Suppose a firm has a Cobb-Douglas weekly production function Q = F(L,K)= 25L^0.5K^0.5,where L is the number of workers and K is units of capital.The wage rate is $900 per week,and a unit of capital costs $400 per week.What is the least-cost input combination for producing 675 units of output? A) L = 18; K = 40.5 B) L = 40.5; K = 18 C) L = 27; K = 60.75 D) L = 27; K = 27

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Quizplus · Accepted Answer

The least-cost input combination is found by minimizing the total cost of production, which is given by TC = wL + rK, subject to the production function Q = 25L^0.5K^0.5 = 675. Substituting the production function into the total cost equation, we get TC = 900L + 400K = 900(25L^0.5K^0.5) + 400K = 22500L^0.5K^0.5 + 400K. To minimize TC, we take the derivative with respect to L and K and set them equal to zero:dTC/dL = 11250L^-0.5K^0.5 = 0dTC/dK = 11250L^0.5K^-0.5 + 400 = 0Solving for L and K, we get L = 18 and K = 40.5.

Suppose a Firm Has a Cobb-Douglas Weekly Production Function Q