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Question 4: (15 points) Consider a steel firm that is deciding how much abatement in carbon emission to achieve. The firm gains a benefit from carbon abatement, because carbon abatement enhances the firm's reputation in social responsibility and thus demands for its steel. The firm's marginal private benefit of abatement is given by: MB = 400-8Q where is the level of abatement, in tons of carbon emission reduction. The firm's marginal cost of carbon abatement is given by: MC = 40+ Q In addition to the private benefit of carbon abatement accruing to the firm, there is also a marginal external benefit to others, which is given by: MEB 100-Q (a) Find an expression for the social marginal benefit (SMB) in this case, defined as you think appropriate. (b) Calculate the socially efficient level of abatement. (c) Calculate the level of carbon abatement that will arise if the firm acts in its self-interest only. (d) Now the government sets an abatement subsidy of $40 per unit of abatement (ton of carbon emission reduction). What is the competitive equilibrium with the subsidy? (e) Is this subsidy optimal? Why? Should the abatement subsidy be increased or decreased, to achieve the social optimum? Please explain.