In a market for a dirty good, the inverse demand function is given by p = 100 - y, and the private marginal cost of production is given by MC = 10 + y. The pollution generated by this industry creates external damages given by the constant marginal external cost of 2 dollars.
(1) Find the competitive equilibrium without regulation (Hint: p = MC)
(2) Find the socially optimal output(Hint: p = MC + 2)
(3) Determine the Pigovian tax that would result in a competitive market producing the socially efficient output