VMT Research Paper

Can A Mileage Based Tax System Replace an Outdated Fuel Tax?

Kaleb Rogers Public Finance 04/03/2013

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Introduction

Public Finance is defined as “the field of economics that studies government activities and the alternative means of financing government expenditures”1. The Rhode Island State Government, as well as those of other states, is currently facing such an issue in the form of the growing gap between transportation revenues and expenditures. The fuel tax, which is a common generator of revenue across all areas of the US, has gradually weakened over the past several years as a means to finance the transportation expenditures demanded by households and businesses. Representative Linda Finn, a member of the Rhode Island House of Representatives, has recently inquired on the implementation of a Vehicle Miles Traveled (VMT) tax, which would levy tax shares on gasoline consumption based on the amount of mileage one drives rather than the gallons purchased to fuel one’s car. The proposal of such a tax reform is in the early stages of development nationwide. The proposal is especially new to the legislative body of Rhode Island. Therefore, in order to examine the pursuit of the VMT tax, this paper will evaluate the studies already performed by other states and institutions. More specifically, The Nevada Department of Transportation and The Oregon Department of Transportation have previously evaluated the transformation from a fuel tax to a VMT tax system. Representative Finn cited both of these documents as a basis for the potential future legislation sought after by the Rhode Island State Government. Furthermore, this paper will describe the necessary cost-‐benefit analysis that the public sector must perform before making an informed decision on the matter. To truly understand the urgency of the reformation of the fuel tax system, one must first understand the intentions of policy makers and econometricians as well as the motivation behind their proposals. The main issue with the current fuel tax is its independency from inflation. The research released by the Nevada Department of Transportation titled, Nevada Vehicle Miles Traveled (VMT) Fee Study describes the lack of progression in the taxable portion of gasoline in the state:

“In 1993, the pump price of a gallon of fuel was about $1.22 and the fuel tax per gallon was about 53 cents…in 2009 the price of a gallon of fuel raised to about $3.10 per gallon, yet the fuel tax per gallon stayed the same – 53 cents per gallon, meaning that the effective fuel rate dropped about 17%” 2

The fuel tax has essentially failed to increase with the price of gasoline and the rate of inflation in general. In real terms the tax revenue generated by the sale of gasoline has effectively declined over the past couple of decades. This decline in revenue is independently a cause for concern due to its loss of influence towards government financing; however, “due to an increase in vehicle miles traveled (VMT), there is an

1 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 5. Print. 2 Tian, Zong Z., Eric B. Herzik, and Et Al. "Nevada Vehicle Miles Traveled (VMT) Fee Study Phase 1." Nevada Department of Transportation, Dec. 2012. Web. <http://www.nevadadot.com/uploadedFiles/NDOT/Documents/VMT%20FEE%20STUDY%20Bk.pdf>.

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increasing demand for highway system expansion”3. The gap between revenues and expenditures in the transportation division of state governments is widened not only by the static fuel tax level, but also by the increased demand for publically provided roads. Furthermore, roads, although generally considered a public good, are more accurately described as congestible public good. This title suggests “crowding or congestion reduces the benefits to existing consumers when more consumers are accommodated”4. Because of the eventual congestion of this public good, an increase in vehicle miles traveled combined with an increasing restriction on state’s infrastructure spending is currently reducing the benefits of active drivers. Visually, Figure 1 in the Appendix shows the marginal cost of a congestible good after N consumers are accommodated. On a congestible road, the demand curve D2 results in more than the efficient output of vehicle miles traveled where MSC>MSB if the cost of travel is zero. Finally, to contribute to the already falling revenues generated by a constant fuel tax rate, the movement towards more fuel-‐efficient cars such as hybrids has further reduced the consumption of gasoline. Gasoline may be viewed as a relatively inelastic good. Due to the increasing necessity of quick transportation by both consumers and firms, the aforementioned price increases in gasoline initially had a negligible effect on the consumers’ quantity demanded in the short run. However, “when it comes to buying a new car, consumers can buy a more fuel-‐efficient one, or one that uses an alternative energy source. Thus, the quantity of gas demanded falls by larger amounts in the long run than in the short run”5. Initially, the constant tax level may have been a minor issue due to the constant levels of fuel consumption in the short run. Unfortunately, in the long run, firms have adapted to the increasing price of gasoline by developing substitutes such as hybrid cars. Consumers, now with an incentive to buy more fuel-‐efficient cars, will consume less gasoline in the aggregate. Therefore, total fuel tax revenues suffer even more so. Next, before evaluating the costs and benefits of the potential VMT fee, one must understand a basic outline of its characteristics. There have been a variety of techniques suggested by several different studies, but researches have suggested some of the more promising options. Mileage metering based on fuel consumption estimates the charges levied on the consumer when purchasing gas, which is based on each vehicles fuel economy rating as well as other attributes. This information can be transmitted through a registration sticker embedded on each vehicle.6 This method is praised for having a relatively low cost and simple transition relative to alternative methods. Conversely, at the other extreme is the option titled, coarse-‐

3 Tian, Zong Z., Eric B. Herzik, and Et Al. "Nevada Vehicle Miles Traveled (VMT) Fee Study Phase 1." Nevada Department of Transportation, Dec. 2012. Web. <http://www.nevadadot.com/uploadedFiles/NDOT/Documents/VMT%20FEE%20STUDY%20Bk.pdf>. 4 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 151. Print 5 Taylor, John B., and Akila Weerapana. Principles of Microeconomics. 6th ed. Boston: Houghton Mifflin, 2009. Cengage Learning. Web. 6 Slone, Sean. "Vehicle Miles Traveled Fees." The Council of State Governments, 2009. Web. 01 Apr. 2013.

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resolution GPS-‐based metering, which is the method used in The Oregon Department of Transportation Pilot Project. This method uses GPS technology to “identify the jurisdiction in which travel takes place without identifying the specific route of travel” 7 This method may be more accurate, and therefore more efficient, than the previous fuel consumption based measurement. Furthermore, this option may be capable of achieving low cost production if developed on a large enough scale. There are several other methods described in the various studies; however, the VMT fee generally consists of two main components: the tracking of vehicle miles traveled and the charge for traveling those miles levied at the fuel station. The common features of the VMT fee across studies are effectively portrayed by Figure 2 in the Appendix, which is taken directly from the study conducted by the Oregon Department of Transportation.8 The next section will begin the cost benefit analysis that must ensue in order to effectively determine if the project is worth consideration.

Cost – Benefit Analysis

In Public Finance, cost-‐benefit analysis is used to determine the merit of

potential public projects. The main intention of this analysis is to ensure that projects with marginal social costs that exceed the marginal social benefits are not considered. Conversely, projects that may yield positive net benefits pass this screening process and are likely to be pursued. The three main steps involved in this analysis are: Enumerating the costs and benefits of the proposed project, evaluating these costs and benefits in dollar terms, and discounting future net benefits to a present value comparable with the current costs of pursuing the project9. To begin this process, the advantages (benefits) and disadvantages (costs) of the project must first be listed and evaluated. Because this paper intends to merely outline the process of this cost-‐benefit analysis, it will not make use of specific enumerated or dollar values.

Benefits

Of all the suggested advantages in the conducted studies, the most obvious and easily quantified benefits are those relating to the potential revenue realized after the reform has been put into place. In 2007, RAND (Research ANd Development) Corporation’s evaluation of the VMT tax, Final Report -‐ Volume III: Section 1 -‐ Technical Issues Papers, concludes that VMT tolling would have significant

7 Slone, Sean. "Vehicle Miles Traveled Fees." The Council of State Governments, 2009. Web. 01 Apr. 2013. 8 Whitty, James. "The Revised VMT Taxation Concept and A New Road Usage Charge Pilot Program." The Oregon Department of Motor Vehicles, 08 Feb. 2012. Web. 01 Apr. 2013. 9 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 234. Print.

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revenue potential limited only by political considerations. Furthermore, the study predicts that the revenue generated would be much more stable due to its dependency on vehicle travel, which also determines road maintenance. Finally, the revenues generated would be more equitably distributed because VMT fees can measure the amount of travel occurring in different jurisdictions and distribute revenue accordingly. 10 For the purpose of the cost benefit analysis, these revenues must first be forecasted into the future. One must predict the aggregate miles traveled per state. Next, the total miles traveled must be applied to the VMT system chosen by the State Government. As will be described in following sections, the Nevada study outlines a variety of VMT structures that will yield alternative revenue levels. Finally, the benefits calculated in this manner must be discounted in order to compare them with the costs of pursuing the project.

A second benefit put forth by various researches is the bold claim that the movement towards a vehicle miles travel based tax system will improve not only the economic efficiency of resource allocation, but also that the change may improve the equity of tax shares levied on users. As in the previous revenue analysis, this statement also depends on the tax structure chosen by the state. To better understand the quality of this proposed benefit, one must understand these various system structures. The paper published by the Nevada Department of Transportation outlines a variety of systems. The four main categories described are the single fee system, the multiple fee system, the generalized user fee system, and the pay-‐as-‐you-‐go system. The single fee system charges a flat tax rate per mile. The multiple fee system groups vehicles into categories based on their makes, models, years of production, etc. and charges a different fee based on the given classification. The generalized user fee system incorporates all of the aspects of the multiple fee system while also defining the charge as a function of the time of day, area of travel, etc. Finally, the pay-‐as-‐you go system can adopt any of the previously described structures, but the total charge must amount to some predetermined value predicted for total transportation expenditures in a fiscal year. This method would avoid an account deficit or surplus from accumulating.11 These various structures listed for the VMT fee generally increase in efficiency as they become more complex.

The single fee, which is the simplest of the four systems, would charge a flat rate per mile traveled. Assuming that the quantity of publicly provided roads has been increasing as suggested by the study, one may consider transportation spending as a public good. Because each individual would pay the same tax share, the single fee model may be viewed in the context of the political equilibrium model under majority rule. The quantity of transportation spending, therefore, will depend on the uniform tax rate chosen, as well as the marginal benefit experienced by 10 "Final Report - Volume III: Section 1 - Technical Issues Papers." National Surface Transportation Policy and Revenue Commission. RAND Corporation, 19 Jan. 2007. Web. 02 Apr. 2013. 11 Tian, Zong Z., Eric B. Herzik, and Et Al. "Nevada Vehicle Miles Traveled (VMT) Fee Study Phase 1." Nevada Department of Transportation, Dec. 2012. Web. <http://www.nevadadot.com/uploadedFiles/NDOT/Documents/VMT%20FEE%20STUDY%20Bk.pdf>.

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individual consumers, in the aggregate, resulting from transportation. Figure 3 in the Appendix outlines the determination of this equilibrium. Assuming constant costs for transportation and infrastructure spending, the average cost of producing one ‘unit of transportation’ is X dollars. The distribution of tax shares at a uniform rate suggests that each of the 5 consumers in the graph will pay a tax of X/5 dollars per gallon. Because of each consumer’s varying marginal benefits, only the median voter will consume his most preferred outcome of transportation (N units) given the tax share determined by majority rule. Due to the fact that only the median voter consumes his most preferred output, there are political externalities present resulting from the inability of other voters to consume their most preferred level of transportation. When such externalities are present, additional gains to voters are possible either through changes in output or tax shares.12 This inefficiency may be viewed as point A in Figure 4 in the Appendix. At this point, Pareto Optimality has not been achieved because there are potential gains in well being to some without reducing the well being of others.13

The progression to more sophisticated structures of the VMT tax system result in increases in efficiency and equity. The movement from the single to multiple fee based system allows for the cost of gasoline to more accurately reflect the marginal benefits experienced by individual consumers. Consumers will also contribute funds that more accurately reflect the car they drive, and therefore the damages caused to the transportation infrastructure, environment, etc. This system may be seen again in Figure 4 as a movement to point B. The change in the allocation of costs based on vehicle make, year, etc. results in a more equitable distribution of taxes reflecting the costs associated with an individuals operation of their vehicle. Furthermore, the use of a more advanced system more accurately reflects the benefit principle of taxation in which the taxes, or marginal costs, of individuals using a government-‐provided good are equal to their marginal private benefits.

Moving on, the generalized user fee system incorporates not only the characteristics of the vehicle but also the time of day and area associated with that individual’s traveling. This method bears the heaviest contrast to the gas tax, which fails to effectively allocate taxes to those who contribute the most damage to the transportation infrastructure. In this case, the consumption of transportation can be seen as generating negative externalities. The generalized fee system would act as a corrective tax to internalize this negative externality and force those who induce greater costs to pay greater taxes, which would cause those with more damaging vehicles to incorporate the marginal external costs of their consumption of transportation in their marginal analysis. 14 This internalization can be seen in Figure 5 of the appendix. On the graph the original Marginal Private Cost fails to

12 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 183. Print. 13 Ibid 14 Ibid

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incorporate the external costs associated with driving a vehicle producing negative externalities. Furthermore, the cost does not consider the time of day the vehicle is being used. The cost of accommodating an additional vehicle during ‘rush hour’ will be much higher than the cost of accommodating the same vehicle in the middle of the night. The generalized user fee system forces the consumer to incorporate those costs, which results in the shifting of the MPC line to the MSC line. The new equilibrium occurs at point B. The tax revenue collected by the internalization is P1CBP2. Vehicle miles traveled are also reduced, which will likely reduce congestion during peak driving hours. The increased revenue may be used to construct new, less congestible roads, develop even more fuel-‐efficient technology, etc. This analysis supports the Council of State Governments claim that “the main goal of the VMT fee is to make the principle of ‘the user pays’ more of a reality”15 Referring back to Figure 1, this analysis would suggest that the marginal cost incurred at point N would begin being compensated for by the consumers contributing to congestion. Finally, this reform would further contribute to the attainment of efficiency and equity represented by the movement from Point A to Point B on the Utility-‐Possibility curve of Figure 4. This efficiency can also be seen in Figure 1, by the efficient output reached at equilibrium E*, when drivers are charged P* for congestible roads and driving hours.

One final point on the efficiency of the VMT tax is worth noting. Assuming the implementation of the generalized user fee system, one may assume that transportation infrastructure moves closer to the spectrum of a pure public good due to the reduced congestion resulting from higher fees at peak driving hours (however, roads still VMT still maintains price excludability). If one accepts this assumption then the efficient output of vehicle miles traveled will occur at the point where the “sum of marginal private benefits of consumers equals the marginal social cost of the good”16. Because the generalized user fee system incorporates all conceivable costs of vehicle miles traveled, one may assume that each individual contributes a tax share equivalent to their marginal private benefit. This equilibrium, called the Lindahl Equilibrium, is portrayed in Figure 6 of the appendix. Unlike the political equilibrium, consumers are assigned a ‘Lindahl Price’, which reflects their marginal private benefit.17 Therefore, the political externalities present in the political equilibrium model are eliminated with a more sophisticated VMT fee structure. The efficient output produced is Q*, and the tax paid by each consumer is equivalent to the marginal private benefit enjoyed by that consumer when vehicle miles traveled equals Q*.

Finally, the pay-‐as-‐you-‐go fee system may incorporate any of the previously discussed methods; however, this method first estimates the total transportation expenditures for an upcoming fiscal year. Based on this prediction, the total vehicle 15 Slone, Sean. "Vehicle Miles Traveled Fees." The Council of State Governments, 2009. Web. 01 Apr. 2013. 16 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 160. Print. 17 Ibid

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miles traveled per area are also predicted. Next, the VMT fee can be determined based on these predictions, which will result in the prevention of a surplus or revenue resulting for the VMT fee.18

In the context of the cost-‐benefit analysis, the various benefits discussed above must been evaluated in dollar terms, summed, and discounted from their future to present values using the social rate of discount. The social rate of discount ‘should reflect the return that can be earned on resources employed in alternative private use’19.

Costs

The next step in evaluating the VMT project is determining the total costs or disadvantages of the project. Some of the costs, like the benefits, are obvious and take the form of expenditures used to finance the project. However, some costs are more difficult to enumerate. Obviously, the costs incurred depend directly on the structural system used to implement the tax. This section will outline the forecasted costs based on the existing research. Furthermore, it will attempt to incorporate actions that may be taken to minimize the more concerning costs.

The costs most easily evaluated are the initial capital expenditures required to finance the project. The aforementioned RAND corporation predicts that the initial investment will be quite substantial:

“Onboard equipment would likely cost around $100 per vehicle. There would also need to be additional upfront investment in the information systems required to collect and distribute revenues. After that, automation should yield cost-‐efficiencies once the investments are made”20.

Like most government projects, the majority of the investment costs are incurred during the early stages of the project. After the projects completion, costs drop substantially as benefits begin to be realized simultaneously. The only remaining expenditures after this initial investment are maintenance, administration, enforcement, etc. These initial implementation costs obviously increase with the sophistication of the system that is chosen. The Mileage Metering Based On Consumption System mentioned earlier would obviously have a very low cost. The single fee system is also expected to have a relatively low cost. As expected, more complex systems such as the multiple fee system and the generalized user-‐fee 18 Tian, Zong Z., Eric B. Herzik, and Et Al. "Nevada Vehicle Miles Traveled (VMT) Fee Study Phase 1." Nevada Department of Transportation, Dec. 2012. Web. <http://www.nevadadot.com/uploadedFiles/NDOT/Documents/VMT%20FEE%20STUDY%20Bk.pdf>. 19 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 238. Print. 20 "Final Report - Volume III: Section 1 - Technical Issues Papers." National Surface Transportation Policy and Revenue Commission. RAND Corporation, 19 Jan. 2007. Web. 02 Apr. 2013.

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system will have “additional costs to implement the various user fee systems because data on gas efficiency has to be obtained for all makes and models”21. One can see the correlation developing here in which the models that yield the highest efficiency tend to also yield the highest implementation costs. Therefore, effective cots-‐benefit analysis is necessary to determine whether the marginal social benefits are less or greater than the marginal social costs.

Some of the other costs addressed by the current research are the costs of enforcement, administration, transition, etc. According to the Oregon Study, the costs of transitioning can be minimized via the ‘pay at the pump system’. The study goes on to outline the methodology that should be used the total costs of the project:

“Administration of the VMT charge is automated and integrated easily into existing transaction processes…The costs would include capital costs for mileage reading equipment at service stations, costs of on-‐vehicle equipment to be determined by auto manufacturers, and state operating costs for auditing, enforcement, administration, and communication”22.

The Oregon Study essentially supports the conclusions held by the RAND corporation that the initial implementation may be somewhat costly, but the system will eventually become low cost and self-‐sustaining while yielding high net benefits into the foreseeable future. This process is also not intended to occur rapidly. The Oregon study predicts that the entire process will occur over a period of about ten years once it has begun. Oregon’s proposal can be seen as incremental budgeting, which “bases the current years budget on the previous year’s budget with only minor changes in funding levels for various programs included in the budget”23. Obviously, such a radical change in the daily operations of nearly all businesses and households cannot occur too rapidly. Rather the process must be somewhat slowly adopted in order to allow necessary time to accommodate the reform.

Finally, arguably the biggest cost, which is inconveniently also the most abstract, is the cost of privacy to those who feel they are being ‘tracked’ by the VMT fee system. In the literature review section of the Nevada Study, the research states “one study revealed that no matter how clearly the privacy protection strategies were explained, there were still people who were against the idea of using GPS technology for charging mileage user fees”24. Obviously, a drastic change in the 21 Tian, Zong Z., Eric B. Herzik, and Et Al. "Nevada Vehicle Miles Traveled (VMT) Fee Study Phase 1." Nevada Department of Transportation, Dec. 2012. Web. <http://www.nevadadot.com/uploadedFiles/NDOT/Documents/VMT%20FEE%20STUDY%20Bk.pdf>. 22 Whitty, James. "The Revised VMT Taxation Concept and A New Road Usage Charge Pilot Program." The Oregon Department of Motor Vehicles, 08 Feb. 2012. Web. 01 Apr. 2013. 23 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 233. Print. 24 Tian, Zong Z., Eric B. Herzik, and Et Al. "Nevada Vehicle Miles Traveled (VMT) Fee Study Phase 1." Nevada Department of Transportation, Dec. 2012. Web. <http://www.nevadadot.com/uploadedFiles/NDOT/Documents/VMT%20FEE%20STUDY%20Bk.pdf>.

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carrying out of everyday operations will meet some political opposition. The solution to such a problem is to develop solutions to the skepticism of the systems critics and to effectively inform the public of such solutions. The Oregon study performs the latter by introducing the fact that,

“The on-‐vehicle device designed did not send an identifying signal out to denote vehicle’s real time travel. Thus, a vehicle’s movements were not tracked by anyone. Also, the on-‐vehicle device did not retain any travel history. No one, therefore with a search warrant or court order could obtain that travel history because no travel history exists” 25

This solution actually sounds quite promising. The argument gains some momentum when one introduces the fact that most modern vehicles have GPS technology embedded in them already. Furthermore, the development of information technology has incorporated GPS components into everything from laptop computers to mobile phones, which most consumers are already likely to possess. Unfortunately, the proposed solution is only a small portion of the cost of privacy. The true bulk of the cost emerges in the communication and persuasion of the public that this solution is actually viable and legitimate. These political transaction costs include all of the “time, effort, and other resources expended to reach and enforce a collective agreement”26. Despite how practical the VMT tax may be in theory, informing and persuading the public may be the largest milestone standing in the way of its implementation.

Like the benefits of the project, the costs must also be summed, so that the two can be compared. The costs that occur in the future may also be discounted to their present value; however, unlike benefits, many costs are generally incurred immediately and represent their present value when they are expended.

Conclusion

After evaluating, enumerating, and discounting all relevant costs and benefits, there are two methods, which may be used to determine the viability of the project. The net benefit criterion, which discounts the summation of the difference between benefits and costs, can be used to rank a specific project. If the calculated value is positive, then the project is worthy of being considered. The second method, the Benefit-‐Cost ratio, operates similarly but rather calculates the ratio of the summation of discounted benefits divided by costs. Projects evaluated in this

25 Whitty, James. "The Revised VMT Taxation Concept and A New Road Usage Charge Pilot Program." The Oregon Department of Motor Vehicles, 08 Feb. 2012. Web. 01 Apr. 2013. 26 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 186. Print.

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manner pass the screening for consideration if the calculated value is greater than one.27

After conducting this previous, positive economic analysis, the final step for informed policymakers and economists is to make a normative economic judgment. Personally, without doing the extensive calculations and developing proxies for the more abstract costs and benefits, I feel the project seems viable. Obviously, the fuel tax is failing to finance the increasing demand for transportation spending, and a drastic change is needed to compensate for the growing deficit. However, this normative analysis is merely an opinion. Unfortunately, “it remains difficult to measure the benefit of government goods and services accurately because differences of opinions exist regarding what benefits and costs to include and how to value the output of various projects”28.

27 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 242. Print. 28 Hyman, David M. Public Finance: A Contemporary Application of Theory to Policy. 10th ed. Mason, OH: South-Western Cengage Learning, 2010,2011. 255. Print.

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Appendix

Figure 1: Congestible Public Good

D1 D2 MSC

P* E* 0 1 N N’

Marginal Cost

Vehicle Miles Traveled

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Figure 2: The Oregon Study Model

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Figure 3: Single Fee System Political Equilibrium Under Majority Rule ΣMB X AC=MC

MB1 MB2 MB3 MB4 MB5 X/5

N Figure 4: Utility Frontier

MB, MC, T


Person A

Person B

B A

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Figure 5: Internalization of Negative Externality MPC+T=MSC MPC P2 B A C P1 D=MSB

Figure 6: Lindahl Equilibrium Using The Generalized User Fee System

E MC=AC=MSC D=ΣMBi=MSB MBA MBB MBC

Q*


Price, Benefit, and Cost


Marginal Benefit and Marginal Cost

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