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You are an efficiency expert hired by a manufacturing firm that uses K and L as...

You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w (price of labor) = $40, r (price of capital) = $100, MPL = 20, and MPK = 40 is the firm minimizing cost? Please explain and show any calculations.

(b) The production function for a competitive firm is Q = K0.5L0.5. The firm sells its output at a price of $10 and can hire labor at a wage of $5.

Marginal Product of labor = 0.5K0.5L0.5

Capital is fixed at 25 units. What is the profit-maximizing quantity of labor? Please show your calculations.

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Answer #1

a. WA W = $40 r= $100 MPL= 20 MPK = 40 Cost minimizing formula: MPL/w = MPK/r 20/40 = 40/100 0.5 = 0.4 Thus, ratio of MPL/w iBy substituting the value of K, MPL = 0.5K^0.5L^0.5 MPL = 0.5*2540.5L^0.5 MPL = 2.5L0.5 Marginal revenue product of labor = M

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