Valuing Environmental Improvements Total and Marginal Benefits

Transcription

1 EC 311 Lecture Notes 3 Page 1 of 19 ECON 311 Lecture Notes 3 Metropolitan State University Allen Bellas FF Chapter 5 Valuing Environmental Improvements Total and Marginal Benefits Consider a river whose initial state is so polluted that it is essentially dead and unusable for any sort of recreational purpose or wildlife habitat, but functions merely as an open sewer. It will take a significant reduction in pollutant levels in the water to bring about any sort of change. After this significant reduction in pollutant levels, the river will start to come back to life, becoming first boatable, then fishable and then swimmable then drinkable. Once the water in the river is so clean that it can be drunk directly by people, additional cleanliness will have little or no additional value. The total value of the river and the marginal value of improvements is shown below. The marginal value of an increase in cleanliness is the slope of the total value of the river.

2 EC 311 Lecture Notes 3 Page 2 of 19 The total value function might take a variety of forms, but if it is continuous and smooth then it probably looks something like the above curve. An Exercise Can you draw the marginal value curve that accompanies this total value curve? For those of you who prefer calculus, the marginal value of an improvement is the derivative of the total value function. This might be expressed in a number of ways: MV(C) TV (c) c 0 dtv(c) dc MV(C)dC

3 EC 311 Lecture Notes 3 Page 3 of 19 These are fancy mathematical ways of saying: So. The marginal value is the slope of the total value The total value is the area under the marginal value As a numerical example, imagine that a river might be classified in the following ways 0. Dead supports no life to speak of and is usable only as an open sewer 1. Boatable you might want to boat on it, but take care not to fall into the water 2. Fishable clean enough to support sport fish, but don t eat too many of them 3. Swimmable clean enough that you d let your kids swim in it most of the time 4. Drinkable walk right up and take a nice cool drink The total value of the river and marginal value of improvements might be: Condition Total Value Marginal Value of Improvement Really Dead Slightly Dead $10 $10 -- $ 0 Boatable $20 $10 Fishable $35 $15 Swimmable $45 $10 Drinkable Very Drinkable $50 $50 $ 5 $ 0 So, in fact, we see that marginal benefits might actually rise at first and then fall.

4 EC 311 Lecture Notes 3 Page 4 of 19 Expressed another way, the total and marginal values shown above might also be the total and marginal values of the achieved pollution reduction. As a side note, we might consider how we would calculate the value of a body of water based on its level of cleanliness. Total and Marginal Valuations In the textbook, Table 5-1 gives the Estimated Benefits (Reduced Damages) in 2010 from Clean Air Act Reductions of Criteria Pollutants. They total $110,000M. In terms of the above graphs, this would be:

5 EC 311 Lecture Notes 3 Page 5 of 19 Economic Efficiency from the Point of View of Reductions Looking at pollution reductions is consistent with the normal mindset of economic analysis because pollution reductions are goods. For economic efficiency, the optimal level of reductions is the level where the marginal cost of a reduction is equal to the marginal benefit (or the marginal value) of a reduction. The standard picture looks like this: However, this picture ignores the section of the above graphs where there are increasing marginal benefits of pollution reductions. The more complete picture looks like: Where is the optimal level of reduction here?

6 EC 311 Lecture Notes 3 Page 6 of 19 This is a bit of a tricky question. In economics, the answer is usually, Where the curves cross. However, in this diagram there are three levels at which the curves cross: A, B and C. To answer the question, imagine that we begin at the point where there are no pollution reductions, point A. As we begin reducing pollution levels, we move from point A to point B. Over this range, the marginal costs are greater than the marginal benefits, so there are some net losses until we get to point B. As we reduce pollution levels beyond B, the marginal benefits are greater than the marginal costs, so there are net gains until we get to point C. Beyond point C the marginal costs are greater than the marginal benefits, so there s really no reason to go there. As long as the net gains area is greater than the net losses area, point C is optimal. If the net losses are greater than the net gains, then point A is optimal. Point B is never optimal because at point B you ve endured all the hard effort and suffered the net losses but haven t yet gotten to Golden Time and the net gains to be enjoyed between points B and C.

7 EC 311 Lecture Notes 3 Page 7 of 19 Effects of Changes in Marginal Costs or Marginal Benefits As the marginal cost of reductions falls, the optimal level of reductions rises. This suggests that the really important thing about pollution control policy may be the level of incentive provided for cost-saving innovations. As the marginal benefit of reductions rises, the optimal level of reductions rises. Among the causes of higher marginal benefits might be: -greater population in the affected area -the area in concern is of particular environmental interest -there are threshold effects of the pollutant. It is worth a further note that the $110B benefits of the CAA in 2010 says nothing about whether this level of total benefits is efficient. That is, it says nothing about how the marginal benefits and marginal costs of pollution reductions compare. In the diagram below, the Clean Air Act moves us from a level of cleanliness C 0 to a level of cleanliness C 1. Assuming that the Clean Air Act should be undertaken, if marginal costs are MC a, then the Clean Air Act goes too far. If marginal costs are MC b then it is efficient and if marginal costs are MC c then the Clean Air Act gives us too little cleanliness.

8 EC 311 Lecture Notes 3 Page 8 of 19 Further, what we should really care about is the ambient quality of water or air and not reductions in emissions. If the analysis is based on the marginal value and marginal cost of emissions reductions then the relationship between emissions and ambient quality should be explicitly described. A fun question is, how might you improve ambient quality without reducing total emissions? 1 In Class Exercise What happens to the following as the marginal cost of abatement falls? 1. Optimal level of abatement 2. Total net benefits of abatement 3. Total variable expenditures on abatement Turning the Analysis Around: Emissions or Effluent on the Horiztonal Axis The book actually does the analysis with the level of emissions on the horizontal axis. This reverses the usual viewpoint of economics as it is typical to put goods on the horizontal axis. This is a bit odd because in economics we usually make graphs with quantities of goods on the horizontal axis, and it is a bit of a challenge to think of emissions as goods. However, if emissions mean not having to spend money to do abatement, then a firm might have some demand for emissions. Alternatively, late at night, after class, in January when the temperatures are well below zero, you yourself might demand some emissions as part of your trip home. If initial emissions are held constant, the picture with emissions on the horizontal axis is just the reverse of the picture with abatement or reductions on the horizontal axis. The difference comes when you consider that initial emissions might change as the result of some policy or other change. The basic picture is: 1 One answer to this question is that you might allow higher levels or rates of emissions when the environment can better handle those emissions, such as when a river has a greater volume of flow or high oxygen levels, when the wind is blowing or, perhaps, when it s raining.

9 EC 311 Lecture Notes 3 Page 9 of 19 although most of the time when this is drawn, the part that is emphasized is because the optimal level of emissions will be at the leftmost intersection of the two curves. It may help to think of the MAC as the demand for or marginal value of emissions. That is, to polluters, the value of emissions is the amount of money they save by being able to emit pollution rather than having to abate it. In these terms, we can think of the above picture in a few ways:

10 EC 311 Lecture Notes 3 Page 10 of 19 A cost-saving technological advance will shift the MAC curve down and reduce the optimal level of emissions.

11 EC 311 Lecture Notes 3 Page 11 of 19 A Pollutant with Extreme Threshold Effects You can draw in a marginal abatement cost (MAC) curve here and see that the desired level of emissions does not change much as costs vary.

12 EC 311 Lecture Notes 3 Page 12 of 19 Chapter 6 Benefit Cost Analysis (BCA) This discussion is taken from A Primer for Benefit Cost Analysis by two men named Bellas and Zerbe, published by Edward Elgar publishing. The book is available in paperback at a price that is outrageously reasonable. What BCA Is Benefit cost analysis is one technique of analyzing proposed or previously enacted projects to determine whether they should be or should have been done, or to choose between two or more mutually exclusive projects. BCA is done by assigning a monetary value to each input into and each output resulting from a project. The values of the inputs and outputs are then compared. In the most basic sense, if the value of the benefits is greater than the value of the costs, the project is deemed worthwhile and should be executed. Projects identified as worthwhile by BCA are likely to generate outputs that are more valuable than the inputs used. In the case of mutually exclusive projects, BCA will identify the project that will generate the greatest net benefit. BCA may also be used to assess the sensitivity of project outcomes to risk and uncertainty. Although the idea is simple, the execution of a good BCA can be difficult. Simply determining what to include as a cost or a benefit can require careful thought and may be subject to difference of opinion. While some inputs and outputs will have well known and stable prices, others may experience price changes as a result of the project. Still other inputs and outputs may not be traded in markets at all, necessitating other valuation methods. Steps in BCA Benefit cost analysis may be thought of as an operation in which there are a number of distinct steps. Not all analyses will require all of these steps. A short-lived project may require no discounting of future benefits. A project that has been or will be conducted many times may involve little risk or uncertainty. In most cases however, to clearly consider any project or choose between projects, the following steps should be taken. 1. Clarify Issues of Standing At the start of an analysis, it should be stated for whom the study is being done and whose costs and benefits will be included. In addressing these issues and calculating benefits or costs to different people or groups it is important to be clear and consistent.

13 EC 311 Lecture Notes 3 Page 13 of 19 Example: A water treatment plant is to be built on the Danube River in Hungary. Who will be given standing for clean water benefits? It might also be desirable to value costs and benefits to different people differently to reflect distributional considerations. Example: A public housing project can distribute units to the very poor who have a WTP of $100/month or to the slightly better off who have a WTP of $200/month. If the units are distributed to the very poor, it must be that they are seen as being more important than the folks who are slightly better off. It is also noting that if a person holds something that they have no right to, the value of that good in their hands is zero. Put slightly differently, the value of a good in the hands of a thief is zero. Example: A public project that returns my stolen car from the thief to me might seem not to create value as it is merely transferring the car from the thief to me, except that the thief really doesn t have standing in terms of the reallocation of the car. Example: A local government might seek to build a bicycle trail and receive federal government assistance to help cover the construction costs. The local government is likely to give standing only to its own constituents and not to other taxpayers, looking only at their net costs rather than the total cost of the project. Most economists would argue that standing should be universal. That is, all people should be given standing. Failing to do so can lead to approval of some unusual projects. Example: Imagine that Minnesota is considering various options to improve water quality in the Mississippi River by reducing sewage discharges into the river. If people living in states downstream from Minnesota are not given standing the result could be a very unusual water quality project. 2. Identify the Alternatives An analysis needs to be clear about which project or projects are under consideration and whether they are mutually exclusive and should seek to include relevant alternatives. The option of doing nothing is often used as a benchmark, but this may be only one basis of comparison. Not considering all possible alternatives is a flaw in a benefit cost analysis and often represents a lack of imagination, but such failures of imagination are not uncommon.

14 EC 311 Lecture Notes 3 Page 14 of 19 Altering the size and duration of the project may be relevant alternatives. For example, a vaccination program that fails a BCA nationally may pass a BCA if it is applied only in a region or among a population with a high incidence of the associated disease. Example: In the discussion of the Tellico Dam, the Tennesee Valley Authority failed to compare the dam with the alternative of using the free flowing river to run a turbine. [Zerbe and Dively, 1994] Example: In an analysis of the costs and benefits of early childhood education and allday kindergarten, the net benefits will likely be much larger if these programs are extended primarily to at-risk children, for whom the benefits are likely quite a bit larger. It s worth noting that benefit cost analyses almost never list all possible alternatives for addressing a problem. They usually consider one option and the status quo. 3. List the Impacts of Each Alternative Project The potential impacts of each considered project should be listed as completely as possible. That is, you should describe what the inputs and outputs or the costs and the benefits of the project will be. This should be done both for the project or projects explicitly under consideration as well as for the status quo or do-nothing alternative. 4. Set Out Assumptions Assumptions are necessarily part of an analysis and some will be better than others. It may be necessary to use assumptions for a wide variety of factors including quantities of goods, costs, market conditions, durations or interest rates. In a responsible analysis, these assumptions will be explicit and attributed to reliable sources when possible. If a range of assumed values is offered then this range should be explicit. Example: In analyzing the benefits and costs of requiring Israeli cyclists to wear helmets, it is necessary to lay out assumptions about the number of bicycle accidents that occur in Israel each year, the number of head injuries that result and the degree to which the severity of these injuries would be reduced if most cyclists were wearing helmets. Assumptions about compliance rates also need to be made. [G.M Ginsberg and D.S. Silverberg, A cost-benefit analysis of legislation for bicycle safety helmets in Israel, American Journal of Public Health, April 1994, 84(4), pp ] It is important that impacts be quantified where possible. Proper evaluation of a project requires knowing what quantities of inputs and outputs will be involved. When quantification is impossible, the impact should at least be mentioned. For example, a project that will limit individuals' personal freedom should mention this fact, even if no attempt will be made to value personal freedom.

15 EC 311 Lecture Notes 3 Page 15 of Assign Values to These Impacts Appropriate monetary values should be attached to each of the impacts when possible. When possible, market values should be used. When this is impossible, there are other techniques. Valuation of benefits can be particularly tricky with projects whose benefits are environmental improvements as environmental quality is not traded in any market, and there are a variety of techniques used in environmental benefit-cost analyses. These are discussed in the next set of lecture notes and include hedonic analysis of property values (HPV), the value of a statistical life (VSL), the travel cost method (TCM) and contingent valuation (CV). 6. Deal with Unquantified Impacts Any impacts that have not been assigned values should be clearly listed so that they may be considered against the explicitly valued costs and benefits. One approach to non-quantified benefits is to calculate how large they would need to be to reverse the BCA results. Often a judgment can be made to the effect that their magnitude is likely or unlikely to be large enough to reverse the decision. By explicitly considering such effects in this way, the analyst can take her analysis beyond hard numbers. For example, in considering a project that will limit personal freedom, the other costs and benefits may be used to calculate the net benefits of the project, excluding any considerations of personal freedom. It might then be left to the reader to determine if he believes that the loss of personal freedom resulting from the project is justified by the other net benefits. 7. Discount Future Values to Obtain Present Values Good or services to be received in the future are generally considered to be of lower value than the same goods or services received immediately. If this idea seems odd to you, ask yourself whether you would prefer to receive some payment or a good or service now or at some point, perhaps very far, in the future. For most projects it is necessary to discount costs and benefits occurring in the future so that their value might be compared with immediate costs and benefits. This discounting is usually done using exponential discounting to calculate present values of all future costs and benefits.

16 EC 311 Lecture Notes 3 Page 16 of 19 That is, the present value of a benefit or cost of $X that will happen at the end of N years is $X 1 i N if discounted at an annual rate of i. For example, the present value of $20,000 to be received at the end of 12 years when future benefits are discounted at a rate of 6% annually would be: The choice of an interest rate for this can be difficult, but many organizations that conduct analyses have standard rates to use in analyses. Generally a higher interest rate is conservative in that it will reduce the value of a project's future benefits more than it will reduce the value of its immediate costs. If a project looks good under a high interest rate, it is probably a good project. The formula above comes from financial markets and may represent how people actually discount the future over the course of their lives, but some research suggests that people discount the near future at a higher rate and the distant future at a lower rate. This point is highly controversial. Issues of discounting are particularly important when a project will have effects across generations, known as intergenerational effects, impacting people not yet born. To put this more clearly, if a project reallocates goods from a middle class family living today to a middle class family living several hundred years from now (or vice versa) should the future value of that transfer be discounted. If so, this suggests that the standing or importance of people who will be born in the future is reduced, perhaps to a great degree. The Rule of 72 The rule of 72 states that if something is growing at a rate of j%, it will take 72/j periods for it to double in size. For example, if an amount of money is earning 12% annually, it will take 72/12=6 years for it to double in value. If an amount of money is earning 2% annually, it will take 72/2=36 years for it to double in value. The discounting example shown above is also an application of the rule of 72.

17 EC 311 Lecture Notes 3 Page 17 of Identify and Account for Uncertainty and Risk Perhaps the failure to deal with risk or uncertainty is the most common shortcoming in BCA. Many aspects of a project may be subject to uncertainty and these sources of uncertainty should be identified as completely as possible. Examples include construction cost estimates that can vary widely, unpredictable weather that may make outdoor activities more difficult, or varying population growth that can increase or decrease the use of facilities. Some attempt should be made to recognize the uncertainty involved in the project. This may be as simple as offering a sensitivity analysis that calculates the value of the project under different outcomes or as complex as a real options analysis. In thinking about risk, it may be helpful to consider whether a project increases or reduces a community s exposure to risk. To put this somewhat differently, does the project resemble an insurance policy? If it does, then a project that appears at first to be undesirable might be worthwhile, just as the individuals within that community willingly purchase insurance whose expected value is less than its price. Example: Consider a village that practices primarily subsistence farming. A proposal to move the villagers to production of cash crops may have a positive expected value, but would expose the villagers to the additional risk of fluctuations in the market price of their cash crops. Because it would increase the risk to which the villagers are exposed, even a positive valuation might not be enough to justify doing this proposal. 9. Compare Benefits and Costs Having calculated (or at least listed) the costs and benefits, they should be compared to determine if the project might have a positive net present value (NPV). If multiple projects are being considered, the project with the highest NPV will usually be chosen. Net present value is the present value of a project's benefits minus the present value of its costs. One prerequisite for determining a net present value is deciding over what time period the project will be evaluated. Some projects have finite lifespans, and it is easy to determine over what period to evaluate their costs and benefits. Other projects will have costs and benefits over an indefinite period of time and it must be decided over how long a period to evaluate the project. If the project will have no costs or benefits after N years, then the present value is B NPV 0 C 0 B 1 C 1 B i 1 i 1 i 1 i N 2 C 2 B... N C N

18 EC 311 Lecture Notes 3 Page 18 of 19 where B t is benefits in period t C t is costs in period t i is the interest rate used in discounting. Time Period Benefits Costs Net Benefits If the interest rate equals 10% then the present value of this can be calculated as NPV NPV So, because the NPV > 0, this is a good project. If this project is re-evaluated at a discount rate of 20%, however, we have NPV NPV So, at the higher discount rate, it's a bad project. In general, because most projects have initial costs and benefits after some period of time, as discount rates rise, the number of projects which look good falls. Here's a graph of how the net present value of the project described above looks at different interest rates: 3 3

19 EC 311 Lecture Notes 3 Page 19 of 19 NPV Interest Rate It should be noted that the curve shown above is downward sloping because the costs of the project occur at the beginning while the benefits come later. Projects are also assessed based on the ratio of the present value of the benefits to the present value of the costs, known as the benefit cost ratio. The interest rate at which the net present value of the project is zero is known as the internal rate of return. For the project shown in the diagram above, this is approximately 16%. 10. Conduct a Post-project Analysis When possible, a follow-up analysis after completion of the project should be conducted to offer direction for the project's managers, determine the quality of the original analysis and to help improve future analyses and projects.