Cost-Benefit Analysis ( Spring 2025)
Assignment #1: Efficiency of the EPA’s Waste Emission Charge
This assignment is worth 100 points and is due by 11:59 pm on March 2, 2025.
You may discuss the assignment and how it can be solved with your classmates, but you must do your own work. Ultimately it is an individual assignment. All calculations and written narratives should be your own.
A Pigovian tax (also spelled “Pigouvian tax”) is a tax assessed on goods and economic activities that create negative externalities for society. The tax is meant to discourage the production or consumption of these goods and activities by creating a financial incentive against them. Ideally, the tax should be equivalent to the external damage caused by the production and use of the good or activity.
In November 2024, EPA implemented a Waste Emissions Charge (WEC) as required under the Inflation Reduction Act (IRA) of 2022. In this law, Congress directed the EPA to collect a Waste Emissions Charge (WEC) on waste emissions of methane from certain oil and gas facilities. The WEC applies to petroleum and natural gas facilities that emit more than 25,000 metric tons of CO2 equivalent per year, that exceed statutorily specified waste emissions thresholds set by Congress, and that are not otherwise exempt from the charge. This methane fee is, essentially, a Pigovian tax on methane emissions. The WEC starts at $900 per metric ton for 2024 reported methane emissions, increasing to $1,200 per metric ton for 2025 emissions, and $1,500 per metric ton for emissions years 2026 and later. More information on this rule can be found at https://www.epa.gov/inflation-reduction-act/waste-emissions-charge.
Also, in December 2023, the EPA released a report that estimated climate benefits using a new set of Social Cost of Greenhouse Gas (SC-GHG) estimates. These estimates incorporate recent research addressing recommendations of the National Academies of Science, Engineering, and Medicine (2017). One set of values in this report was the Social Cost of CH4 (i.e., the social cost of methane) using three near-term Ramsey discount rates. That report can be found at https://www.epa.gov/system/files/documents/2023-12/epa_scghg_2023_report_final.pdf.
The Regulatory Impact Analysis for EPA’s 2024 final rule implementing the methane waste emissions charge (WEC) is posted on the class site. For this assignment, you will assess the economic efficiency associated with the WEC as specified by Congress and compare it to alternative methane fee values based on EPA’s report on the social cost of greenhouse gases.
Background information on a Pigovian tax with a negative externality that can be abated
In week 3, we framed a Pigovian tax in the context of a bag tax, but then we switched to describing a more general “negative externality” from a generic polluting good. We described this in a way in which the externality's damage was added to the supply curve. The graph we used looked as follows.
In this graph, the marginal social cost is higher than the marginal private cost because the consumers do not consider the damage from the externality. As a consequence, the market supplies too much of this polluting good.
In this scenario, placing a Pigovian tax increases the price of these goods, which drives some buyers out of the market and reduces some deadweight loss. If the Pigovian tax is set equal to the social damage caused by the externality, then the benefits of the tax (B + C + F) exceed the cost or the lost market transactions (B +F), and the optimal amount of external damage is reduced, resulting in benefits equal to the deadweight loss, (C).
This is the standard approach to illustrate the benefits of a Pigovian tax, but it has several assumptions embedded in the example. In particular, this example assume that the externality is entirely inseparable from the output of the market good. Notice that we didn’t discuss “abating” the pollution, or doing something to continue consuming the same amount of the good but reducing pollution involved. In this example, the only way to reduce the external damage was to consume less of the market good.
An alternative is if it is possible to reduce the pollution from the production of the good, but at some cost to the supplier. This is what we mean by “abatement.” Firms producing the market good can reduce the damages from the pollution by expending some amount of money, referred to as “abatement costs.”
For example, imagine a factory that produces some market good, but that production also cause air pollution. The firm can continue to make the good but can reduce the air pollution by, say, releasing the pollution through a tall smoke stack to increase dispersion, using less pollution-intensive inputs, or putting a device on the smokestack that removes pollutants from the exhaust stream. Each of these is possible but may come at a different cost. A rational firm looking to reduce pollution will choose the least costly approaches first and then move on to the next most expensive as more pollution is reduced.
To illustrate this, we can focus exclusively on the damage function from the externality and not include the supply curve. That is, we are only looking at the difference between S* and S# in the graph above. We can put emissions on the x-axis and the monetary cost of that pollution on the y-axis. This would look like the following.
We assume that the total damages rise as emissions increase, so the total damage function increases. A common assumption is that the damages rise at an increasing rate, so the total damage function curves upward. The marginal damages from pollution emissions is the slope (or the first derivative) of the total damage function, which we represent as an increasing, linear marginal damage function. This doesn’t have to be the case. If the total damage function was an upward-sloping linear function, then the marginal damage function would be a horizontal line equal to the slope of the total damage function. In either case, the marginal damage at any level of emissions is the cost incurred from the last unit of pollution. The total damages are the area under the marginal damage curve (or the integral under the marginal damage function), labeled “D” in the graph above.
We can illustrate the abatement costs similarly, as follows.
If the firm is not abating any pollution, then the total abatement cost is zero. With no abatement, emissions are at the maximum amount the firm will produce. If the firm chooses to reduce emissions, the total cost of that abatement will rise, and the emissions from the firm will decline. This is represented as a total abatement curve that slopes downward as emissions increase. If total abatement increases at an increasing rate as emissions are reduced, the total abatement curve looks like we have drawn it. Similar to the discussion above, the marginal abatement cost function is the slope (or first derivative) of the total abatement curve, and is represented by a linear, downward-sloping line. The marginal abatement cost is the cost of reducing one more unit of emission at any level, and the total abatement cost is the area under the marginal abatement cost curve, labeled “C” in the graph above.
Combining these two graphs, the marginal abatement cost (MAC) function slopes downward and the marginal damage function (MD) function slopes upward.
The optimal level of emissions is (hopefully, unsurprisingly) where the marginal damages of emissions equals the marginal cost of abating those emissions. As you learned from the lectures, this optimal level of emissions can be achieved by setting a tax equal to the point of this intersection of MD and MAC. The welfare impacts of this tax are as follows.
· The tax would encourage the firm to reduce emissions to e*. This reduction would require the firm to pay a total of C in abatement costs (remember, total abatement costs are the area under the MAC function). In addition, the firm would have to pay the tax rate for all emissions it still produces, so it would pay A + B in taxes. So, the total cost to the firm would be A + B + C.
· Those affected by the emissions can be considered third parties, and they gain the benefit of the area under the portion of the damage function that has been reduced. So, third parties benefit by C + D. Note that this area differs from how we displayed the total damages above. Before the tax, the total damages the third parties endured was B + C + D. After the tax, the third parties only suffer B. So, the benefits to these third parties are C + D.
· The government receives the tax revenue of A + B, and presumably will transfer that tax money to various people in society.
· So, the social benefit of this action is area D.
This is the scenario we are addressing with the methane fee. Oil and gas facilities produce fossil fuels, but some of that production releases methane emissions. Methane emissions cause climate damage, and the government is imposing a tax to reduce the emissions and the associated damage. If the tax is set equal to the marginal damages at the optimal level, e*, then the tax is an optimally efficient Pigovian tax. As it turns out, marginal damages from climate damages can be represented as a flat line. This is because the total damage function is almost linear for small amounts of emission reductions, so the marginal damage function can be represented as a horizontal line.
In this case, the firm suffers total costs of A + C, comprised of C in total abatement costs and A in tax expenditures. Third parties gain benefits of C + D from reduced methane emissions. Finally, the government gains tax revenue of A. So, the total benefit is D.
1. Familiarize yourself with the 2024 Regulatory Impact Analysis of the Waste Emissions Charge.
a. Read the Executive Summary (from page 1-1 to 1-10) to get a general sense of the rule.
b. Notice that the Executive Summary says the following.
The social cost of energy market impacts is the loss in consumer and producer surplus value from changes in natural gas market production and prices. The economic impacts analysis uses a partial equilibrium model and estimates that the impact of the gas market is minimal, with the largest impact occurring in the first few years with a price increase of less than 0.1% and a quantity reduction of less than 0.1%.
As a consequence, you will not analyze the social cost of energy market impacts. You will only analyze the total cost of the the engineering costs for methane mitigation actions implemented by the oil and natural gas industry to reduce WEC obligations and compare those costs to the social benefits.
c. Read the introduction to Chapter 5 and Section 5.1 (from page 5-1 to the top of page 5-6) to understand the EPA’s approach to estimating the social cost of methane mitigation. Also read the section on the oil and gas sector’s methane mitigation potential and the WEC transfer payments (from the last paragraph on page 5-15 to page 5-17)
d. Read the introduction to Chapter 6 and Section 6.1 from page 6-1 to the top of page 6-14 to understand the EPA’s methodology to estimate the climate benefits from methane mitigation. Note that there is more information in Section 6-14 (from page 6.15 to page 6-12) but you will not need this information for this assignment. There is a lot of information in the pages you will read, but only Tables 6-1 and 6-2 contain the information you will need for this assignment. Avoid getting bogged down in the details and read the chapter for a general understanding.
e. Reach Chapter 7 (from page 7-1 to page 7-9) to understand how to compare the costs and benefits that you will calculate.
2. (20 points) Develop a conceptual understanding of estimating the costs of methane abatement using a methane fee. Using the data for 2026 from the RIA, estimate the quantity of methane emission abatement that would be induced using the congressionally mandated WEC and the methane emission abatement that would occur if the WEC were set at the EPA’s Social Cost of CH4 using the three near-term Ramsey discount rates. Calculate the social cost of the methane mitigation, the tax revenue (which is an economic transfer rather than a social cost), and the social benefits associated with these four possible WEC values.
a. (2 points) Draw a graph with the marginal abatement curve as we have done in class. Put dollars (in 2019$) on the Y-axis and methane emissions (in thousands of metric tons) on the X-axis. Draw a downward sloping, linear marginal abatement curve, from some y-intercept near the top of the y-axis to an x-intercept near the right side of the x-axis, and label this curve “MAC.”
b. (2 points) Draw the congressionally mandated methane tax rate. Draw a horizontal, straight line starting near the bottom quarter on the y-axis, and extend this line the same length as the x-axis. Label this line as “WEC.” This line will represent the congressionally-mandated WEC.
c. (2 points) Draw EPA’s estimates of the social cost of methane emissions at the three near-term Ramsey discount rates of 1.5%, 2.0%, and 2.5%. Draw three more horizontal lines above the WEC, each one progressively higher than the previous one, but all of them below the y-intercept for the MAC line. Label these three progressively higher curves, “SC-GHG 2.5%,” “SC-GHG 2.0%,” and “SC-GHG 1.5%,” respectively. These lines represent the EPA’s Social Cost estimate of the social damages from methane emissions, depending on the near-term Ramsey discount rates. These would also be EPA’s estimates of the benefits of reducing methane emissions.
d. (2 points) Label the methane emissions that would occur if the WEC were implemented at the congressionally mandated value. On the x-axis, indicate the amount of methane emissions that would be expected to occur with the WEC.
e. (5 points) Using what you have learned in class, label the areas of the graph representing the abatement cost associated with a methane fee equal to the MAC, the tax revenue, and the benefits associated with this reduction if the benefits were equal to the WEC and the EPA’s the social cost of methane emissions at the three near-term Ramsey discount rates. Using letters (e.g., A, B, C, etc.), label the areas in your figure. Then report the area (e.g. A) or sum of areas (e.g., A+B) that represent the following values.
i. The total cost of abatement for the methane emission reductions that would occur if the WEC were implemented.
ii. The tax revenue that would be expected from the WEC.
iii. The benefits of this emission reduction assuming the benefits could be measured using three different values.
1. Benefits per ton are equal to the SC-GHG 2.5% value.
2. Benefits per ton are equal to the SC-GHG 2.0% value.
3. Benefits per ton are equal to the SC-GHG 1.5% value.
f. (2 points) Label the methane emission that would occur if the methane fee were set equal to the EPA’s Social Cost of CH4 using each of the three near-term Ramsey discount rates. On the x-axis, indicate the amount of methane emissions that would be expected to occur with if the methane fee has had been set at the Social Cost of CH4 using each of the three near-term Ramsey discount rates of 1.5%, 2.0%, and 2.5%.
g. (5 points) Label the areas of the graph representing the abatement cost, the tax revenue, and the benefits if the methane fee were set equal to the EPA’s Social Cost of CH4 using each of the three near-term Ramsey discount rates. Use letters that you used to label your graph in part 2.e. (Add more letters if you need them.) For each of the SC-GHG values (at the near-term Ramsey discount rates of 1.5%, 2.0%, and 2.5%), report the area (e.g. A) or sum of areas (e.g., A+B) that represents the following values.
i. The total cost of abatement for the methane emission reductions.
ii. The tax revenue that would be expected.
iii. The benefits of this emission reduction, assuming that the benefits are only measured at the SC-GHG value for the discount rate being evaluated.
Note that unlike part 2.e, where you had three benefits for one methane tax (equal to the congressionally mandated WEC), here you will have one benefits measure for each SC-GHG value. In other words, when evaluating the SC-GHG 2.5%, you will report the total cost of abatement, the tax revenue, and the benefits assuming that the SC-GHG 2.5% value is used consistently for the methane fee and the benefits measure. You will not use the benefits for the SC-GHG 2.0% and SC-GHG 1.5% when analyzing the SC-GHG 2.5% value. Similarly, you will evaluate the SC-GHG 2.0% and SC-GHG 1.5% values assuming that they are used consistently for the methane fee and the benefits measure, each with only one benefits measure. (If you get confused, send us a message or ask in the discussion section for this assignment.)
3. (35 points) Re-draw your marginal abatement curve graph from part 2 with values for 2026 and calculate the areas that you specified in parts 2.e and 2.g.
a. (4 points) Obtain the necessary data from the 2024 Regulatory Impact Analysis of the Waste Emissions Charge and report the values for 2026 and report that data here.
i. From Table 1-5, report the following.
1. WEC Payments in Policy Scenario (million nominal $).
2. WEC Payments in Policy Scenario (million 2019$).
ii. From Table 5-10, report the value in 2026 for the following.
1. Net Methane Emissions Subject to WEC in Baseline (thousand metric tons).
2. Net Methane Emissions Subject to WEC in Policy Scenario (thousand metric tons).
3. Charge Specified by Congress (nominal $ per metric ton)
iii. From Table 5-9 report the value in 2026 for Total Technical Abatement Potential (kt).
iv. From Table 6-1, report the value in 2026 for the Estimates of the Social Cost of CH4, (in 2019$ per metric ton CH4) for the three Near-Term Ramsey Discount Rates.
b. (2 points) Convert the Charge Specified by Congress from nominal $ per metric ton to 2019$. Using the data for the WEC Payments in Policy Scenario that you extracted from Table 1-5, create a deflator for 2026 that can be used to convert nominal dollars to 2019 dollars. Use this deflator to convert the 2026 Charge Specified by Congress that you extracted from Table 5-10 from nominal $ per metric ton to 2019$ per metric ton. Report the Charge Specified by Congress (2019$ per metric ton) for 2026 here.
c. (5 points) Calculate the Net Methane Emissions Subject to WEC in a Policy Scenario in which the methane fee was set equal to the EPA’s Social Cost of CH4 using each of the three near-term Ramsey discount rates (1.5%, 2.0%, and 2.5%). If the methane fee has been set using one of the EPA’s Social Cost of CH4 values, then abatement would occur to point where the marginal cost of abatement is equal to the appropriate SC-GHG value. You can find this abatement level by solving for the marginal abatement curve and setting it equal to the appropriate SC-GHG value. Note that your graph has price on the y-axis and quantity on the x-axis, so, technically, it is an inverse marginal abatement cost curve. The formula for the marginal abatement cost curve can be found as follows
i. The intercept of the of the marginal abatement curve is where your MAC curve intersects the x-axis, which is the Net Methane Emissions Subject to WEC in Baseline from Table 5-10.
ii. The slope of the marginal abatement curve can be calculated as “rise over run” using the values you extracted from Table 5-10, but the “rise” is the change in net emissions between the policy scenario and the baseline, and the “run” is the WEC charge specified by Congress (in 2019$).
Report the formula for your marginal abatement curve here (and show your work) and report the net methane emissions subject to WEC assuming that the fee was set equal to the EPA’s Social Cost of CH4 using each of the three near-term Ramsey discount rates (1.5%, 2.0%, and 2.5%). Note, the net methane emissions subject to the WEC cannot be less than zero!
d. (5 points) Calculate the reductions in methane emissions due to mitigation in 2026 for your four cases (the congressionally mandated WEC value, and a methane fee equal to the EPA’s SC-GHG at the three discount rates) and confirm that these reductions do not exceed the total technical abatement potential for that year. Report the adjusted reductions in methane emissions in 2026 for these scenarios. The reductions in methane emission due to mitigation are calculated at as the Net Methane Emissions Subject to WEC in Baseline less the Net Methane Emissions Subject to WEC in Policy Scenario that you parts 3.a and 3.c. Compare this value to the Total Technical Abatement Potential from Table 5-9. Confirm that the calculated emission reduction does not exceed the technical potential and report the adjusted reduction for 2026 for each scenario here.
e. (4 points) Re-draw your marginal abatement curve graph from part 2 with the 2026 values for the following variables added to the appropriate axis.
i. Net Methane Emissions Subject to WEC in Baseline.
ii. Net Methane Emissions Subject to WEC in Policy Scenario for your four cases (the congressionally mandated WEC value, and a methane fee equal to the EPA’s SC-GHG at the three discount rate).
iii. The WEC Charge Specified by Congress (2019$ per metric ton).
iv. The Estimates of the Social Cost of CH4, (in 2019$ per metric ton) for the three Near-Term Ramsey Discount Rates (1.5%, 2.0%, and 2.5%).
f. (5 points) Using this graph and values, calculate the areas that you identified in part 2.e.
i. The total cost of abatement for the methane emission reductions that would occur if the WEC were implemented.
ii. The tax revenue that would be expected from the WEC.
iii. The benefits of this emission reduction assuming the benefits are measured using three different values.
1. Benefits per ton are equal to the SC-GHG 2.5% value.
2. Benefits per ton are equal to the SC-GHG 2.0% value.
3. Benefits per ton are equal to the SC-GHG 1.5% value.
g. (5 points) Using this graph and values and assuming that the methane fee was set equal to the EPA’s Social Cost of CH4 using each of the three near-term Ramsey discount rates, calculate the areas that you identified in part 2.g.
i. The total cost of abatement for the methane emission reductions.
ii. The tax revenue that would be expected.
iii. The benefits of this emission reduction.
h. (5 points) Report the net benefits (benefits minus costs) from mitigation for 2026 under the following scenarios.
i. The congressionally mandated WEC and benefits valued using the SC-GHG 2.5% value.
ii. The congressionally mandated WEC and benefits valued using the SC-GHG 2.0% value.
iii. The congressionally mandated WEC and benefits valued using the SC-GHG 1.5% value.
iv. A methane fee based on the SC-GHG 2.5% value and benefits values using the SC-GHG 2.5% value.
v. A methane fee based on the SC-GHG 2.0% value and benefits values using the SC-GHG 2.0% value.
vi. A methane fee based on the SC-GHG 1.5% value and benefits values using the SC-GHG 1.5% value.