Can you please help me with the problem about negative externality below?

4. (Negative production-consumption externality.) A steel plant is closely located near a lake where a boat rental store is also located. The steel plant faces the following inverse demand curve: 105 = 200 qs, where 395 is the price of steel and qs is the quantity of steel. The plant's cost function is cs(qs) = 29%. Similarly, the boat rental store faces the inverse demand function: 193 = 100 qB 293, where :03 is the price of a boat rental and 113 is the quantity of boat rentals. In words, as the steel plant produces more steel, the demand for boat rentals decreases (because pollution makes a boat ride less pleasant). The store's cost function is given by: CB (.93) = 0.51%. (Note: Throughout this question, you can assume that 800s are satised.) (a) (6) Solve the private prot maximization problems for the plant and the store. For both businesses, calculate the optimal quantities, prices and prot levels. (b) (6) Solve for the socially efcient solution. In other words, assume that a social planner owns both businesses. Similar to part a), nd quantities, prices, and the joint prot level. Specify how much each business contributes towards joint prots. (c) (2) Compare the rm/ joint prot levels between parts a) and b). (d) (4) You work for the environmental agency regulating pollution in the lake. If you want to implement a quota, on which business would you impose the quota? And at what level would you set it? In terms of quantities, prices and prot levels, for both rms, what are the new equilibrium levels? (Hint: You need no further calculations.) (e) (6) Instead, consider now imposing a Pigouvian excise tax on the steel plant. Solve the new prot maximization problem for the steel plant, and nd the equilibrium excise tax, t*, that achieves the socially efcient outcome. (f) (6) Finally, let's consider the Coasian solution, i.e., implementing and enforcing property rights and allowing trade. As the government agency you decide that the boat rental store has the right to a clean lake. Furthermore, you create a \"pollution rights market\" where the steel plant can buy from the boat rental store the rights to pollute the lake, i.e., the steel plant can pay a price, 3%, for the right to pollute enough to produce one unit of steel. Without using any shortcuts, and by solving the prot maximization problems for both businesses, nd the equilibrium price of the pollution rights, 1)}. Conrm that the equilibrium quantities and prices for both businesses are identical to those from the socially efcient solution