EBF 200, Section 2 Fall 2017 Homework 5 Due at the beginning of class on Thursday, December 7th. Your homework must be typed and stapled. Please show ALL work and FULLY explain ALL answers. Please be thorough. No hand written assignments will be graded. You may use Excel to produce graphs, although other software programs can be used as well. If you need assistance with Excel, please visit the TAs or instructor during office hours. All graphs should use at least 50 points (non-integer numbers allowed). Provide all the data that you use in your graphs. 1.) (30 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 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. 2.) (30 points) The documentary Gasland became notorious for showing homeowners with private water wells with homes near hydraulic fracturing sites lighting the water from their faucets on fire. In addition, there are numerous other potential hidden costs from hydraulic fracturing that impact homeowners that have been much discussed and debated in the popular and scientific presses. Requiring leases to be negotiated with homeowners located near potential drilling sites prior to the commencement of drilling may provide a way for homeowners to internalize the hidden costs of hydraulic fracturing through Coasian bargaining. Suppose that a 'representative' homeowner, denoted by subscript has a marginal cost function given by: = 3, where is the number of wells drilled within 100 miles of the homeowner by Marcellus Gas LLC, an unconventional gas producer. The total costs to the homeowner are given by: = 1.5 2 . The marginal benefit (profits) to Marcellus Gas LLC, denoted by the subscript , is given by: = 0.5 + 50, and total benefits given by: = 0.25 2 + 50. a. Suppose homeowners have the property right. How many wells are drilled prior to entering negotiations? What is welfare for homeowners prior to entering negotiations? What is welfare for the gas firm prior to entering negotiations? b. Now suppose that there are no transaction costs and the two economic agents enter into negotiations. Since homeowners have the property right, assume as we have done in the past that they receive the entirety of the Coasian surplus. What is the number of wells that emerge after negotiations? What is the Coasian surplus after negotiations? What is welfare for homeowners after negotiations? What is welfare for the gas firm after negotiations? c. Do you think that Coasian bargaining is likely to achieve the Pareto efficient outcome in this case? Why or why not? d. Suppose the government instead wished to impose a Pigouvian tax on the gas firm to achieve the Pareto efficient number of wells. At what level should the tax be set to achieve this objective? Would the gas firm prefer this outcome to the Coasian solution obtained in part b? Would consumers prefer this outcome to the Coasian solution? e. If instead, gas firms had the property right, would they prefer the resulting Coasian outcome to the tax from part d? 3. (40 points) The supply and demand for gasoline are given by: Demand: P = 100 - Q Supply: P = 0.2+Q Suppose the marginal external costs of gasoline consumption (in dollars per unit of gasoline) are 0.5Q and the total external costs of gasoline consumption are 0.25Q2. Construct a column of values of from 0.1 to 5 in Excel. a.) Add as one column in Excel, the Pareto optimal allocation as a function of , for each value of . b.) Add as a column in Excel the total external costs under the Pareto optimal allocation from a. c.) Add as a column in Excel the total wealth under the Pareto optimal allocation from a. d.) Add as two columns in Excel (one for price, one for quantity), the no policy competitive equilibrium as a function of , for each value of . e.) Add as a column in Excel the marginal elasticity of supply, , evaluated at the competitive equilibrium from d. f.) Add as a column in Excel the marginal elasticity of demand, , evaluated at the competitive equilibrium from d. g.) Add as a column in Excel the total external costs under the no policy competitive equilibrium from d. h.) Add as a column in Excel the total wealth under the no policy competitive equilibrium from d. i.) Consider a Pigouvian tax of $20/gallon on gasoline. Add as two columns in Excel, the after tax competitive equilibrium as a function of , for each value of . j.) Add as a column in Excel the total external costs under the after tax competitive equilibrium from i. k.) Add as a column in Excel the total welfare under the after tax competitive equilibrium from i. l.) Add as a column in Excel the change in total external costs due to the tax relative to the no tax competitive equilibrium, . m.) Add as a column in Excel the efficiency costs due to the presence of the tax, (this is just the standard DWL due to the tax, ignoring external costs). n.) o.) Add as a column in Excel the change in total wealth due to the tax relative to the no tax competitive equilibrium, . p.) Add as a column in Excel the change in total wealth due to the tax relative to the Pareto optimal allocation, . q.) In Excel, plot on the y-axis and on the x-axis. r.) In Excel, plot on the y-axis and on the x-axis. s.) In Excel, plot on the y-axis and on the x-axis. t.) In Excel, plot on the y-axis and on the x-axis. u.) In Excel, plot on the y-axis and on the x-axis. v.) Explain your results from t, given l, r, and s. For what value of does the Pigouvian tax lower welfare? w.) Explain your results from u, given l and p. For what value of does the Pigouvian tax get closest to the Pareto optimum? Explain why this is so