Please help solve all parts

Question 15 (30 points) For a Mining(M) firm and a Farming(F), letting P indicate the price of output and C represent total cost, please use the information below to answer the following questions. Note that Mining production affects the farming activity and it enters the Cost function of farming as an externality. a PM = 10, CM(M) = 0.5M2 + 3M + 2, CM (0) = 0 P; = 7, (It-(F) = 0.5F2 + 0.5FM, CF (0) = 0 Determine the level of output for each firm and total level of profit when the Mining firm and farming rm act independently without regard for their impact on the other rm. Determine the level of output for each firm and total level of profit when the mining firm and farming rm merge. If the right to clean air is given to the Farming firm, it can legally stop the Mining firm to producing any pollution (and hence, no production) if required. What will be the maximum profit and output of both firms? If the right to pollute is given to the Mining firm, no one can legally stop the Mining firm from extracting metals and pollution. What will be the maximum prot and output of both rms? Assume that all assumptions of Coase theorem hold here. . What does the Coase theorem state in this type of situation? Argue its logic of the expected consequences, as stated in the theorem. Now, let's introduce transaction cost. Any transaction will be costly and the buyer will have to pay 1.5% as the court fee. That means, in order to buy the second rm, the rst rm will have to pay 1.5% more and vice versa. Does introduction of this transaction cost change your answer in part (e)? If yes, why? If no, why not