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 nitrogen-rich fertilizers 'run off' farmer's fields when it rains, 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. Suppose the government is considering imposing a tax, = $180/ton on the farmers who live within 100 miles of the Chesapeake Bay for each ton of nitrogen fertilizer they apply to their fields. Farmer's demand for fertilizer, , is given by: = 300 1.5. Fertilizer producers supply fertilizer according to the following marginal cost function: = 30 + 3. Suppose the marginal external costs that fertilizer imposes on marine life in the waterway is given by: = 90.

a. What is the competitive equilibrium without the tax? How much total wealth is created in this case? (remember to include the total external costs!)

b. What is the competitive equilibrium with the tax? How much total wealth is created in this case? (remember to include the total external costs!)

c. How does total wealth under the competitive equilibrium with the tax compare to total wealth under the competitive equilibrium without the tax?

d. What is the Pareto optimal equilibrium? How much total wealth is created in this case?

e. How does total wealth under the competitive equilibrium without the tax compare to total wealth under the Pareto optimum equilibrium?

f. How does total wealth under the competitive equilibrium with the tax compare to total wealth under the Pareto optimum equilibrium?

g. What would the tax need to be to maximize total wealth? Explain your answer.