3. Suppose that the market for a certain good has an inverse demand of = 200 . The aggregate private marginal cost for the firms that produce the good is = 20 + . However, production of the good also creates pollution with an external marginal cost of = 10 + /2. a) If this is a perfectly competitive market with no regulation, what is the equilibrium price and quantity produced? b) Suppose instead that the market is a monopoly. Calculate the profit-maximizing price and quantity. c) Determine the socially efficient price and quantity for the good. d) Calculate the socially optimal Pigouvian tax to levy on the competitive firms to make them produce at the socially efficient level.