The external marginal cost of producing coal is MC external = 8Q while the internal marginal cost is MC internal = 6Q. The inverse demand for coal is given by P = 180 4Q and MR = 180 - 8Q. (a) What is the socially efficient level of output? Please show your calculations. (b) Given these costs and market demand, how much output would a monopolist produce in the absence of any government action to require the socially efficient outcome? Please show your calculations. (c) Discuss any action the government might take to induce firms in this industry to produce the socially efficient level of output.4.(5 points) The external marginal cost of producing coal is MC external = 8Q while the internal marginal cost is MC internal = 6Q. The inverse demand for coal is given by P = 180 4Q and MR = 180 - 8Q. (a) What is the socially efficient level of output? Please show your calculations. (b) Given these costs and market demand, how much output would a monopolist produce in the absence of any government action to require the socially efficient outcome? Please show your calculations. (c) Discuss any action the government might take to induce firms in this industry to produce the socially efficient level of output.