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.

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

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