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Question 3: (26 points) In many waterways the limiting factor for algae growth is nitrogen. Algae populations may explode (bloom) when nitrogen is introduced into the waterway. This can occur when fertilizer producers released untreated nitrogen-rich wastewater, carrying nitrogen into the waterway. Large algae blooms create problems for economically valuable marine life because algae consumes the oxygen marine life needs to survive. The demand for fertilizer, F, is given by: PD = 250-3F. Fertilizer producers supply fertilizer according to the following marginal cost function: Ps= 10 + F. Suppose the marginal external costs (per ton of fertilizer) that fertilizer production on marine life in the waterway is given by: MEC = 40. What is the competitive equilibrium? How much total wealth (social surplus) is created in this case? Remember to include the total external costs! (b) What is the Pareto optimal equilibrium? How much total wealth is created in this case? (c) Now the government is considering imposing a tax, t = $80/ton, on fertilizer producers who live within 100 miles of the Chesapeake Bay for each ton of nitrogen fertilizer they produce. What is the competitive equilibrium with the tax? How much total wealth (social surplus) is created in this case? Remember to include the total external costs! (d) Is $80 per ton the optimal tax to correct this externality problem? Why? What should the optimal tax be?