3) (10 points ) In the analysis of the optimal level of a public good , G, suppose that each person's utility unction is quasilinear Show that the optima G is unique and independent of and if society has adequate resources DUGG + PR. Remember that the optimal level of a public goods is the sum of the individual MRSs . 4) (30 points ) Consider the emissions of an atmospheric pollutant , benzene . The graph below illustrates the market for benzene Market for Benzene 500 450 400 350 Marginal Cost of Abatement ($/ton) Firm 2 Firm 1 50 2 6 B 10 12 14 16 18 20 Millions of tons of Benzene a) How much will the firms pollute before any policy intervention ? b) If the government implemented a cap -and -trade system , distributing a total of 12 million permits with 6 million to each firm , who would sell and who would buy permits ? Explain in words and graphically c) How much would the seller be willing to accept , and how much will the buyer be willing to pay ? d) What is the equilibrium price of permits , and the equilibrium quantity of benzene production ? After the exchange of permits on the open market , how much does each firm emit ? Describe using a graph