Making dresses in a labor intensive process. Indeed, the production function of

Question

Making dresses in a labor intensive process. Indeed, the production function of a dress making firm is well described by the equation Q=L - L^2/800, where Q denotes the number of dresses per week and L is the number of labor hours per week. The firms cost of hiring an extra hour of labor is $20 per hour (wage plus fringe benefits.) The firm faces the fixed selling price, P = $40. a.) How much labor should the firm employ? What are its resulting output and profit? b.) Over the next 2 years, labor costs are expected to be unchanged, but dress prices are expected to increase to $50. What effect will this have on the firm's optimal output? Explain. Suppose that inflation is expected to increase the firm's labor cost and output price by identical (percentage) amounts. What effect would this have on the firm's output. c.) Finally, suppose that MCL =$20 and P=$50 but that labor productivity (output per labor hour) is expected to increase by 25%over the next 5 years. What effect would this have on the firm's optimal output? Explain.

Explanation / Answer

Revenue = PQ =40L-(L^2)/200 Marginal Revenue= 40-L/10 Marginal Revenue = Marginal Cost 40-L/10 = 20 Solving for L: L=200 200 units of labor are employed Now plug in the labor employed into the production function: Q(200) = 200-(200^2)/800 = 150 150 dresses are produced Profit = Total Revenue-Total Cost TR = 40*Q=40*150=$6000 TC = 20*L = 20*200=$4000 6000-4000=$2000 The profit is $2000 The other questions have the same process, you just have to findthe quantity produced again by equation marginal revenue andmarginal cost and solve for quantity. Report Abuse

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