Suppose that the long-run cost function of a price-taking firm is

C(q)=q² and that the output (per-unit) price is p>0. Now the government imposes a per-unit tax t such that 0tp

(After the tax, the firm earns a revenue of pt per unit of output produced.)

** Part a (5 marks)

State the firm's long-run profit maximization problem in terms of p,q,t.

** Part b (5 marks)

Find the tax revenue tq earned by the government given p=3 and t=1, given that the firm optimizes its profit.

** Part c (5 marks)

Show that the firm would/would not consider shutting down (produce zero units) given t=2 and p=3.

** Part d (5 marks)

Now suppose that the government can change t. Find the level of t that optimizes the tax revenue, given p=2.