The long-run average cost for production of hard-disk drives is given by AC(Q) = wr(12020Q + Q2),

Question:

The long-run average cost for production of hard-disk drives is given by AC(Q) = ˆšwr(120ˆ’20Q + Q2), where Q is the annual output of a firm, w is the wage rate for skilled assembly labor, and r is the price of capital services. The corresponding long-run marginal cost curve is MC(Q) = ˆšwr(120 ˆ’ 40Q + 3Q2). The demand for labor for an individual firm is

The price of capital services is fixed at r = 1.
a) In a long-run competitive equilibrium, how much output will each firm produce?
b) In a long-run competitive equilibrium, what will be the market price? Note that your answer will be expressed as a function of w.
c) In a long-run competitive equilibrium, how much skilled labor will each firm demand? Again, your answer will be in terms of w.
d) Suppose that the market demand curve is given by D(P) = 10,000/P. What is the market equilibrium quantity as a function of w?
e) What is the long-run equilibrium number of firms as a function of w?
f ) Using your answers to parts (c) and (e), determine the overall demand for skilled labor in this industry as a function of w.
g) Suppose that the supply curve for the skilled labor used in this industry is Î“(w) = 50w. At what value of w does the supply of skilled labor equal the demand for skilled labor?
h) Using your answer from part (g), go back through parts (b), (d), and (e) to determine the long-run equilibrium price, market demand, and number of firms in this industry.
i) Repeat the analysis in this problem, now assuming that the market demand curve is given by D(P) = 20,000/P.