Consider the production of a competitive firm under the prevailing market price p* = $65. The inverse supply curve is the firm's MPC (marginal private cost) equaling 5 + q where q represents the quantity the firm produces. This firm's product causes pollution to the water nearby, resulting in the MSC (marginal social cost) equaling 5 + 1.2q. Note the MSC equals MPC (5+q) plus the marginal external cost (0.2q). (i). (10 marks) Find the social optimal output of the firm. (ii). (10 marks) Find the value of the Pigou tax. (iii).(20 marks) Find the value of the dead weight loss (DWL) caused by the externality if nothing is done to address the problem.