Consider a firm that produces an output using two inputs so that x=f(l₁,l₂). Pollution is proportional to one of the inputs. The polluting firm has market power in the market for l₁. Denote the inverse supply function for l₁ by w₁(l₁). Assume that the polluting firm is subject to an emission tax.

(a) Solve the polluting firm’s profit maximization problem. Distinguish the cases where l₁ is the polluting input or clean input, respectively.

(b) Derive the comparative static effects on raising the emission tax rate, again distinguishing the cases when l₁ is the polluting or clean input.

(c) Determine the second-best optimal tax rate for the two cases.

(d) How could the regulator achieve the first-best outcome?