Each firm belonging to a competitive industry has the following long-run cost function

C(q) = 10q 2q2 + q3 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/q2 2 + 2q = 0. The solution to this is q = 2.)

d. How much revenue does the tax policy in part (c) raise?