A competitive industry is in long-run equilibrium. Market demand is linear, p = a bQ, where a > 0, b > 0 and Q is market output. Each firm in the industry has the same technology with cost function c(q) = k 2 + q 2 (here q is an individual firm's output quantity and k is just a constant, not capital). (a) Solve for the long-run equilibrium market quantity and number of firms.

(b) Suppose the government imposes a per-unit tax t > 0 on every producing firm in the industry. Describe what would happen in the long run to the number of firms in the industry. What is the post-tax market equilibrium price? (Again, assume whatever is necessary of the parameters to ensure that this is positive and less than a.)