Question: each firm belonging to a competitive industry has the following...
Each firm belonging to a competitive industry has the following long-run cost function
C(q) = 10q − 2q^2 + q^3
where q denotes the output of a representative firm.
Firms can enter and exit the industry freely. The industry has constant costs: input prices do not change as industry output changes. The market demand facing the industry is given by
Q = 20 – P
(a) Derive the long-run industry supply curve.
(b) How many firms operate in the industry?
(c) Suppose a regulator imposes a lump-sum tax of 8 on each firm. Does the
output produced by a firm rise or fall as a consequence of this policy? Explain.
(Hint: Consider the following equation:
−(8/q^2) − 2 + 2q = 0
(d) How much revenue does the tax policy in part (c) raise?