rate is $12 and the rental rate for capital is $48. Show that the firm is not minimizing cost when it employs 40 workers (L) per day and 15 machines (K) per day. c. How should this firm adjust its use of capital and labor to minimize the cost? You do not need to solve for an actual amount of each. Just indicate the direction of change of each assuming it stays on the same isoquant. Briefly explain your answer.

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a To determine the returns to scale of the production function we examine the relationship between inputs labor and capital and output quantity produc... View the full answer