Making dresses is a labor-intensive process. Indeed, the production function of
ID: 2441664 • Letter: M
Question
Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q=L-L2/800, where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $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 is its resulting output and profit?
b. Over the next two 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 instead 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 once again that MCL=$20 and P=$50 but that labor productivity (i.e., output per labor hour) is expected to increase by 25 percent over the next five years. What effect would this have on the firm’s optimal output? Explain.
Explanation / Answer
a) QL = L^2/800
R = P*QL = 40*L^2/800 = L^2/20
MRL =L/10
Now for optimization
MCL = MRL
L/10 = 20
L=200
QL = 200*200/800 = 50
Profit = 40*50 - 20*200 = -2000
b) QL = L^2/800
R = P*QL = 50*L^2/800 = L^2/16
MRL =L/8
Now for optimization
MCL = MRL
L/8 = 20
L=160
QL = 200*200/800 = 32
Profit = 32*50 - 20*160 = -1600
Now if MCL = 20+20*25% = 25
QL = L^2/800
R = P*QL = 50*L^2/800 = L^2/16
MRL =L/8
Now for optimization
MCL = MRL
L/8 = 25
L=200
QL = 200*200/800 = 50
Profit = 40*50 - 25*200 = -3000
c) QL = L^2*1.25/800 = L^2/640
R = P*QL = 50*L^2/640 = 5L^2/64
MRL =5L/32
Now for optimization
MCL = MRL
5L/32 = 20
L=128
QL = 128*128/640 = 25.6
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.