Endangered Species and Optimal Environmental Policy

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  • Journal of Environmental Management (1996) 47, 381389

    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 rms have adverse impacts upon endangeredspecies, we analyse the case when the marginal benet function of theendangered species is known, while uncertainty enters the marginal costfunction of species protection (modied operations). Marginal cost and benetfunctions 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 classicationendangered 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 classied as a purepublic good. (This denition 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

    38103014797/96/080381+09 $18.00/0 1996 Academic Press Limited

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    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 ndings 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 benets of the wolf (Canis lupus) and the white-backedwoodpecker (Dendrocopos leucotos), respectively, both of which are classied 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


    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 rms' 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 rms' activities and z. To nd the economic optimal population of this species, andhence, the optimal degree of modication of the rms' activities, we must know: (1)the social marginal benet (MB) of the endangered species (i.e. the marginal benetsto the public from increasing the population of the endangered species) and; (2) themarginal costs (MC) of modied operations to the rm (i.e. the negative marginalbenets that the rmsin our case reduced forestry operations and wolf-killed live-stockabsorb 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 rms, their cost-minimizingbehavior will normally lead to a number of z less than social optimum. Obviously, anexternality is present here. The rms' decision to reduce z affects the utility level of the

  • P. Fredman and M. Boman 383




    z2 z* z3 z4z



    C D

    A B


    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 rms. One possible way to reach z is to protect and/or increase the populationof this endangered species by modifying the rms' 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 rm). 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)

  • Endangered species policy384

    equal to z3z, 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 z2z1 (area C), while under a permit the equivalent error is equal to zz2(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 rst have some knowledge of the slope ofthe MC function relative to the slope of the MB function. Expressed in terms of socialloss (areas AD 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


    [MB(z)MC(z, u)]dz (2)

    where MC is given by (1), and MB(z)=cdz. 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 benet in social welfareunder the two policy instruments. The original proof, derived by Weitzman (1974),yields:

    W( f )W(z)=E[u2](bd)/2b2 (3)

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

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

  • P. Fredman and M. Boman 385



    E[MC] MC







    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 therm 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.


    In 1993, a CV study was undertaken to measure the economic benets 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$1SEK 775, 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 benets 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

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    economic benets 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 exible 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 signicantlyseparated at the 5% level, and there is no signicant 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.


    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 popula...


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