2. (15 points) Pollution in steel industry has been the problem for many countries in the history. Suppose there is a monopoly rm with private cost function (3(9) : 2:92 +8. Besides the private cost, the production of steel also generate a pollution cost (1y) : 392/2. Suppose the aggregate inverse demand function is p : 120 103;. Use a graph to clarify your solution. (a) Compute the social optimal output, prices, and total surplus. Mark the social optimal point as point A in the graph, with horizontal axis representing output quantity. (b) \\Vithout government intervention, the monopolist will ignore the pollution cost. Solve for the monopoly price, output, and prot in this case. What is the social welfare? Mark the point as B. Compare it to the result in (a). What causes the difference? (c) Suppose the government can force the rm to pay the pollution cost. Solve for the monopoly price, output, and prot in this case. What is the social welfare? Mark the equilibrium as C. Compare it to the results in (a) and (b). \\Vhat causes the differences