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Please help me answer the question attached!
The production function of a firm is well-described by the equation Q = L - L^2/1000, where Q denotes the quantity of output produced per week and L is the number of labor hours employed per week. This production function implies that the marginal product of labor (MPL) is given by MPL= 1 - L/500. The firm's additional cost (wages plus benefits) of hiring an extra hour of labor is $25 per hour, and the firm's fixed cost is $15,000. The output market is perfectly competitive, and the market equilibrium price is $100 per unit.
a. How much labor should the firm employ if it wants to maximize profits? What is its resulting output and profits?
b. Suppose the firm's fixed costs increase to $20,000. What effect would this have on the firm's profit-maximizing hiring, output and profits?
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