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Journal of Environmental Management (1996) 47, 381–389

Endangered Species and Optimal Environmental Policy

Peter Fredman and Mattias Boman

Department of Forest Economics, Swedish University of AgriculturalSciences (SUAS), S-901 83 Umea, Sweden

Received 24 July 1995; accepted 6 October 1995

This paper presents a theoretical model for developing an optimalenvironmental policy for endangered species management. It is argued that thechoice between Pigouvian taxes and quantitative permits is dependent upon thespecies under consideration, and therefore no policy prescription can be givenfor wildlife management in general. Under the assumption of negative externaleffects, where operations by the firms have adverse impacts upon endangeredspecies, we analyse the case when the marginal benefit function of theendangered species is known, while uncertainty enters the marginal costfunction of species protection (modified operations). Marginal cost and benefitfunctions are estimated from empirical data obtained in three different Swedishstudies. It is shown that the optimal policy for a species that primarilyrepresents an existence value is a quantitative regulation set equal to theminimum viable population (MVP). 1996 Academic Press Limited

Keywords: environmental policy, endangered species, tax, quantitativeregulation, existence value, minimum viable population (MVP).

1. Introduction

Endangered species management is a controversial and complex issue. The classification“endangered” is a subjective concept, created by our perceptions of the state of theworld. Nevertheless, endangered species can be a politically and managerially usefulconcept. Used correctly, it can help us to improve the management of the environmentand natural resources.

From an economic point of view, endangered species can be classified as a purepublic good. (This definition is only valid under the restriction that hunting of theendangered species is forbidden, which is generally the case. If hunting is allowed thespecies will swiftly change from a pure public good to a mixed public good, see Boadwayand Bruce, 1993.) As such, the “consumption” of endangered species is fully accessibleto all, and one person’s consumption does not diminish the consumption by others. Itis well known that the provision of public goods is often prone to invoke negative (orpositive) externalities. Since the presence of externalities in the economy is a source of

3810301–4797/96/080381+09 $18.00/0 1996 Academic Press Limited

Endangered species policy382

market failure, the socially optimal quantity of the good (species) may not always beproduced. Consequently, society may want to correct such market failures. Thiscorrection can be done through different methods, but the basic idea is to mimic thecompetitive market through some form of regulatory policy.

In this paper, we shall focus on two such approaches: Pigouvian taxes and quantitativepermits. First, we will make a formal analysis and compare the two in terms of socialwelfare. Next, we will combine the theoretical results with some empirical findings fromthree recent Swedish studies in order to derive some policy prescriptions regardingendangered species. Two of these studies are contingent valuation (CV) surveys, aimedat estimating the economic benefits of the wolf (Canis lupus) and the white-backedwoodpecker (Dendrocopos leucotos), respectively, both of which are classified as en-dangered in Sweden. The third study estimated the social costs for various wolfpopulation densities in Sweden. The policy prescriptions are based on an economicanalysis, where the objective is to maximize social welfare. We also argue that theseprescriptions cannot be generalized, since they are heavily dependent on the kind ofexternality/species under consideration.

2. Methods

2.1.

In this section, we will examine two types of policy instruments; Pigouvian taxes(referred to as a fee) and quantitative permits, both of which can be used as tools bya regulating authority to achieve the economic optimal level of some environmentalgood when negative externalities are present. We will also show the conditions underwhich one policy instrument is preferable to the other, at least in theory.

This presentation only considers the two limiting cases of quantitative regulationsand pure taxes. Dasgupta (1982) has shown that under uncertainty the optimal policyis, in general, neither of these two cases. It is rather to use a tax that is a function ofthe quantity of pollutants discharged (in this case, degrading the woodpecker’s habitatand hunting the wolf). However, Dasgupta also points out that for administrativereasons the planner may be forced to consider only the two limiting cases. If this is thecase, and the environmental resource displays a threshold effect, Dasgupta proposesthe use of quantitative regulation.

Assume our environmental good, z, is the number of individuals of an endangeredspecies in some designated area. This species is adversely affected by the firms’ operations(i.e. forestry in the case of the woodpecker and hunting in the case of the wolf) andfor simplicity we presume a negatively sloped linear relationship between the extent ofthe firms’ activities and z. To find the economic optimal population of this species, andhence, the optimal degree of modification of the firms’ activities, we must know: (1)the social marginal benefit (MB) of the endangered species (i.e. the marginal benefitsto the public from increasing the population of the endangered species) and; (2) themarginal costs (MC) of modified operations to the firm (i.e. the negative marginalbenefits that the firms—in our case reduced forestry operations and wolf-killed live-stock—absorb as an external cost of the provision of the species). Both are assumedto be linear functions of the endangered species population density as depicted in Figure1. Since property rights are generally allocated to the firms, their cost-minimizingbehavior will normally lead to a number of z less than social optimum. Obviously, anexternality is present here. The firms’ decision to reduce z affects the utility level of the

P. Fredman and M. Boman 383

z1

MB

f*

z2 z* z3 z4z

MC''E[MC]

MC'

C D

A B

S

Figure 1. Social welfare loss under different policy instruments given uncertainty in the MC function.

public negatively, without the public being able to control the outcome. Let E[MC]denote the expected MC function. Then, if MC is known with certainty, E[MC]=MCand z∗ is the Pareto-optimal outcome, since MB to the public is exactly offset by MCto the firms. One possible way to reach z∗ is to protect and/or increase the populationof this endangered species by modifying the firms’ operations. The regulating authoritycan do this either by means of a quantitative regulation, that is, decide a maximumallowable cut/hunting intensity, or by introducing a fee relative to the cut/huntingintensity in the area. In the woodpecker case, this could imply a fee per cubic metre(or hectare) of forest cuttings in woodpecker habitats. Similarly, a fee could be chargedfor each wolf killed.

If the MB and MC functions are known with certainty, a properly designed fee orquantitative permit will produce the same outcome. This result is easy to see in Figure1 where z∗ represents the optimal population level, which can be achieved either by apermit equal to z∗, or by a fee equal to f∗. Hence, under certainty the authority canchoose either of the two policy instruments to achieve economic efficiency. However,when uncertainty enters the MB and MC functions, the regulating authority can nolonger be sure of the output produced by the policy instrument used. Our concern hereis when uncertainty enters the MC function while the MB function is known withcertainty (the uncertainty in the MC function is on behalf of the environmentalauthorities, not the firm). If uncertainty enters the MB function, and the MC functionis known, it is easy to show that the error in social welfare is equal for the two policyinstruments because the source of the externality will respond to the policy along theMC curve (Baumol and Oates, 1988). However, the empirical analysis of this studyrelies on known MB estimates, while the MC function is less well known. As statedpreviously, E[MC] denotes the expected MC function which takes the form

MC=a+bz+u (1)

where u is a random component, E(u)=0, and E(u2)=r2 is the variance. From Figure1, we can now draw the following conclusions:

• When MC(z)<E[MC(z)], that is, when MC=MC′, the error under a fee is equalto z4−z3, or area B in terms of social welfare, while under a permit the error is


equal to z3−z∗, or area A in terms of social welfare. Accordingly, under a feepolicy the output of z will be excessive, while a permit policy produces aninsufficient number of z.

• When MC(z)>E[MC(z)], that is, when MC=MC″, the error under a fee is equalto z2−z1 (area C), while under a permit the equivalent error is equal to z∗−z2(area D). In this case the output relative to the optimal z is the reverse; a feepolicy produces insufficient z, while a permit policy is excessive.

The results derived above will give the regulating authority information about thedirection of the expected error of the policy programme used. However, they will notgive much guidance regarding which policy instrument to use, i.e. which policy willperform best and produce the smallest error (least social loss) when marginal costs areuncertain. To solve this problem, we must first have some knowledge of the slope ofthe MC function relative to the slope of the MB function. Expressed in terms of socialloss (areas A–D in Figure 1), we will make a more formal calculation to illustrate thismatter.

Our objective is to achieve the optimal value of z, obtained either by a permit (z∗)or by a fee ( f ∗), that maximizes the expected value of social welfare (W ):

W=E PZ

0

[MB(z)−MC(z, u)]dz (2)

where MC is given by (1), and MB(z)=c−dz. By substituting the optimal values of z,under a fee and permit regime, respectively, back into (2), we derive expressions ofW( f ∗) and W(z∗) and are able to compare the expected net benefit in social welfareunder the two policy instruments. The original proof, derived by Weitzman (1974),yields:

W( f ∗)−W(z∗)=E[u2](b−d)/2b2 (3)

where b(d) is the absolute value of the slope of the marginal cost (benefit) curve.Expression (3) is taken from Baumol and Oates (1988). Their presentation assumes

linearity in the marginal cost and benefit functions, similar to Adar and Griffin (1976).Weitzman (1974) worked with total cost and benefit functions and assumed linearapproximations of the marginal functions.

From expression (3) we can see that if b>d then a fee is preferred, while if b<d apermit policy is better. We also see that when the slopes of the two curves are equal(b=d ), the two policies are also equal in terms of social welfare. (This analysis is basedupon a number of assumptions, such as linearity in the MB and MC functions, randomdisturbance in the MC function and risk neutrality. One or more of these may not berelevant to real world problems.)

In this paper, we will focus on the two cases of a horizontal (d=0) and a vertical(d→∞) MB function, as depicted in Figures 2(a) and 2(b). Some general policyimplications follow from these two extreme cases. In the case of d=0, a fee will alwaysbe preferred to a permit regime. This is easy to realize since the fee ( f ∗) and the MBcurve will now coincide. In the other case, when d→∞, a quantitative permit yieldsthe optimal solution if the quantity is set equal to MB. From Equation (3) and Figures2(a) and 2(b) we can also see that the variance of u has no effect upon the choice ofpolicy instrument; it will only affect the magnitude of the difference between the two.


z

f*

E[MC] MC

MB

z

E[MC]MC

MB

z*

SS

Figure 2. (a) Optimal policy (f ∗) given a horizontal MB function, d=0. (b) Optimal policy (z∗) given avertical MB function, d→∞.

We can now draw the following conclusions:

• When the MB function is horizontal (vertical) and known with certainty, whileuncertainty enters the MC function, a fee (quantitative permit) will produce thesocial optimal quantity of z, our environmental good.

These conclusions will hold when the ex ante E[MC] function turns out to be erroneous,both regarding the absolute value of the slope and the magnitude of the intercept,compared with the ex post real MC function.

Finally, it is easy to realize that the wrong choice of policy instrument can haveundesirable effects when the MB function is vertical. This is due to the fact that thefirm reacts to a given fee along the MC curve, without considering the quantitativeoutcome. Thus, when using a fee, if the value of b or the magnitude of the MB/MCintercept turns out to be less than expected, an overprovision of the endangered specieswill occur. However, more important, if the value of b or the magnitude of the MB/MC intercept turns out to be greater than expected, then the provision of the specieswill be less than expected by the policymaker. This may be quite a fatal outcome whendealing with endangered species.

2.2.

In 1993, a CV study was undertaken to measure the economic benefits of the white-backed woodpecker in Sweden (see Fredman, 1994a, 1994b). Different samples ofrespondents stated their willingness to pay (WTP) for three different population densities,the current density and two larger, hypothetical ones. These populations were describedin words rather than exact numbers and mean WTP was estimated at SEK(US$1≈SEK 7·75, May 1994) 444, 416, and 368, respectively. Regression analysisindicated a non-positive (zero) marginal willingness to pay as a function of populationdensity (Fredman, 1994b). This result can, to some extent, be explained by the largenumber of respondents who ranked the existence of the species as their number onepriority for preservation. Similar results were also found by Stevens et al. (1991) whostudied the benefits of the bald eagle, Atlantic salmon, wild turkey and coyote in NewEngland. Since existence value is not related to any use of the species (rather it callsfor a value related to the human knowledge of the species existence) a zero marginalvalue above the minimum viable population is expected.

Another CV survey, conducted in the fall and winter of 1993/94, estimated the


economic benefits of various wolf population densities in Sweden (Boman and Bostedt,1994). In the scenario, presented in connection with the elicitation question, thesuggested wolf population was guaranteed to be at least the size of a minimum viablepopulation, MVP (Gilpin and Soule, 1986), that is, the viability of the population wasguaranteed if the project to which the respondents were asked to contribute was realized.A flexible Box-Cox functional form was used to derive the mean WTP (willingness topay, WTP, was estimated using a discrete choice elicitation question in both surveys),which was found to be SEK 1777, 709, 976 and 1415 for wolf populations of 25, 100,700 and 1000 individuals, respectively. However, these means were not significantlyseparated at the 5% level, and there is no significant marginal WTP for an increase inthe wolf population to levels above the MVP. A majority of the respondents also rankedthe existence of the wolf as the most important reason for preserving the species inSweden.

2.3.

Prior to the wolf survey presented above, a study was undertaken to derive the socialcosts for various population densities of the “four big” predators in Sweden, i.e. bear,wolf, wolverine and lynx (Boman, 1995). One assumption was that total costs areassigned mainly to predator-killed domesticated and semi-domesticated animals (e.g.sheep and reindeer). Of course, there are other costs as well, such as those related toresearch and administration. However, these costs are independent of the populationdensity and may, therefore, be treated as constants in the total cost estimates which donot affect the marginal cost of an increase in a predator population. In the case of thewolf, the total cost function was found to be linear. Using a number of estimationtechniques, the maximum marginal cost of an increase in the Swedish wolf populationwas found to be in the range SEK 87 000 to SEK 95 000, annually. In the followingwe will assume the intermediate marginal cost of SEK 91 000 per year and individual.Similar cost functions for protection of the white-backed woodpecker in Sweden havenot been estimated. However, the need for such functions may be limited as will becomeobvious in the next section.

3. Results

3.1.

Given the empirical results above, it is now possible to draw some conclusions regardingthe optimal environmental policy. We have learned that the WTP is positive for boththe wolf and the white-backed woodpecker, while the marginal WTP of a populationdensity increase is zero. Furthermore, in both surveys a majority of the respondentsrank the existence of the species as their first priority. The interpretation of these resultsis that respondents in the two surveys have a positive WTP for some minimum viablepopulation that will secure the continued existence of the species. But a zero marginalvalue implies that respondents are not willing to pay for an increase in the populationdensity above this level. From this we may draw the conclusion that existence value isa major component of the total value of these two wildlife species (see Fredman, 1994b).


0 MVP

z

MB

MC

MC

MC

MB

S

Figure 3. Estimated marginal benefit (MB) and possible marginal cost (MC) functions of two endangeredspecies.

Figure 3 features the MB function in the proximity of MVP, and z is the populationdensity. From this figure we can see that the MB function features a discrete jump atz=MVP. This jump should be equal to the aggregated mean WTP, that is, the totalbenefits. Population densities less than MVP (dotted line) represent a zero marginalvalue to society because such populations will become extinct in the long run. In thecase of the wolf, the marginal cost function was estimated to be constant for z>MVP,and in Figure 3 this marginal cost can be represented by the horizontal MC function,while the other two cost functions are arbitrary chosen.

Let us now pick up the previous discussion on optimal policies under a horizontal,alternatively a vertical, marginal benefit function. We found that these conditions callfor a fee, and a quantitative permit, respectively, to obtain the social optimal quantityof z. They also hold when uncertainty enters the marginal cost function. After inspectionof Figure 3, the optimal policy now becomes quite obvious:

• For populations in the proximity of MVP a quantitative permit yields the optimalpolicy, while populations greater than MVP call for a fee equal to zero.

The practical implementation of this is, of course, to set a quantitative regulation equalto MVP. However, optimality requires that MB=MC, and since MB is equal to theaggregated mean WTP at z=MVP, optimality is achieved as long as the MC is equalto, or less than, the aggregated mean WTP.

In order to clarify, we may think of the population density at MVP as one unit ofz. The MB at MVP is then equal to the aggregated mean WTP for z=MVP, while theMC (in the case of the wolf) is equal to 91 000 times the number of wolf individualsat MVP.

The aggregated mean WTP is derived by multiplying mean WTP by 5 949 000, thenumber of Swedes aged between 17 and 74 years (Anon., 1994), which also equals thesampling frame of the CV survey. This computation rests on the assumption that meanWTP is equal for respondents and non-respondents to the two CV surveys. In the caseof the wolf in Sweden, it is reasonable to believe that the MC at MVP (SEK 91 000times the number of wolf individuals at MVP) is below the total aggregated benefit ofan MVP which adds up to the staggering amount of SEK 7252×106. For the white-backed woodpecker no cost functions are available; however, it is likely that the MCis also below the aggregated mean WTP of SEK 2435×106 in this case.


Note that the aggregation procedure used assumes an equal weight (equal to one)for all individuals. This assumption implies, as Kanninen and Kristrom (1993) pointout, that projects which benefit wealthier individuals are more likely to pass the Kaldorcriterion than projects which benefit poorer individuals.

If the two empirical examples presented here are representative for endangeredspecies in general, the optimal policy is a quantitative permit set by the regulatingauthority with knowledge of the minimum viable population. In the case of the white-backed woodpecker, such a policy would imply that forestry operations should not beallowed when they degrade the natural habitats of the woodpecker to such an extentthat the overall population runs the risk of being reduced to a level below the MVP.Similarly, a feasible policy for a wolf population would be to issue enough huntingpermits to keep the population at the MVP level, no more and no less. Note that thisreasoning holds only as long as non-use (existence) values dominate. Other species,such as the moose in Sweden (see Mattsson, 1990), may also represent a significant usevalue in addition to the non-use values and, as a result, necessitate quite a differentpolicy. Consequently, any attempt to design a general wildlife policy will be misguided.As pointed out earlier, fatal consequences may follow from the wrong choice of policyinstrument if we have a vertical MB function. For example, in Figure 3 if MC>E[MC],a fee policy will cause extinction since f=MC will occur below MVP. In addition, notethat in the special case when b→0 the social loss under a fee regime will approachinfinity (this follows from Equation 3). (In the case of a horizontal MC function andno uncertainty, a fee could result in any population density z, including extinction.Note, this is true in the case of the wolf where the MC function is estimated to behorizontal.) Special care is, therefore, advised in any attempt to employ economicpolicy instruments in wildlife management when dealing with endangered species.

4. Discussion

The use of economic policy instruments as a means of achieving an optimal en-vironmental policy, in terms of species survival and biodiversity conservation, is currentlyreceiving increasing attention in Sweden (Eriksson and Hedlund, 1993). At the sametime, environmental authorities emphasise the importance of maintaining biodiversityfor future generations. Obviously, we have a quantitative objective to accomplish hereand, in this context, the choice of policy instrument may be crucial.

The aim of this paper was to investigate the theory of optimal environmental policywith respect to endangered species. Of course, such a short note on this complex issuewill not yield the optimal policy solution. At best it might give us a clue to the directionin which we need to move in order to reach the optimum. It is important to rememberthat this paper approaches the problem from a purely economic point of view, undera number of simplifying assumptions. There are ecological considerations which arenot included, and the practical feasibility of implementing a fee or quantitative permitis outside the scope of this model. However, the importance of having an objectivecriterion that can serve as a benchmark against other “non-economic” ingredients inthe decision-making process of creating an environmental policy has been pointed outby Weitzman (1974). The problem also features a time aspect. Decisions taken todayregarding our natural resources will necessarily have unknown effects upon futuregenerations. Since species extinction is an irreversible process, the regulating authoritycan use this as an argument to apply a quantitative policy. A quantitative policy will,in contrast to a fee, guarantee a certain quantity of the environmental commodity,


quite an important argument in endangered species management. As we have seen, aquantitative policy is also cost-effective under certain circumstances.

Finally, it is important to remember that the conclusions drawn in this paper holdonly when the species, to a large extent, represents a non-use (existence) value. Aspointed out earlier, there is probably no single policy instrument that is optimal for allwildlife species. For species representing a significant use value the marginal benefitsof populations larger than MVP is expected to be positive, and the problem may requirequite a different policy solution.

We would like to thank Professor Soren Wibe (Dept. of Forest Economics, Swedish Universityof Agricultural Sciences, SUAS), Professor Runar Brannlund (Dept. of Economics, Universityof Umea), Dr. Per Lundberg (Dept. of Animal Ecology, SUAS), Professor Bengt Kristrom (Dept.of Forest Economics, SUAS) and Goran Bostedt (Dept. of Forest Economics, SUAS) for theirvaluable comments on earlier versions of this paper. The research was financed by the researchprograms “Natural Resource and Environmental Economics Applied to Forestry and Agriculture”and “Production-Nature-Environment”, financed by the Swedish National Council for Forestryand Agricultural Research (SJFR) and by the Faculty of Forestry, SUAS, respectively.

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