Home > Chapter 6: FRAMEWORK OF ANALYSIS
Section Three
Benefit–Cost Analysis
In the last few chapters we have used the concepts of “abatement costs” and “damages” without explaining in any detail how we might measure their magnitudes in particular situations. In the next three chapters, this question is addressed. The focus is on benefit–cost analysis in Chapter 6 as one of the tools economists use to find efficient outcomes and methods available for estimating benefits and costs that can be used to estimate marginal damages and marginal abatement costs relevant to environmental policy decisions in Chapters 7 and 8.
Chapter 6
Framework of Analysis
Policy decisions require information, and, although the availability of good information doesn’t automatically mean that decisions also will be good, its unavailability will almost always contribute to bad decisions. There are a variety of alternative frameworks for generating and presenting information useful to policy-makers, calling for different skills and research procedures. We focus on benefit–cost analysis as one such method of quantifying the theoretical concepts addressed thus far and as a decision tool that governments may use to evaluate policy options and environmental infrastructure investments. A brief discussion of cost effectiveness analysis concludes the chapter.
Benefit–Cost Analysis
Benefit–cost analysis (BCA) is to the public sector and social valuations what a profit-and-loss analysis is to a private-sector firm. If an automobile company contemplated introducing a new model of car, it would want to get some idea of how its profitability would be affected. The cost side would include all costs of production and distribution of its goods: labour, raw materials, energy, emission-control equipment, transportation, and so on. Revenues are the firm’s “benefits” and are calculated as the market price of its goods times the quantity sold. The firm then compares expected revenues with anticipated costs to see if it should introduce the new model. Benefit–cost analysis is an analogous exercise for programs in the public sector. There are two critical differences between social benefit–cost analysis and private investment decisions:
1. Benefit–cost analysis is a tool for helping to make public decisions— what policies and programs to introduce—done from the standpoint of society in general rather than from that of a single profit-making firm.
2. It incorporates social valuation of all inputs and outputs related to the project whether or not they are transacted in private markets.
A major challenge for benefit–cost analysis is how to value non-market costs and benefits. Information about market prices, costs, and profits is very important in this process; it provides useful facts about private valuations. The techniques developed for benefit–cost analysis begin with these private values and compute social values when there is a divergence between the two, as is often the case with environmental issues. Chapters 7 and 8 examine a variety of techniques for social valuation. This chapter looks at how to undertake a benefit–cost study assuming one has already measured the benefits and costs.
Benefit–cost analysis has led two intertwined lives. The first is among its practitioners, economists inside and outside public agencies who have developed the techniques, tried to produce better data, and extended the scope of the analysis. The second is among the politicians and administrators who have set the rules and procedures governing the use of benefit–cost analysis for public decision making. In Canada, benefit–cost analysis has not been officially legislated for use by government agencies at the federal or provincial level. It has been used somewhat randomly, and at times for political self-interest, rather than as a technique for objective decision making. By contrast, in the United States benefit–cost analysis has a much stronger legislative history. It was first mandated for use in conjunction with the United States Flood Control Act of 1936. That act specified that federal participation in projects to control flooding on major rivers of the country would be justifiable “if the benefits to whomever they accrue are in excess of the estimated costs.” Procedures had to be developed to measure these benefits and costs to determine if this criterion was satisfied for any proposed flood-control dam or large levee project. This process has taken many years and, indeed, techniques for measuring non-market benefits and costs are still being developed today.
Guide to Benefit–Cost Analysis in Transport Canada: http://www.tc.gc.ca/eng/corporate-services/finance-bca-101.htm
Links to Benefit- Cost analysis websites: http://www.costbenefitanalysis.org/tenbestedvcbnlinks.htm. <NOXMLTAGINDOC> <DOCPAGE NUM="105"> <ART FILE="NEWWEB~1.EPS" W="72pt" H="52.293pt" XS="100%" YS="100%"/> </DOCPAGE> </NOXMLTAGINDOC>
The status and role of benefit–cost analysis in public natural resource and environmental decision making is still controversial. Some criticisms of the technique include the following:
Public agencies only use benefit–cost analysis in ways that would help them justify ever-larger budgets.
Benefit–cost analysis is really an attempt to short-circuit the process of political discussion and decision that should take place around prospective public projects and programs.
Benefit–cost analysis is a way of curtailing public programs because of the difficulty of measuring benefits relative to costs.
One can find examples to support each of these points. Perhaps because of these problems, benefit–cost analysis is not widely used in Canada by governments. Some programs have been evaluated from a benefit–cost perspective; for example, the examination in the mid-1970s of the proposed Mackenzie Valley natural gas pipeline (which was not built), and resource development projects in British Columbia (such as Northeast Coal, which was undertaken). But, in recent years, little formal analysis has been done by government agencies. Nevertheless, benefit–cost analysis remains an important analytical tool that is used widely throughout the world. And, while full benefit–cost studies may not be done by governments, the measurement of social benefits and costs has become an important ingredient in public-policy decisions.
The Basic Framework
Benefit–cost analysis involves measuring, adding up, and comparing all the benefits and all the costs of a particular public project or program. There are essentially four steps in a benefit–cost analysis:
1. Specify clearly the project or program, including its scale and the perspective of the study.
2. Describe quantitatively the inputs and outputs of the program.
3. Estimate the social costs and benefits of these inputs and outputs.
4. Compare these benefits and costs.
Each step is covered in general terms and examples are given below.
Scale and Perspective of a BCA Project or Program
Benefit–cost analysis is a tool of public analysis, but there are actually many publics. If you were doing a benefit–cost study for a national agency, the “public” normally would be all the people living in the particular country. But if you were employed by a city or regional planning agency to do a benefit–cost analysis of a local environmental program, you would undoubtedly focus on benefits and costs accruing to people living in those areas. At the other extreme, the rise of global environmental issues requires a worldwide perspective.
Once the perspective is determined, there should be a complete specification of the main elements of the project or program: location, timing, groups involved, connections with other programs, and so on.
There are two primary types of public environmental programs for which benefit– cost analyses are done:
1. Physical projects that involve direct public production, such as public waste treatment plants, beach restoration projects, hazardous-waste incinerators, habitat improvement projects, and land purchase for preservation.
2. Regulatory programs that are aimed at enforcing environmental laws and regulations, such as pollution-control standards, technological choices, waste disposal practices, and restrictions on land development.
How do analysts determine the scale of the project or which regulatory program to select? There are a number of different approaches to this issue. The key one that links BCA to our theoretical model is the socially efficient scale:
The socially efficient scale maximizes the net social benefits from the project. Net social benefits are maximized where MAC = MD.
Consider Figure 6-1 (Figure 5-6 from the previous chapter). It shows the standard emission-control model, with marginal damage (MD) and marginal abatement cost (MAC) functions. The figure can be used to prove that the socially efficient scale maximizes net social benefits where the MAC = MD.
Figure 6-1: The Socially Efficient Scale of a Public Project
The socially efficient scale of a public project or regulation to reduce emissions is determined where the MAC curve intersects the MD curve. This is at E* = 10 tonnes of emissions per month. The socially efficient scale maximizes the net benefits from the project—areas a + d. If the target of the project is to reduce emission to 12 tonnes, the net benefits are only area a. This is not the socially efficient scale.
Proof
Assume first that no emissions are controlled: E = 15. A public program is proposed that would lower emissions to 12 tonnes. At 12 tonnes of emissions, the total benefits of the program are the total damages reduced. This equals areas (a + b) = $81.1 Total abatement costs are equal to area b = $18.2 The net benefits of the program are therefore equal to area a = $63.
1. The simplest way to compute areas a plus b is to calculate the difference between total damages at the initial emissions level of 15 and total damages at the target of 12 units. This will be the difference between two triangles. At 15 units, MD = $30 per unit. This can be found graphically or by using the equation for marginal damages: MD = 2E. Total damages measured from 0 to 15 units are $225. At 12 units, MD = $24 per unit emitted. Total damages measured from 0 to 12 units are $144. The difference is $81.
2. At 12 units of emissions, MAC per unit are $12. This is found graphically or by substituting the 12 units into the marginal abatement cost function: MAC = 60 – 4E. Area b is then the area of the triangle between 15 and 12 units of abatement.
For an emission reduction program to give maximum net benefits, however, it would have to reduce emissions to E* = 10 tonnes of emissions, the level at which MD = MAC. Net social benefits at 10 tonnes equal (d + a) = $75.3 The net gain from being at the socially efficient scale of 10 tonnes rather than 12 tonnes of emissions is thus area d, which equals $12. This may not seem like much, but try multiplying by $1-million to get a feel for what might be the amounts at stake in practice.
3. Again, the simplest way to compute the net social benefits is to calculate the change in total damages (TD) due to the policy and subtract from this the change in total abatement costs (TAC). At E* = 10, the change in TD = area (a + b + c + d), which equals $125 (TD at 15 emissions are $225, TD at 10 emissions are $100). The change in TAC = area (c + b), which equals $50. The net social benefits are therefore area (a + d) = $75. Be sure you can prove that net social benefits are at a maximum when MD = MAC.
The problem for the benefit–cost analysis of a specific proposal is how do decision-makers know that 10 units of emissions is the socially efficient level? If they can graph or write equations for the MAC and MD curves, computing E* is straightforward, as Figure 6-1 illustrates. When the MAC and MD curves are not readily identifiable, a procedure called sensitivity analysis is undertaken. This means recalculating benefits and costs for programs somewhat larger and somewhat smaller than the target chosen; that is, a program with somewhat more and less restrictive emission reductions to determine which level maximizes net social benefits. Chapter 7 examines ways to quantify the MD curve (or the benefits of reducing environmental contaminants), while Chapter 8 looks more extensively at the cost side of the equation. The key point is that benefit-cost analysis is an attempt to quantify the theoretical relationships that show the benefits of reducing emissions net of the costs of doing so.
Description of the Program’s Inputs and Outputs
The next step is to identify the relevant flows of inputs—the costs of the program or project, and the outputs—the benefits. For some projects this is reasonably easy. If we are planning a wastewater treatment facility, the engineering staff will be able to provide a full physical specification of the plant, together with the inputs required to build it and keep it running. The output is also well defined—the flow of treated water per day or year. For other types of programs it is much harder, because both the inputs and outputs are more difficult to quantify—for example, an information program to inform the public of the energy intensity of household appliances or working with industry on pollution prevention programs. A key component of any measurement of inputs and outputs is their time dimension. Most environmentally related projects or programs do not usually last for a single year, but are spread out over potentially long periods of time. The analyst must predict what the values will be for each year that the project or program lasts.
Measurement of Benefits and Costs of the Program
The next step is to put values on input and output flows: to measure costs and benefits. Economists measure benefits and costs in monetary terms. As noted above, this does not mean solely in market-value terms, because in many cases benefits and costs are not directly registered on markets. Nor does it imply that only monetary values count in some fundamental manner. Monetary units provide a single metric into which we can try to translate all of the impacts of a project or program so that benefits and costs can be compared to each other and to other types of public activities. Monetary units are very powerful in decision making: when deciding whether to implement a new environmental tax in the next federal budget the Minister of Finance will want to know the dollar value of all the benefits and costs of the tax compared to other options. As Chapters 7 and 8 will show, it is often difficult to impute monetary values for all environmental impacts of a program. Sometimes the best analysts can do is provide a rough estimate (guess?) of the impacts and illustrate whether the results of the study vary with different estimates of the benefits or cost. The important point is to be very clear about how the estimate is obtained and how confident one is of the estimate.
Comparison of Benefits and Costs
How do we compare benefits and costs? The principles are simple:
Compute the net benefits (NB) of the project or program.
Net benefits are the difference between total benefits and total costs. Total benefits are the total damages forgone (the area under the MD curve), and total costs are the total abatement costs incurred (the area under the MAC curve).4 Maximizing the difference between total benefits and total costs corresponds to the point where the MAC and MD curves intersect.
4. Remember that abatement costs measure all the costs the polluters incur in reducing their emissions. These include the costs of actual abatement equipment plus loss in profits if output is reduced, diverting workers from producing goods to producing waste management and so on. Total damages measure all the impacts of the emissions on people and the environment. When dealing with people’s valuations of damages, the metric is estimates of willingness to pay to reduce emissions.
If the project lasts more than a year, we must discount any future costs and benefits before computing net benefits. The next section shows how discounting is done.
If there is more than one project that can accomplish the same target or goal, we select the program/project that yields the largest net benefits, subject to any budget constraints the government faces.
We illustrate these principles using examples that get increasingly more complex. First we show how to compute the net benefits when there is just one program under consideration and no discounting is needed, then we look at a case where there are different options that accomplish the same target. One must be chosen. Finally, we consider what happens when governments have fixed budgets.
How to Compute Net Benefits
Example: Regulatory program to control wastes from pulp mills
The government is contemplating enacting a regulation that requires all pulp and paper mills to reduce their discharges to air and water. These emissions reduce downstream water quality in the river on which they are located and contribute to serious air pollution in the vicinity of the plants. The estimates of costs and benefits are the totals over the life of the program. Costs of the program include private-sector costs of compliance in the form of pollution control costs: $580-million for capital equipment and $560-million for operating costs to control emissions. Public-sector monitoring and enforcement is also required to ensure companies comply with the regulation. These costs total $96-million. Total costs are thus $(580 + 560 + 96) = $1,236. There are three major benefit categories. Downstream recreators (fishers and boaters) benefit from improved water quality: their WTP for these benefits is $1,892-million. Agricultural operators in the vicinity of the plants have a reduction of $382-million in damages to crops and livestock because of reduced airborne emissions. Hence, their benefits are these forgone damages. Finally, there are intangible benefits such as improvement in habitats for many species. Suppose we have no way of measuring these in monetary terms, so just show them as some quantity A. Total benefits are thus $(1,892 + 382 + A) = $2,278 + A.
Total benefits and costs can be compared in several ways. One way is to subtract the total costs from total benefits to get net benefits. This is the numerical counterpart to what Figure 6-1 illustrated graphically: we are finding the maximum net benefits from the program to attain the socially efficient equilibrium. Net benefits are $(2,278 + A – 1,236) = $1,042-million plus A. This is the standard method of comparing benefits and costs and the approach we follow in all other cases. Maximizing the net benefits corresponds to the point where the MAC = MD curve in our standard environmental framework.
Another criterion that is sometimes used is the benefit–cost ratio, found by taking the ratio of benefits and costs. This shows the benefits the project will produce for each dollar of costs. In this example, the benefit–cost ratio is $(2,278 ÷ 1,236) = 1.8 plus A. There is a major problem with the benefit–cost ratio. The socially efficient program size that we have argued is the appropriate scale of the project is not the one that gives the maximum benefit–cost ratio. Look back at Figure 6-1. At E* = 10 units, the benefit–cost ratio is equal to (a + b + c + d) ÷ (b + c) = $(63 + 18 + 32 + 12)/$44 = 2.84. At 12 units of emissions, the benefit–cost ratio is (a + b) ÷ b = $(63 + 18)/$18 = 4.5. The benefit–cost ratio is higher at 12 units because it is dependent on the relative size of the project’s total benefits and total costs, not its net benefits. But, as we have argued, it is net benefits that should matter to society, not total values. The benefit–cost ratio may be used to make sure that, at the very least, benefits exceed cost, but beyond this it is a misleading indicator in planning the appropriate scope of public programs.
Discounting and Choosing among Projects that Achieve the Same Policy Goal
What if there is more than one way to achieve a particular policy goal? What rule do we use to select one of the options? What if each option involves costs and benefits that occur over more than one year? How, then, are net benefits computed? We answer both these questions using another example.
Example: Investment in upgrading a municipal sewage treatment plant5
Suppose our goal is to improve water quality by investing in better municipal sewage treatment in the community. This is a public project that involves three different levels of treatment, each with a different stream of benefits and costs. The options are:
1. Enhanced tertiary treatment: discharges pure water with no household waste products, viruses, or bacteria;
2. Tertiary treatment: discharges water with no household waste products, but may contain some bacteria and viruses.
3. Secondary treatment: eliminates most household waste products, but may contain some bacteria and viruses.
A normal reaction to the description of these options might be to say, “let’s go for the best treatment possible.” But is that socially efficient?
Table 6-1 presents the costs and benefits for each option. These differ among the options in both magnitude and over time. Assume the project lasts for six years. In practice, this sort of project would likely extend beyond the six years, but we end it here to make calculations simpler. Year 0 is the time period from when the project starts to the end of the first year. Each project will involve some construction (capital) costs as the plant upgrades must be installed. For the two tertiary projects, there are no benefits until the end of this period (year 1) because the plants are not fully operational until then. The secondary treatment upgrade can be completed more quickly and hence generates some benefits in the initial period (year 0). Year 1 shows some start-up costs for each option, and for the years thereafter the costs shown are operating costs. Note also that the benefits of each type of sewage treatment differ. The benefits of enhanced tertiary treatment rise over time, while those of the other options are constant once the plant begins full operation.
Table 6-1: Costs and Benefits for Three Ways to Upgrade a Municipal Sewage Treatment Plant
5. We have chosen a physical project to illustrate benefit–cost principles. The same principles apply to regulatory programs. One could easily substitute another example, such as three policies to reduce greenhouse gas emissions. Each could have a different benefit and cost stream reflecting different timing, who is affected, and how.
Our task is first to compute the net benefits. When the costs and benefits differ over time, we must apply discounting to add and compare these costs and benefits. Discounting has two facets: first, the mechanics of doing it; then, the reasoning behind the choice of discount rates to be used in specific cases. We take these up in turn.
A cost that will occur 10 years from now does not have the same significance as a cost that occurs today. Suppose, for example, that one has incurred a cost of $1,000 that she must pay today. To do that she must have $1,000 in the bank, or in her pocket, with which to pay the obligation. On the other hand, suppose she has a commitment to pay $1,000 not today, but 10 years from now. If the rate of interest she gets in a bank is 5 percent, and she expects it to stay at that level, she can deposit $613.90 in the bank today and it will compound up to $1,000 in 10 years, exactly when she needs it. The formula for compounding this sum is:
$613.91(1 + .05)10 = $1,000
We can now turn this around and ask: What is the present value of this $1,000 obligation 10 years from now? Its present value (PV) is what we would have to put in the bank today to have exactly what is needed in 10 years, and is found by rearranging the above expression:
Present value = $1,000/(1 + .05)10 = $613.91
The present value is found by discounting the future cost back over the 10-year period at the interest rate, now called the discount rate, of 5 percent. If it were higher—say, 8 percent—the present value would be lower and equal $463.20. The higher the discount rate, the lower the present value of any future cost.
The same goes for a benefit. Suppose you expect someone to give you a gift of $100, but only at the end of six years. This would not have the same value to you today (i.e., the same present value) as $100 given to you today. If the applicable discount rate is 4 percent, the present value of that future gift would be $100(1 + .04)6 = $79.03.
The general formula for discounting is:
Present value = m/(1+r)t
where m is the value in any time period; r is the interest rate used, which is known as the discount rate; and t is the number of years involved. The present value for year 0 in our example is m/(1+r)0 = m; for year one it is m/(1+r); for year two: m/(1+r)2; and so on. If we are considering a project that goes on forever, the PV formula6 is simply PV = m/r.
6. The present value formula for t going to infinity converges to m/r because [m/(1 + r)t ] is a geometric progression with ever-smaller values for the denominator.
Example: Application of discounting to the sewage plant options.
Our task is to compute net benefits in each time period, then discount these to year 0 so that the stream of net benefits for each project can be calculated. The steps are as follows and values are reported in Table 6-2.
1. Calculate net benefits. Net benefits are simply total benefits in each year minus total costs. These are calculated from Table 6-1 and shown on the top half of Table 6-2. In year 0, for example, for tertiary treatment the total costs = $50, total benefits = 0, net benefits = –$50.
2. Calculate the PV of net benefits for each year. Take the current value and divide by the appropriate discounting factor: 1/(1+r)t for r = 5% and t = 0, 1, 2, 3, 4, 5. The results are shown on the bottom half of Table 6-2. For example, in year 3 the PV of NB for the secondary plant = $10/(1.05)3 = ($10/1.1576) = $8.64.
3. Sum the present values of net benefits for each year to get the net benefits of each project over its expected duration. Add up for each treatment option the PV stream from year 0 to year 5. For example, for enhanced tertiary the sum of the PVs = $(–100 + 0 + 27.21 + 43.19 + 49.36 + 47.01) = $66.77 million.7
7. These calculations can readily be done on a spreadsheet.
The tertiary plant is clearly the option with the maximum present value of net benefits, and the one to be selected under our benefit–cost decision rule. Note why this project “wins” and the enhanced tertiary project has a lower PV of net benefits. The enhanced tertiary project has very high initial capital costs. These costs are not discounted because they occur in the initial period. The benefits rise over time, but because the large benefits occur later in time (years 4 and 5) their present values are lower than a project that generates smaller current-value benefits in early years. The tertiary project is a case in point. The current values of its benefits are never larger than those of the enhanced tertiary plant ($50-million), but they occur early in time (starting in year 1), so in present-value terms these benefits will add more to the total than the enhanced plant’s later benefits. The tertiary plant also has much lower capital and start-up costs than the enhanced plant, again contributing to its higher PV of net benefits. The secondary treatment plant is a clear “loser.” While its total costs are relatively low, its benefit stream is too small to dominate the two tertiary plants.
Table 6-2: Net benefits for three Ways to Upgrade a Municipal Sewage Treatment Plant:Current Values and Present Values
Sensitivity
Analysis
An important issue in benefit–cost analysis is how robust these results are to the assumptions the analyst makes. Assumptions may enter in many ways for any project. Consider two key assumptions in this example:
1. The interest rate is 5 percent.
2. The projects last five years after construction is completed.
As noted earlier, sensitivity analysis is generally performed in a BCA study to see if changes in key assumptions affect the ranking of projects. To illustrate how important sensitivity analysis can be, assume that projects last seven years and that the net benefits in current dollars for each additional year are the same as in year 5. Consider only the two tertiary plants. The PV of two more years of net benefits of $60-million for the enhanced plant is $44.78-million for year 6 and $42.64-million for year 7. Adding these to the PV of net benefits for years 0 to 5 yields a sum of $154.19-million. Following the same procedure for the tertiary plant, its PV of net benefits for six years is $26.12-million, and $24.88-million for the seventh year. Its PV of net benefits for seven years is now $143-million. The ranking of the two tertiary plants changes. For a project lasting seven years with the flows of costs and benefits as shown, the enhanced tertiary plant offers the maximum PV of net benefits. This is because it has much higher PV of net benefits in those two years than does the tertiary plant. Will changing the interest rate change the ranking of these projects? We leave that as one of our problems at the end of the chapter. We consider the importance of the interest rate chosen for discounting more fully below.
The Role of Government Budgets and Multiple Programs
Under some circumstances, there may be grounds for sizing programs at less than that which maximizes net benefits. Consider a regional public agency in charge of enforcing air-pollution laws in two medium-sized urban areas. The agency has a fixed and predetermined budget of $1-million to spend. Two possible ways to proceed are to (1) put all the money into one enforcement program in one of the cities or (2) divide it between two programs, one in each city. Suppose the numbers are as follows:
| Costs | Benefits | Net benefits | |
| One-city program | $1,000,000 | $2,000,000 | $1,000,000 |
| Two-city program | |||
| City A | 500,000 | 1,200,000 | 700,000 |
| City B | 500,000 | 1,200,000 | 700,000 |
In this case, the net benefits of allocating the fixed budget into two half-sized programs exceed the net benefits of putting it into just one. The principle is to
allocate resources so that the net benefits produced by the total budget are maximized.
In the example above, the net benefits from adopting the two-city program are $1.4-million, which clearly exceeds the $1-million from the one-city program for the same total cost.
Choice of the Discount Rate
Discounting is a way of aggregating a series of future net benefits into an estimate of present value. In many projects, the outcome depends greatly on which particular discount rate we use. Using a very low rate would essentially be treating a dollar in one year as very similar in value to a dollar in any other year. A very high rate says that a dollar in the near term is much more valuable to us than one later on. Thus, the higher the discount rate, the more we would be encouraged to put our resources into programs that have relatively high payoffs (i.e., high benefits and/or low costs) in the short run. The lower the discount rate, on the contrary, the more we would be led to select programs that have high net benefits in the more distant future.
It is important to first distinguish between nominal interest rates and real interest rates:
Nominal interest rates are what you actually see on the market.
Real interest rates are nominal rates adjusted for inflation.
Example: Real and nominal interest rates
Suppose you deposited $100 in a bank at an interest rate of 8 percent. In 10 years your deposit would have grown to $216. But this is in monetary terms. Suppose that over that 10-year period prices increase 3 percent per year on average. Then the real value of your accumulated deposit would be less; in fact, the real interest rate at which your deposit would accumulate would be only 5 percent (8 percent – 3 percent), so in real terms your deposit would be worth only $161 after the 10 years.8
8. These are slight approximations. The deposit would actually be worth $160.64 and the real rate of accumulation would be 4.89 percent.
Principles for dealing with real and nominal values are
1. If the cost or benefit estimates are expected real costs or benefits—that is, adjusted for expected inflation—use a real interest rate.
2. If the estimates are nominal figures, use a nominal interest rate.
3. If cost and benefit estimates are for a number of years and inflation is expected to occur, then these values should be adjusted for inflation. A standard index to deflate these values should be used. Examples are the gross national expenditure deflator or a selling price index for intermediate goods. The deflated costs and benefits are then discounted by a real discount rate.9
9. Most introductory economics texts explain how to deflate nominal values using a price index. Real values are calculated by taking the nominal value and dividing by one plus the rate of inflation. The rate of inflation for, say, the period 1999–2000 can be calculated by taking a price index (e.g., the consumer price index) for 2000 divided by the price index for 1999. The formula is the real value in time t = (nominal value in t +1)/(1+p), where p is the rate of inflation between t and t+1.
The choice of a discount rate has also been a controversial topic through the years. For example, differing views about the net benefits to society of reducing greenhouse gases have been based on the choice of discount rate. New Footnote #1 Some of the key arguments are summarized here.
New Footnote #1: See Nicholas Stern, The Economics of Climate Change. Great Britain Treasury (2007) and the critique of Stern’s choice of discount rate by William Nordhaus, “Critical Assumptions the Stern Review on Climate Change” Science (317), 13 July 2007 (available at www.sciencemag.org).
The discount rate reflects the current generation’s views about the relative weight to be given to benefits and costs occurring in different years. But even a brief look will show that there are dozens of different interest rates in use at any one time—rates on normal savings accounts, guaranteed investment certificates, bank loans, government bonds, and so on. Which rate should we use? There are essentially two schools of thought on this question. The first is that the discount rate should reflect the way people themselves think about time. Any person normally will prefer a dollar today to a dollar in 10 years; in the language of economics, they have a positive rate of time preference. People make savings decisions by putting money in bank accounts that pay certain rates of interest. These savings account rates show what interest the banks have to offer to get people to forgo current consumption. We might, therefore, take the average bank savings account rate as reflecting the average person’s rate of time preference.
The problem with this is that there are other ways of determining people’s rates of time preference, and they don’t necessarily give the same answer. Many studies have shown that people are remarkably inconsistent when it comes to time preference. They may also have subjective rates that are much higher than current interest rates offered by financial institutions for their savings.
The second approach to determining the “correct” rate of discount is based on the notion of investment productivity. When investments are made in productive enterprises, people anticipate that the value of future returns will offset today’s investment costs; otherwise, these investments would not be made. The thinking here is that when resources are used in the public sector for natural resource and environmental programs, they ought to yield, on average, rates of return to society equivalent to what they could have earned in the private sector. Private-sector productivity is reflected in the rates of interest banks charge their business borrowers. Thus, by this reasoning, we should use as our discount rate a rate that reflects the interest rates that private firms pay when they borrow money for investment purposes. These are typically higher than savings account interest rates.
With the multiplicity of interest rates the real world offers, and these different arguments for choosing a discount rate, practices could differ among agencies in the public sector. To reduce the potential for a multiplicity of rates being used, governments often specify an official discount rate to be used by all their agencies and ministries. However, there is a difficulty with a fixed rate when economic conditions are changing and interest rates fluctuate. We can conclude that although discounting is widely accepted, the rate controversy is far from being resolved.
Discounting and Future Generations
The logic of a discount rate, even a very small one, is inexorable. A billion dollars, discounted back over a century at 5 percent, has a present value of only slightly over $7.6-million. The present generation, considering the length of its own expected life, may not be interested in programs having very high, but long-run, payoffs like this. The following example illustrates the effects of discounting over a long period of time.
Example: The effects of discounting
Figure 6-2: The Effects of Discounting for 100 Years
Discounting is a process that expresses the value to people today of benefits and costs that will occur at some future time. As the time increases between today and the point where these benefits and costs actually occur, their present value diminishes. Figure 6-2, panel (a) shows how much the present value of $100 of net benefits, discounted at 3 percent, diminishes over 100 years. By year 40, $100 is “worth” just over $30 in present-value terms; by year 100, it is just over $5.
The effect the rate of discount has is shown in panel (b). Net benefits of $100 to be received 100 years from now are illustrated for discount rates ranging from 0 to 6 percent. While 6 percent may not seem like a high discount rate, it will lead to a negligible present value of $100 in 100 years.
The logic is even more compelling when we break down net benefits into the stream of benefits and costs over time. One of the reasons that environmentalists have looked askance at discounting is that it can have the effect of downgrading future damages that result from today’s economic activity. Suppose today’s generation is considering a course of action that has certain short-run benefits of $10,000 per year for 50 years, but which, starting 50 years from now, will cost $1-million a year forever. This may not be too unlike the choice faced by current generations on discharging accumulative toxic wastes, or on greenhouse gas emissions from fossil fuel combustion. To people alive today the present value of that perpetual stream of future cost discounted at 10 percent is approximately $85,000.10 These costs may not weigh particularly heavily on decisions made by the current generation. The present value of the benefits ($10,000 a year for 50 years at 10 percent, or $99,148) exceeds the present value of the future costs. From the standpoint of today, therefore, this might look like a good choice, despite the perpetual, and potentially very large,cost burden placed on all future generations.
10. The present value of $85,000 is calculated as follows. The present value of a stream of $1-million forever is $1-million divided by the interest rate ($1-million/.1 = $10-million). But we don’t incur these costs until 50 years from now. The present value of $10-million incurred in 50 years is $10-million/(1+r)50 = $10-million/117.39 = $85,186.
The problems associated with using positive discount rates for environmental programs with long-run impacts are difficult to resolve. Some people take the view that the appropriate discount rate is zero for long-run environmental projects. And, why should current generations have the ‘right’ to make decisions that may not incorporate the well being of future generations. But we have to be very careful here. A great deal of harm has been done to natural and environmental resources by using very low discount rates to evaluate development projects. With low discount rates, it is often possible to justify very disruptive public infrastructure projects, such as hydroelectric dams, because enough distant and uncertain benefits can be accumulated to outweigh the tremendous near-term costs.
Given these uncertainties about discounting when looking at very long-run environmental impacts, we may want to fall back on additional criteria to help us in making current decisions. One of these might be the concept of sustainability discussed in Chapter 1. Sustainability connotes the idea that we should avoid courses of action that reduce the long-run productive capabilities of our natural and environmental resource base. Society may also want to avoid making decisions that are irreversible, or that preclude taking other options in the future. Dealing with long-run impacts remains a very thorny issue, one for which benefit–cost analysis is not well suited.
Distributional Issues
The relation of total benefits and total costs is a question of economic efficiency. As noted in Chapter 1, decisions about the environment are not just about efficiency, but also about equity -- who gets the benefits and who pays the costs. In public-sector programs, the distribution of benefits and costs must be considered along with efficiency issues, which implies that benefit–cost analyses must incorporate studies of how net benefits are distributed among different groups in society. In this section we introduce some of the main concepts of distribution analysis.
Consider the following numbers, which refer to the annual values of a particular program accruing to three different individuals who, we assume, all have the same income. Abatement costs show the costs of the program to each individual; these may be higher prices on some products, more time spent on recycling matters, higher taxes, or other factors. The reduced damages are measures of the value of the improvements in environmental quality accruing to each person.
| Person A | Person B | Person C | |
| Reduced environmental damages ($/year) | 60 | 80 | 120 |
| Abatement costs ($/year) | 40 | 60 | 80 |
| Difference | 20 | 20 | 40 |
Costs and reduced damages are different for person A and person B, but the difference between them ($20/year) is the same; hence, the difference as a proportion of their income is the same. With respect to these two people, therefore, the program is horizontally equitable; recall from the definitions of equity in Chapter 1, horizontal equity treats people in the same circumstances identically.The program is not horizontally equitable for person C, because this individual experiences a net difference of $40/year. Since person C is assumed to have the same income as the other two people, he or she is clearly better off as a result of this program; horizontal equity in this case has not been achieved.
Consider the numbers in Table 6-3. These show the impacts, expressed in monetary values, of three different environmental quality programs on three people with, respectively, a low income, a medium income, and a high income. This enables us to look at vertical equity – how the program affects people in different circumstances. Each person benefits from a project from reduced damages and incurs costs in the form of their share of total abatement costs. The “difference” row reflects each person’s net benefits: reduced damages minus abatement costs. In parentheses next to each number is shown the percentage that number is of the person’s income level. These percentages help illustrate three types of distributional impacts a program can have. These potential impacts are proportional, regressive, and progressive programs and policies.
1. Proportional. The program takes the same proportion of income from each income level. In Table 6-3, program 1 is proportional because its net benefits to each person take 1 percent of that person’s income.
2. Regressive. The program provides higher net benefits to high-income people than to low-income people as a proportion of their income. Program 2 is regressive because the high-income person’s benefits represent 5 percent of her income while the proportion decreases as the person’s income level falls.
3. Progressive. The program provides net benefits that represent a higher proportion of the lower-income person’s income than it does of the rich person’s income. Program 3 is progressive because the lowest-income person has the highest net benefits as a share of his income. Net benefits as a share of income fall as income rises.
Thus an environmental program (or any program for that matter) is proportional, progressive, or regressive, according to whether the net effect of that policy has proportionally the same, greater, or less effect on low-income people as on high-income people.
Table 6-3 also illustrates another equity issue—how the benefits and costs are distributed to each income group. For example, although the overall effects of program 2 are regressive, the abatement costs of that program are in fact distributed progressively (i.e., the cost burden is proportionately greater for high-income people). But in this case damage reduction is distributed so regressively that the overall program is regressive. So, also in program 3, although the overall program is progressive abatement costs are distributed regressively.
Table 6-3: Vertical Equity*
*Figures in the table show annual monetary values. Numbers in parentheses show the percentage of income these numbers represent.
These definitions of distributional impacts can be misleading. A program that is technically regressive could actually distribute the bulk of its net benefits to poor people. Suppose a policy raised the net income of one rich person by 10 percent, but raised each of the net incomes of 1,000 poor people by 5 percent. This policy is technically regressive, although more than likely the majority of its aggregate net benefits go to poor people.
It is normally very difficult to estimate the distributional impacts of environmental programs, individually or in total. To do so requires very specific data showing impacts by income groups, race, or other factors. In general, environmental and health data are not collected by income and race. Thus, data on environmentally related diseases don’t typically allow the comparison of differences across socio-economic and racial groups. Nor is it easy to estimate how program costs are distributed among these groups, because these depend on complex factors related to tax collections, consumption patterns, the availability of alternatives, and so on. Despite the difficulties, however, benefit–cost analyses should try to look as closely as possible at the way in which the aggregates are distributed through the population.
Uncertainty
In applications of benefit–cost analysis to natural and environmental resources we are projecting events well off into the future, and when we do this we run squarely into the fact that we have no way of knowing the future with certainty. Uncertainty can arise from many sources. We may not be able to predict the preferences of future consumers, who may feel very differently than we do about matters of environmental quality. For studies of the long-run impacts of climate change, future population growth rates are important, and it is impossible to know these with certainty. Uncertainty may arise from technological change. Technical advancement in pollution-control equipment or in the chemistry of materials recycling could markedly shift future costs of achieving various levels of emission control. Nature itself is a source of uncertainty. Meteorological events can affect the outcomes of pollution-control programs; for example, in some cases we are still uncertain of the exact ways human activities impact natural phenomena.
How should we address the fact that future benefits and costs are uncertain; that is, that future outcomes are “probabilistic”? If we know something about how these future probabilities manifest themselves, we may be able to estimate the “most likely” or “expected” levels of benefits and costs. Consider the problem of predicting the effect of certain policy changes on oil spills. In any given year there may be no tanker accidents, or one, or several; the exact number is not known. But there is enough information to calculation the risk that a spill will occur. Economists use the word ‘risk’ to denote a situation where estimates can be made of the probability that an uncertain event will occur. If no estimate can be made of the likelihood of the event occurring, the event is ‘uncertain’. Popular language however often mixes up the use of the two terms. Suppose we can estimate the risk of an oil spill. . The objective is to calculate the annual number of spills anticipated under different types of oil-spill-control policies. One way of doing this is to estimate the expected value of oil spills anticipated in a year’s time. Where would we get the information for this? Data may have been collected over a long period of time on past oil spills and could be used to calculate actual long-run averages. If this information isn’t available, engineers, scientists, or people familiar with the problem might provide estimates. These estimates can be used to develop a probability distribution of the number of oil-tanker accidents, as shown in Table 6-4.
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Table 6-4: Calculating the Expected Number of “Large” Oil Spills
Table 6-4 presents probabilities of having different numbers of tanker accidents in a year. The numbers are hypothetical. For example, the probability is .77 that there will be no tanker accidents, .12 for one accident, .07 for two accidents, and so on. Expected values are computed as the number of spills times the probably of that event occurring, summed over all possible events. This produces a weighted average of the probably of an event, as shown in Table 6-4. In Table 6-4, the expected number of tanker accidents is .39 per year. One could then go on and estimate the expected quantity of oil that will be spilled and, perhaps, the expected value of damages. Thus, in this case, we are able to proceed by estimating expected values of probabilistic events, in particular the expected values of benefits and costs.
To recap,
an expected value is a weighted average: the number of times the event occurs times its probability of occurrence, summed over all possible events.
This approach is appropriate if we have reliable estimates of the probabilities of future events. But in many cases these may not be available, because we have not had enough experience with similar events to be able to know the future probabilities of different outcomes with muchconfidence. One approach, made possible by the computer, is to carry out a scenario analysis. Suppose we are trying to predict the long-run costs of reducing CO2 emissions as a step toward lessening the greenhouse effect. These costs depend critically on the future pace of technological developments affecting the energy efficiency of production. We have little experience with predicting technical change over long periods of time, so it is unrealistic to try to estimate the probabilities that technical change will occur at different rates. Instead, we run our analysis several times, each time making a different assumption about the rate at which technical change will occur. Thus, our results might consist of three scenarios, with different results based on whether future technical change is “slow,” “moderate,” or “fast.”
There is, however, another difficulty in using expected values on which to base decisions. Expected values are appropriate when analyzing a relatively large number of recurrent situations; repeated observations reduce the impact of unusual outlying events. In the oil-spill case, the annual number of spills is expected to approach its expected value. But for unique events that will occur only once, we may want to look beyond expected-value decisions. Consider the following numbers:
| Program A | Program B | ||
| Net benefits | Probability | Net benefits | Probability |
| $500,000 | .475 | $500,000 | .99 |
| $300,000 | .525 | –$10,000,000 | .01 |
| Expected value: | $395,000 | Expected value: | $395,000 |
These two programs have exactly the same expected value. But suppose we had only a one-time choice between the two. Perhaps it relates to the choice of a nuclear plant versus a conventional power plant to generate electricity. With program A, the net benefits are uncertain, but the outcomes are not extremely different and the probabilities are similar—it’s very nearly a 50–50 proposition. Program B, on the other hand, has a very different profile. The probability is very high that the net benefits will be $500,000, but there is a small probability of a disaster (the plant explodes, killing hundreds of people and creating irreversible environmental damage). If we were making decisions strictly on the basis of expected values, we would treat these projects as the same; we could flip a coin to decide which one to choose. If we did this, we would be displaying risk-neutral behaviour, making decisions strictly on the basis of expected values. On the other hand, if this is a one-shot decision, we might decide that the low probability of a very large loss in the case of project B represents a risk to which we do not wish to expose ourselves. In this case, we might be risk averse, preferring project A over project B.
In environmental pollution control, risk aversion may be the best policy in a number of cases. The rise of planetary-scale atmospheric change opens up the possibility of catastrophic human dislocations in the future. The potential scale of these impacts argues for a conservative, risk-averse approach to current decisions. Risk-averse decisions are also called for in the case of species extinction; a series of incremental and seemingly small decisions today may bring about a catastrophic decline in genetic resources in the future, with potentially drastic impacts on human welfare. Global issues are not the only ones where it may be prudent to avoid low risks of outcomes that would have large negative net benefits. The contamination of an important groundwater aquifer is a possibility faced by many local communities. And in any activity where risk to human life is involved, the average person is likely to be risk-averse.
Case Study: Benefit-Cost Analysis of Reducing Sulphur in Fuels
Crude oil can contain considerable amounts of sulphur that persists when oil is refined into gasoline. The sulphur in gasoline contributes to the release of sulphur dioxide, an air contaminant associated with a host of environmental problems including acid precipitation that damages crops, forests, acidifies vulnerable lakes and kills aquatic life (see Chapter 17). Sulphur dioxide (SO2) also has significant adverse health impacts especially to people with asthma and other lung diseases. In 1994, the Canadian Council of Ministers of the Environment (CCME) created a task force to examine methods of reducing the sulphur in gasoline and other means of reducing SO2 such as increasing vehicle efficiency. The task force took a number of years to collect data, consult experts and stakeholders that would be affected by changes in the regulations. By 1997, sulphur content in gasoline was on average 360 parts per million (ppm) across Canada, with much higher levels in urbanized provinces. Ontario’s average was over 530 ppm. The CCME’s goal was to phase in over time tighter restrictions to reduce substantially the amount of sulphur in Canadian gasoline.
Regulations came into force in 2002 with an interim requirement limiting sulphur in gasoline to an average level of 150 parts per million, and never to exceed 200 ppm. This was to allow the refining industry to adapt to the regulations. Effective January 1, 2005, the average level was reduced to 30 ppm, and the level at any time not to exceed 80 ppm. That regulation stands today.
Glenn Jenkins, Chun-Yan Kuo, and Aygul Ozbafli used the data generated by the CCME studies to undertake a benefit-cost analysis for the Treasury Board of Canada to determine the level of sulphur reduction in gasoline that generated the maximum present value of net benefits. New Footnote #2 They calculate the costs and benefits of moving from a ‘base case’ – the level of sulphur that existed in gasoline in 1997 to six other scenarios of increasing regulatory stringency with sulphur levels from 360 ppm down to 30 ppm. They assumed the new regulation would come into force January 1, 2001. Costs and benefits are forecast out to 2010.
New Footnote #2: Jenkins, G., Kuo, C-Y., and A. Ozbafli, “Cost-Benefit Analysis of Reducing Sulphur in Gasoline”, manuscript, (December 2009). An earlier version of the paper is available as a Queen’s University Economics Department Working Paper No. 1134, “Cost-Benefit Analysis on Regulations to Lower the Sulphur in Gasoline” (March 2007) at: www. …..}
Two categories of cost are measured: administrative costs of the government and the compliance costs of oil refiners as they adjust their processes to remove sulphur from gasoline. The authors estimate annual administrative costs to be $60,000 per year for each of the scenarios. Seventeen refineries existed in Canada at the time of the study; each with somewhat different characteristics and costs of adjusting their physical plant and processes to meet the regulation. The capital investment needed to meet the targets is assumed to be incurred in 2000, with changes in annual operating cost beginning in 2001. All costs are measured in 1995 prices. Starting with total production of 36 billion litres per year, they assume gasoline output rises by 0.7 percent per year to reflect rising demand. Table 6-5 shows the costs by region for Canada.
Table 6-5: Total Investment and Annual Operating Costs by Scenario and by Region (millions of Canadian dollars in 1995 prices)
| Scenario |
Costs |
Atlantic and Quebec | Ontario |
Prairies and British Columbia | Canada |
| Base Case
|
Investment Cost
Annual Operating Cost |
79.0
28.5 |
47.0
34.2 |
83.0
11.1 |
209.0
74.0 |
| Alternative Scenarios | |||||
| Scenario 1: 360 ppm | Investment Cost
Annual Operating Cost |
81.0
16.6 |
96.0
7.0 |
0
0.3 |
177.0
23.9 |
| Scenario 2: 250 ppm | Investment Cost
Annual Operating Cost |
144.0
28.5 |
196.0
16.0 |
20.0
16.5 |
360.0
61.0 |
| Scenario 3: 200 ppm | Investment l
Cost
Annual Operating Cost |
226.0
31.7 |
213.0
24.0 |
146.0
7.7 |
585.0
63.4 |
| Scenario 4: 150 ppm | Investment Cost
Annual Operating Cost |
243.0
38.4 |
266.0
35.1 |
188.0
15.0 |
697.0
88.5 |
| Scenario 5: 100 ppm | Investment Cost
Annual Operating Cost |
282.0
45.3 |
392.0
48.9 |
219.0
22.8 |
893.0
117.0 |
| Scenario 6: 30 ppm | Investment Cost
Annual Operating Cost |
532.0
49.7 |
650.0
47.5 |
606.0
21.9 |
1,788.0
119.1 |
Sources: Jenkins, Kuo, and Ozbafli (2009) who cite as data sources: Kilborn, Inc.,The Costs of Reducing Sulphur in Canadian Gasoline and Diesel, Phase III, (March 1997); and Government of Canada, Final Report of the Government Working Group on Sulphur in Gasoline and Diesel Fuel – Setting a Level for Sulphur in Gasoline and Diesel, (July 14, 1998), Table 2.3
Jenkins and co-authors focused on the health benefits of reducing sulphur in gasoline; they did not have the data to incorporate the broader environmental impacts generated by sulphur emissions. Thus, their benefits are likely a lower bound estimate. Estimates of the damages from air pollution (and thus the benefits of reducing air pollutionn) require information about a chain of effects. The authors take four steps to estimate benefits for each of the scenarios: (1) the change in vehicle emissions caused by changes in the level of sulphur in gasoline; (2) the change in ambient air quality affected by changes in emitted pollutants by vehicles; (3) the impact on human health caused by changes in ambient air quality; and (4) the measurement of the impacts on health in monetary values. Health impacts of pollution are difficult to measure with precision, thus the authors provide low, central, and high values for each relationship between ambient air pollutant concentrations and the health responses. The central estimate is generally in the middle of the range and represents the most likely health effect by experts who study these relationships. Each of the estimates is then given a probability weight to create a probability distribution of expected total health benefits of lowering sulphur emissions. Table 6-6 illustrates the author’s estimates of the health benefits.
Table 6-6: Total Reductions of Health Effects for Canada over the 20-Year Period
(number of cases)
| Health Effects |
Alternative Scenarios | |||||
| Scenario 1: 360ppm | Scenario 2: 250ppm | Scenario 3: 200ppm | Scenario 4: 150ppm | Scenario 5: 100ppm | Scenario 6: 30ppm | |
| Premature Mortality | 829 | 1,169 | 1,385 | 1,591 | 1,810 | 2,100 |
| Chronic Respiratory Disease | 3,013 | 4,184 | 5,040 | 5,752 | 6,555 | 7,600 |
| Respiratory Hospital Admissions | 533 | 735 | 874 | 1,002 | 1,126 | 1,324 |
| Cardiac Hospital Admissions | 423 | 593 | 717 | 814 | 924 | 1,076 |
| Emergency Room Visits | 2,694 | 3,733 | 4,524 | 5,153 | 5,854 | 6,800 |
| Asthma Symptom Days | 1,307,842 | 1,814,497 | 2,185,633 | 2,500,763 | 2,840,451 | 3,300,000 |
| Restricted Activity Days | 634,343 | 882,402 | 1,062,847 | 1,212,450 | 1,377,466 | 1,600,000 |
| Acute Respiratory Symptoms | 4,364,822 | 6,049,747 | 7,249,041 | 8,323,223 | 9,470,413 | 11,000,000 |
| Child Lower Respiratory Illness | 37,798 | 52,078 | 63,228 | 71,131 | 82,277 | 93,000 |
Note: The number of health effects is a simple summation of cases occurred over the 20-year period.
Source: Jenkins, Kuo, and Ozbafli (2009).
The value of improved health outcomes is estimated using methods that are explained in Chapter 7. These include how much people would be willing to pay to reduce the risk of an adverse health impact and the value of a statistical life. Data for these estimates comes from a number of studies undertaken in Canada and the United States. Table 6-7 provides the costs and benefits by year. Note that benefits begin in 2001, and after 2007, the costs and benefits are the same each year. The authors assume a real discount rate of 7 percent to compute all the present values.
Table 6-7: Annual Incremental Benefits and Costs by Scenario ($ millions, 2000 prices)
Source: Source: Jenkins, Kuo, and Ozbafli (2009).
The distribution of benefits and costs is very revealing and shows clearly the costs are borne by the refiners, while the benefits received by the public. Table 6-8 illustrates.
Table 6-8: Present Value of Net benefits by Stakeholder and by Scenario ($ millions, 2000 prices)
| Scenario |
Refiners |
Refinery Workers | Consumers and Individuals | Governments | Total |
|
| Provincial | Federal | |||||
| Scenario 1: 360 ppm | (117.0) | 0 | 2,097.6 | 5.8 | (0.6) | 1,985.8 |
| Scenario 2: 250 ppm | (272.9) | 0 | 2,595.9 | 7.9 | (0.6) | 2,330.0 |
| Scenario 3: 200 ppm | (339.7) | (4.8) | 3,029.9 | 9.6 | (0.6) | 2,694.3 |
| Scenario 4: 150 ppm | (444.8) | (14.5) | 3,328.4 | 10.8 | (0.6) | 2,879.4 |
| Scenario 5: 100 ppm | (578.4) | (19.3) | 3,580.5 | 12.4 | (0.6) | 2,994.6 |
| Scenario 6: 30 ppm | (826.9) | (19.3) | 3,646.6 | 14.1 | (0.6) | 2,813.9 |
Table 6-9 summarizes the net present values of each of the scenarios. All the NPVs are positive, indicating that a reduction from the high levels of sulphur that existed prior to regulation is warranted. The maximum net present value (NPV) occurs with scenario 5, a reduction in average sulphur concentrations to 100 ppm. Notice that there is not much difference between scenarios 4, 5, and 6. The study could not obtain data on the reduction in damages to the environment. The authors thus caution that these scenarios underestimate total benefits. Sensitivity analysis on key assumptions is also undertaken and finds that lowering emissions to 150 or 30 ppm results in zero probability that the NPV will be negative. The authors recommend that the standard be set at 30 ppm. The government set the regulations for sulphur to be effective January 1, 2005 at an average level of 30 parts per million with a never-to-be-exceeded maximum of 80 ppm. They allowed an interim step from July 2002 to the end of 2004 at 150 ppm with a level never to exceed 200 ppm at any time starting July 1, 2002 until the end of 2004. Refiners moved more quickly to the 30 ppm limit and none of them shut down as a result of the regulation.
Table 6-9: The Net Present Value of Alternative Scenarios to Reduce Sulphur in Gasoline ($millions, 2000 prices)
| Scenario | Net Present Value
@7% |
| Scenario 1: 360 ppm | 1,985.8 |
| Scenario 2: 250 ppm | 2,330.3 |
| Scenario 3: 200 ppm | 2,694.3 |
| Scenario 4: 150 ppm | 2,879.4 |
| Scenario 5: 100 ppm | 2,994.6 |
| Scenario 6: 30 ppm | 2,813.9 |
Source: Jenkins, Kuo, and Ozbafli (2009).
[CATCH END OF CASE STUDY}
Cost-Effectiveness Analysis
Suppose a community determined that its current water supply was contaminated with some chemical, and that it had to switch to some alternative supply. Suppose it had several possibilities: It could drill new wells into an uncontaminated aquifer, it could build a connector to the water-supply system of a neighbouring town, or it could build its own surface reservoir. A cost-effectiveness analysis would estimate the costs of these different alternatives with the aim of showing how they compared in terms of, say, the costs per million gallons of delivered water into the town system. Cost-effectiveness analysis, in other words, essentially takes the objective as given, and costs out various alternative ways of attaining that objective. One might think of it as one-half of a benefit–cost analysis, where costs—but not benefits—are estimated in monetary terms. The reason benefits need not be measured is that they are the same – the water supply will be safe; it is the costs of reaching this outcome that differ. Cost effectiveness looks for the lowest cost way of reaching the outcome.
A cost-effective project or policy is the one that achieves a given level of benefits at the lowest cost among all the possible policy/project options.
Table 6-5 shows some of the results of a study done for a remedial action plan to reduce phosphorus (P) concentrations in the Bay of Quinte in Lake Ontario. The study was done for the International Joint Commission, a bilateral organization that studies and makes recommendations to governments for water-related issues along the Canada–U.S. border. Phosphorus comes from leaching of fertilizers into waterways, from sewage treatment plants processing domestic household wastes, and from industrial sources. Excessive amounts of phosphorus lead to algal blooms and eutrophication of water bodies, which depletes oxygen in the water and kills fish and other aquatic life. The secondary sewage treatment plants currently existing in the region cannot remove enough of the phosphorus to prevent eutrophication. The results show the estimated costs of reducing phosphorus concentrations in a region of the bay by 1 microgram per litre (µg/L).
International Joint Commission: www.ijc.org<NOXMLTAGINDOC> <DOCPAGE NUM="123"> <ART FILE="NEWWEB~1.EPS" W="72pt" H="52.293pt" XS="100%" YS="100%"/> </DOCPAGE> </NOXMLTAGINDOC>
Treatment of wastewater from water treatment plants is by far the most cost-effective alternative. A reduction of 1 µg/L costs $98,000, as compared to a tenfold next higher cost (diversion of Lake Ontario water). Cost-effectiveness analysis is a powerful tool when benefits of a project or policy are identical. It emphasis the importance of examining alternative options and finding the one that minimizes social costs for a given target.
Table 6-10 can also illustrate that cost coefficients must be interpreted with care. Although the wastewater treatment has the lowest costs per unit of phosphorus reduced, it may not be the best way to reduce phosphorus concentrations in this bay. Perhaps a combination of policies is better. There are a number of additional concerns. Each of the technologies has limits as to the total amount of phosphorus it is capable of reducing; so, depending on what the desired total reduction is, different combinations of these techniques will have to be used. There may be other techniques that could be more cost-effective but were difficult to measure costs for. An example is phosphorus removal from industrial sources. These cost figures also involve quite different mixes of capital to operating costs. Treatment plants are capital-intensive, while the diversions and alum treatment involve high operating costs. This might be an important budgetary concern for governments. Pollution problems may also be multifaceted. One technique (e.g., tertiary treatment plants) may have benefits in addition to phosphorus reduction, while others (dumping alum into the lake, for example) may have some other adverse environmental impacts.
Table 6-10: Cost-Effectiveness of Different Options for Reducing Phosphorus Concentration in the Bay of Quinte, Lake Ontario
Source: Adapted from Bay of Quinte Remedial Action Plan Committee, “Discussion Paper,” September 1989.
Cost-effectiveness is thus only one step in reaching a decision about environmental policy. A full benefit–cost analysis is clearly superior. However, due to data limitations, especially difficulties in measuring benefits, cost-effectiveness studies may be the only approach possible. It may also make sense to do a cost-effectiveness analysis even before there is a strong public commitment to the objective you are costing out. Once a cost-effectiveness analysis is done, people may be able to tell, at least in relative terms, whether any of the different alternatives would be desirable. They may be able to say something like: “We don’t know exactly how the level ofbenefits in monetary terms, but we feel that they are more than the costs of several of the alternatives that have been costed out, so we will go ahead with one or both of them.”
Summary
In previous chapters we put the issue of environmental improvement in a trade-off type of format, where there is willingness to pay (benefits) on one side and abatement costs on the other. In this chapter we started to focus on the problem of measuring these benefits and costs. To do this, researchers have to use some underlying analytical framework to account for these benefits and costs. We focused on the primary approach used in resource and environmental economics: benefit–cost analysis. The rest of the chapter was devoted to a discussion of the main conceptual issues involved in benefit–cost analysis. These are
the basic analytical steps involved,
determining the appropriate size of a project or program,
calculating the present value of net benefits,
issues in discounting of future values,
distributional issues, and
uncertainty.
We briefly discussed cost-effectiveness analysis—seeking the lowest-cost alternative among options that all yield the same benefits—and environmental impact analysis. Having discussed the basic structure of benefit–cost analysis, we will turn now to problems of actually measuring the benefits and costs of specific environmental programs.
Key Terms
Benefit–cost ratio, 110
Compounding, 111
Cost-effectiveness analysis, 122
Discount rate, 112
Discounting, 111
Expected value, 120
Horizontal equity, 118
Nominal interest rates, 114
Present value, 111
Probability distribution, 120
Progressive programs and policies, 118
Proportional programs and policies, 118
Real interest rates, 114
Regressive programs and policies, 118
Risk-averse, 122
Risk-neutral, 122
Scenario analysis, 121
Sensitivity analysis, 108
Socially efficient scale, 106
Vertical equity, 118
Analytical Problems
1. Suppose the government of a municipality is trying to determine how to deal with pesticide contamination of its water supply. It wants to undertake a benefit–cost analysis of two alternative policy options for controlling pesticides:
Upgrading its municipal water treatment plant to remove the pesticides, or
Banning the use of the offending pesticides in the metropolitan area.
Assume that either technique reduces the pesticides to a level that does not adversely affect human health. The costs of these control options are as follows:
Municipal treatment upgrades: Capital costs = $20-million. The new plant is constructed over the course of the initial year. It starts operating at the end of this year. Once the plant begins operation, it has operating costs of $1-million per year. Once constructed, the plant lasts for five years, then must be replaced with a new plant.
Pesticide ban: annual operating costs due to substitution of non-toxic methods of controlling “pests” = $3.5-million each year.
Let the discount rate be 5 percent. The municipality’s planning horizon is 10 years. Suppose the present value of the benefits of the project are $40-million. Which project should the municipality adopt?
Assume now that the benefits differ by the type of treatment option chosen. In particular, they remain at a present value of $40-million for the pesticide ban, but there would be additional benefits in the form of less damage to ecosystems from the treatment plant. How high would these benefits have to be each year to make the government indifferent between choosing the treatment plant or the pesticide ban?
2. Using the numbers from Table 6-1 for the three different options to upgrade municipal sewage treatment to illustrate the impact of choosing different interest rates to discount the net benefits, compute the present value of each project if the interest rate is 2.5 percent, then 10 percent, and finally, 20 percent. What would happen to these present values if the benefits from each project did not begin until year 2 instead of year 1? (That is, shift the benefit stream to the right by one year.)
Discussion Questions
1. Are low discount rates “good” or “bad” for the environment? Defend your answer.
2. Distinguish between horizontal and vertical equity. Which is more important a goal for benefit–cost analysis? Defend your answer.
3. Why might governments opt for projects with low risks and low returns?
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