The production function for a competitive firm is Q = K^.5L^.5.The firm sells its output at a price of $10, and can hire labor at a wage of $5.Capital is fixed at one unit.The maximum profits are A)5. B)10. C)15. D)none of the statements associated with this question are correct.

Question

Quizplus · Accepted Answer

The firm's profit function is given by:π = PQ - wL - rKπ = 10Q - 5L - rSubstituting the production function into the profit function, we get:π = 10K^.5L^.5 - 5L - rSince capital is fixed at one unit, we have:π = 10K^.5L^.5 - 5L - rTaking the derivative of the profit function with respect to L and setting it equal to zero, we get:dπ/dL = 5K^.5L^-.5 - 5 = 0Solving for L, we get:L = 1Substituting L = 1 into the production function, we get:Q = K^.5L^.5 = K^.5Substituting Q = K^.5 into the profit function, we get:π = 10K^.5 - 5 - rSince capital is fixed at one unit, we have:π = 10K^.5 - 5 - r = 10 - 5 - r = 5Therefore, the maximum profit is $5.

The Production Function for a Competitive Firm Is Q =