THREATENED SPECIES AS PUBLIC GOODS AND PUBLIC BADS AN APPLICATION TO WILD PREDATORS IN SWEDEN by Göran Bostedt Dept. of Forest Economics Swedish University of Agricultural Sciences S-901 83 Umeå E-mail:
[email protected] Abstract This paper discusses Pareto efficient allocations of an environmental commodity, which is both a public good and a public bad, with an application to the Scandinavian problem of conserving wild predators that are killing semi-domesticated reindeer. The paper begins by briefly outlining this conflict. This is followed by a theoretical analysis employing a diagrammatic tool called the Kolm triangle, which is an analogue of an Edgeworth box in an economy with a public good. Bargaining, Pareto improving reallocations and the shape of the Pareto set are discussed, using a simple model, where one of the agents is involountarily contributing to a public good. The paper concludes with an analysis of income-loss compensations and incentives for illegal hunting of predators. Keywords: Bargaining, Compensations, Illegal hunting, Kolm triangle, Public goods Reindeer, Wild predators JEL Categories: D74, H41, Q28
I. INTRODUCTION Assume for a moment the position of a casual (presumably non-Scandinavian) observer of Swedish conditions, equipped with the knowledge that almost 98% (Boman & Bostedt 1997) of the Swedish people consider the wolf (Canis lupus) to be a public good. You may then wonder why the present Swedish wolf population only numbers approximately 30 wolves. Why is the Swedish wolf population so endangered1? The reason, which almost any Swede would be able to inform you, is that there is at least one group for whom the wolf is not a public good, but a public bad, namely the reindeer herders in the northern part of Sweden. This also holds for the other big predators in the Swedish mountain region, the wolverine (Gulo gulo), the lynx (Lynx lynx), and, to a certain extent, the brown bear (Ursus arctos). In other words, large predators in northern Sweden are both a public good and a public bad. Traditionally, economic theory texts concerning public goods (e.g. Cornes and Sandler 1986; Baumol and Oates 1988) usually consider the case in which the public commodity is a "good" for everyone. The case that we will deal with here involves an environmental commodity, a wild predator population, that is not actively produced by society (although it is assumed that the population can be controlled through hunting) and which has no direct effect on the income of most agents - let us call them the non-reindeer herders - but which negatively affects the income of some - the reindeer herders. This commodity will be refered to as both a public good and a public bad. The publicness comes from the fact that, for the non-reindeer herders, the existence of a certain predator population can be enjoyed by one person without reducing the available consumption for another. For the reindeer herders, a large predator, such as the wolf, is a public bad because the semi-domesticated reindeer move around in almost all of the northern half of Sweden and an increase in the predator population may occur anywhere in that area. The purpose of this paper is, first, to analyze Pareto efficient allocations of an environmental commodity, which is both a public good and a public bad, with an application to the predator-reindeer situation. However, it should be emphasized that the generality of the situation (i.e. that an environmental commodity is seen as a "good" by some but not all) makes the model applicable to many other situations as well. The second aim is to analyze how actual allocations are affected by possible actions such as bargaining, illegal hunting and compensation, and by different property rights entitlements. The paper is structured as follows: the next section contains a brief outline of the reindeer herding tradition and the historic development of the conflict. Then we introduce the theoretical framework using a diagrammatic tool known as the Kolm triangle and discuss efficient allocations and bargaining. We then turn our focus to issues concerning compensations and illegal hunting. The final section contains some concluding remarks.
II. PREDATORS AND THE REINDEER HERDERS -
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AN OUTLINE OF A CONFLICT The reindeer (Rangifer tarandus) has been more or less domesticated in Scandinavia for at least as long as there is written evidence (the oldest documents are from about 880 A.D.). Today there are around 320 000 reindeer in Sweden, owned by about 2 500 reindeer herders (Statistics Sweden 1997). Although the reindeer may seem wild to the casual observer, hiking or driving in northern Sweden, they are in fact all privately owned and truly wild reindeer are practically non-existent. Reindeer herding is now a modern business geared mainly towards meat production, and administered through small family companies formed by the reindeer herders (RH in the following). However, even though the RH of today use modern equipment, the basics of reindeer herding have changed fairly little over the centuries. The reindeer are allowed, with some exceptions, to follow their yearly cycle and search around for natural grazing grounds. The basic idea behind this traditional method is to allow grazing grounds to replenish themselves as the reindeer move from the high mountains to the coast and back again. One disadvantage with this method is that it becomes difficult to protect the reindeer from predators. The reindeer has always been subject to strong selective predation by natural predators, historically, mainly the wolf (Bjärvall et al. 1990). In recent centuries the Swedish predator populations have, however, decreased dramatically. When the wolf was made a protected species in 1966, about 10 animals remained. Today (spring 1997) the Swedish wolf population is increasing fairly rapidly and numbers more than 30 animals, most of them living south of the reindeer herding area (Ahlén and Tjernberg 1996). The wolverine, lynx and bear populations in Sweden now number approximately 150, 700 and 670 animals, respectively (Ahlén and Tjernberg 1996), a large part of them within the reindeer herding area. With regard to the effects of predation on the reindeer industry, information from a government commision report (SOU 1983:67) which reports the number of reindeer killed, and from Boman (1993) on the total reindeer stock, the losses in the period 197282 ranged between 1 and 1.7% of the total stock in each year. During the 1990s, however, the situation has changed due to the increase in the predator populations. Recent joint estimates by the Sami Council (Sametinget) and the Swedish Environmental Protection Agency (Naturvårdsverket) claim that, given the present predator populations, the yearly losses will be between 25 000 and 35 000 reindeer, i.e. between 8 and 11% of the total stock per year (Sametinget 1996). At the same time, concern for the impoverishment of biological diversity has grown steadily in Sweden during the 20th century , as in the rest of the industrialised world. In the last twenty years, at least four surveys have been carried out of Scandinavian attitudes towards predators. The first was undertaken by Andersson, Bjärvall and Blomberg (1977), and was sent to a stratified sample of the Swedish population including RH. The main finding was that, on average, the respondents in all subsamples were more or less positive towards the wolf2, with the notable exception of the RH who showed very negative attitudes. Similar results were found in a study by Norling, Jagnert and Lindahl (1981), and in a Norwegian CV study by Dahle, Solberg and Sødal (1987). A recent Swedish mail CV study of the benefits of preserving a Swedish wolf population
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(Boman and Bostedt 1994, and Boman and Bostedt 1997) showed that 72% considered the existence of wolves in Sweden to be important3. In the discrete choice WTP question different subsamples were asked to consider different potential wolf population sizes. The findings showed no significant increase in the benefit estimates with an increasing "supply" of wolves. This is interpreted as implying that the respondents mainly valued "securing" the survival of the wolf, and not the wolf population level in itself. This introduction has tried to briefly highlight the main issues in the reindeer-predator conflict. Even though much has been written, especially in the daily press, about this conflict few attempts have been made to analyze the problem from an economic point of view (Boman 1995, is an exception). This is somewhat surprising, as the conflict is definitely of interest to the social scientist. However, as mentioned earlier the analysis can also been seen as an example of a typical situation when a public good is also a public bad. III. EFFICIENT ALLOCATIONS - A THEORETICAL ANALYSIS This analysis will utilize a diagrammatic tool, called the Kolm triangle, to illustrate various results. The Kolm triangle can be looked upon as an analogue of an Edgeworth box for an economy with two agents (or two groups of agents), one private good and one pure public good. As will be shown, the Kolm triangle can also be used to illustrate the case when the public good provides disutility (i.e. is a bad) for one of the agents. The Kolm triangle first appeared in a text by Serge-Christophe Kolm on public economics (Kolm 1970). It is described in considerable detail in Schlesinger (1989) and Ley (1996). However, despite its apparent usefulness, it seldom appears in the literature4. Ley (1996) provides a handful examples of texts where the Kolm triangle has been used as a graphic device. To briefly introduce the reader to the workings of the Kolm triangle, we will begin by illustrating the ordinary case when the public good provides positive utility for one of the agents, Agent 1. The agent consumes one private good X1, and one public good, G, which is shared with another agent (or group of agents). He/she has a preference ordering over the pairs (X1, G) that can be represented by a differentiable and strictly quasiconcave utility function U1 X1 , G . Figure 1 illustrates an allocation of X1, X2 and G in a Kolm triangle, where X2 represents Agent 2's consumption of the private good. The Kolm triangle is equilateral, and any point inside the triangle represents a theoretically feasible allocation (for further details see Ley 1996). The distance from the left side of the triangle to the allocation point Z is equal to X1, while the corresponding distance from the right side is equal to X2. The vertical distance from the base line to Z equals the amount of the public good, G.
b g
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Figure 1. An allocation in a Kolm triangle How then can preferences for an agent who derives positive utility from the public good be represented in a Kolm triangle? Starting from an arbitrary allocation Z as in Figure 2 below and using a revealed preference argument, one can argue that allocations on an indifference curve passing through Z must be in the "upper left" and "lower right" region.
. Figure 2. An indifference curve for Agent 1 in a Kolm triangle Let us now consider the case when the public commodity is a public bad for one of the agents, for instance Agent 2, i.e. ∂ U2 ∂ G < 0 . If the marginal utility of a decrease in G is
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decreasing, i.e. if ∂ 2U ∂ G 2 > 0 , and if ∂ 2U2 ∂ G∂ X2 ≥ 0 (or at least not too large in absolute value), then the indifference curves will have the general shape exemplified in Figure 3.
Figure 3. Indifference curve for Agent 2 when the public commodity is considered to be a bad. Is this a relevant description of the RH when G is the predator population in the reindeer herding area? It can be argued that maybe the RH do not dislike the predators per se, only the fact that they reduce their income. Then the indifference curve would be parallel to the right hand side of the triangle (assuming X2 is the representative RH's consumption of the private good). However, it is not necessary to assume that the RH dislike predators per se to get the shape of the utility function depicted in Figure 3. It only needs to be assumed that they hold preferences over where the resources for private consumption come from, i.e. that they would rather live on their own reindeer herding than on reallocations from the other Swedes. This will be discussed further later. Let us initially disregard the compensation paid to RH and assume that the legal protection of the predators is strictly observed. What allocations will then be realised? Note that we are not dealing with a Nash equilibrium, since the outcome is not a result of a choice process, at least not on the part of the RH. What we are dealing with is a case of involuntary, rather than voluntary, contribution to a public good. We will denote the private consumption of the non-reindeer herder (or NRH for short) by X1 and the private consumption of the RH by X2. Initially we will assume that both groups are of equal size, although we will relax this assumption later. As shown in Boman (1995), each predator will reduce the total reindeer stock, and consequently, the income of a representative RH by a certain amount each year. By assuming a linear relation (i.e. the predators impose a constant marginal cost on the RH) and by choosing the units of the public good in a suitable way, we can make the marginal rate of transformation equal to one.
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If X1 and X2 (i.e. the distribution of income) in the absense of predators is given by point A in Figure 4 below, the RH's budget line is given by the line segment AB. In the absense of compensation or other reallocations between the two (groups of) agents, all realised allocations will be on this segment. Note that while the private consumption possibilities of the RH change along AB, the private consumtion of the NRH is unchanged, since he/she does not contribute to G. This important feature cannot be illustrated in an ordinary (Edgeworth) box-type diagram. At B the predator density is so high that it makes reindeer herding physically impossible. Most likely, the RH will find the business unprofitable and abandon it long before this. Let us denote the initial allocation in the absense of compensations Z. Figure 4 shows this allocation along the segment AB, and the indifference curve for the NRH, U 10 , and for the RH, U 02 , that passes through Z.
Figure 4. An allocation when Agent 2 is involuntarily contributing to the public good and the corresponding negotiation set. Obviously, since the indifference curves cross at Z, this allocation cannot be Pareto optimal. All allocations within the ellips bordered by U 10 and U 02 are Pareto superior to Z. Thus there should be room for bargaining. However, for bargaining to take place, there must be some incentive for the NRH to take part in such a process. Here it is important to note that the predator population will increase in the absense of hunting. If the NRH can rely on the RH to abide by the decided legal protection of the predators they can just sit tight, watch the allocation move up along AB, and let the RH pay the cost for the recovery of the predator population. The problem for the NRH is that they cannot rely on this, since there is always the implicit threat that some RH - or other livestock owners, if they have reason to - will illegally hunt the predators, despite sanctions5. The RH incentives for illegal hunting will of course increase with the size of the predator population. This gives the NRH an incentive for bargaining to reach Pareto sanctioned allocations. This in turn implies that the set bounded by U 10 and U 02 can be
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regarded as a negotiation set, or Nash bargaining set, with Z as the conflict point. A bargaining process would then involve compensations to the RH for the damages caused by the increasing predator population. The allocation Z' represents the largest Pareto sanctioned predator population, given the initial allocation Z. A Nash solution (which is Pareto optimal by definition) must then lie between z and z'. However, one underlying assumption in the above reasoning is that both parties agree on Z as the conflict point, i.e. that no compensation is paid to the reindeer herding party for the predator population associated with Z, only for increases above this level. Another distinct possibility is that the reindeer herding party adopts A as the conflict point, arguing that they have a right to an economic situation corresponding to one where no predators exist in the reindeer herding area. If the NRH agree upon A as the baseline for bargaining, a lens-shaped negotiation set similar to the one depicted in Figure 4, but with allocation A as the conflict point, can be constructed. On the other hand if, in this case, the NRH maintain that Z should be the baseline for negotiation, the negotiation set may become empty, in which case bargaining will fail. One possible outcome of such a situation is that some RH will resort to illegally hunting predators. The incentives for illegal hunting will be discussed further below. Figure 4 illustrates a case where movements towards a Nash solution in the Pareto set involve reallocations from the NRH to the RH. However, one might conceptually imagine reverse cases, as depicted in Figure 5 below. Here, if the initial predator population is larger than G0 the RH have an incentive to pay the NRH to be allowed to hunt some of the animals.
Figure 5. The Pareto set
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Naturally, the shape of the Pareto set depends on the preferences of the agents. In general, the predator population associated with an efficient allocation depends on the initial assignment of rights. However, when both agents have quasilinear preferences the Pareto set is simply a horizontal line. This result is, of course, the famous Coase theorem (Coase 1960). It has been said earlier (e.g. Varian 1993), but it is worth restating, just how special the conditions are for the Coase theorem to hold, and the no income effects assumption is not likely to hold in the case of wild predators in the Swedish mountain region. This means that the outcome of a Coasian bargaining process is not likely to be independent of the initial assignment of rights. However, the reasoning this far only holds when the number of NRH equals the number of RH. In reality, the NRH outnumber the RH by about 3 400 to 1. Is it still possible to use the Kolm triangle to illustrate allocations when one party substantially outnumbers the other party? The answer is yes - it just gets somewhat more tricky. To give a principal illustration of this case, let us for simplicity assume that there are twice as many NRH (who all have identical preferences) as there are RH. We will then search for the allocation denoted Z' in Figure 4, which marks the outer bound of the negotiation set6. The Kolm triangle in Figure 6, below, shows allocations for one representative of each agent. As illustrated, the allocation Z' can no longer be represented by only one point in the triangle. This is due to the fact that each RH can receive transfers from two NRH. Accordingly, Z' 1 represents the consumption point for the representative NRH at the allocation Z', while Z' 2 represents the consumption point for the representative RH (which, for the reason stated above, is not constrained to be within the triangle). In Figure 6, ∆X represents the transfer associated with Z' from each NRH to each RH, who then receives 2 * ∆X . The negotiation set in this case becomes separated into two subsets, where consumption points for the NRH must lie in the area bounded from above by a straight line between Z' and Z' 1 (not shown in figure) and from below by U 10 . Correspondingly, the associated consumption points for the RH must lie in the area bounded from above by U 02 and from below by a straight line between Z' and Z' 2 (not shown in the figure).
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Figure 6. Allocations when Agent 1 outnumbers Agent 2 by two to one. The above shows that the Kolm triangle framework can easily handle cases where the relative size between two groups of agents differ. It should come as no surprise that the allocation Z' = Z' 1 , Z' 2 involves a higher predator population when the NRH outnumbers the RH by two to one. This suggests that it would be possible to compensate the RH for large increases in the predator populations. The problem with this is that it would imply that an increasing fraction of the RH's income would come from transfer payments rather than directly from reindeer herding. To see this, compare Z, where all of the resources for private consumption come from reindeer herding, with Z' 2 , where the majority comes from transfer payments. There are strong reasons to believe that there is a limit to the extent to which it is possible to fully compensate the RH for increases in the predator populations through transfer payments. This is simply because the RH have preferences not only with regard to private consumption, but also as to where the resources for private consumption come from7. This would imply that the indifference curves for the RH become horizontal, or nearly horizontal, above certain levels of G.
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IV. COMPENSATIONS AND ILLEGAL HUNTING We now change our focus slightly and look at the efficiency of compensation schemes and the incentives for illegally hunting predators. We substitute "the government" for NRH, as we will be dealing with cases where the government acts as counterpart to the RH. We concentrate on the efficiency associated with government policies, rather than on efficient allocations in general. Suppose that the initial allocation is somewhere on the RH's budget line and that the government decides that the RH should be fully
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compensated for the income loss caused by the predators8. Is this a Pareto sanctioned decision and is the post-compensation allocation closer to the Pareto set than the without-compensation allocation? These are two different questions, and the answer to the first one is no, while the answer to the second one is maybe. Consider the allocation Z in Figure 7 below. This allocation may be on, below, or above the Pareto set. In the first case there are no possible Pareto sanctioned reallocations. In the two other cases Pareto sanctioned reallocations involve mutually beneficial payments from the NRH to the RH to allow increases in the predator population (i.e. movements to the "northwest" of Z) or vice versa (i.e. movements to the "south-east" of Z), respectively. A pure income-loss compensation at the initial predator population is illustrated in Figure 7 as a move from Z to Z'. Such a one-dimensional change can never be a Pareto sanctioned reallocation. Another way to say this is that, if the government's ambition is to make Pareto sanctioned changes, compensation must be discussed in close conjunction with discussions concerning the size of the predator population. Whether the postcompensation allocation Z' is closer to the Pareto set than Z is a totally different question, which cannot be given a definite answer based purely on economic theory. However, one thing is certain - if the government's ambition is to fully compensate the RH, the income-loss compensation (denoted ∆ X ) fails. This is clearly visible in Figure 7, since Z' involves a lower utility level, U 02 , than the one associated with allocation A, U 12 , where no predators exist in the reindeer herding region. This is due to the assumption that the RH have preferences regarding where the funds for private consumption come from, i.e. they would rather live on reindeer herding than compensation. These assumptions also imply that if the RH is given a choice between a pure income-loss compensation (and no right to hunt predators) and the right to protective hunting, which both result in the same ex post income level, the RH would always choose hunting. This also means that the RH would be willing to pay a certain sum - for instance in lobbying costs - to get hunting rights. Full compensation entails a further leftward movement from Z' until the RH obtains the same utility level as in A, U 12 . This may, however, prove to be expensive, especially if the predator population continues to grow.
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Figure 7. Income-loss compensation, protective hunting, and illegal hunting. If the legal right to protective hunting is always prefered to income-loss compensation schemes, what about illegal hunting of predators? What strategy is optimal, to accept the compensation and the current predator population, or to hunt illegally? Here we concentrate on the incentives that may make RH into illegal hunters of predators, but it should be remembered that other groups, such as farmers with livestock, may also have an incentive to hunt illegally. The analysis extends to the latter group as well. As we analyze illegal hunting, we move away from bargaining towards a non-cooperative game theoretic situation. To analyze assumed illegal hunting, we need to add some assumptions about what happens should the illegal hunter get caught. If the legal protection is not enforced at all, illegal hunting is risk-free and the illegal hunter can gradually reduce the predator population and still collect compensation for the reindeer (or livestock) killed by the remaining predators. This compensation will then diminish but will be replaced by the (prefered) income from the reindeer herding business. In terms of Figure 7 this means that the illegal hunter can move along the illustrated straight line from Z' to A. If there is a certain expected risk of getting caught for each predator that is illegally hunted, α (0 ≤ α ≤ 1 ), combined with a penalty, F, this straight line rotates counter clock-wise, as indicated in Figure 7. However, there might still be an incentive for illegal hunting if α and/or F are sufficiently low9. Assume that G0 is the predator population associated with allocation Z' (and Z), and w2 is the without-predators income from reindeer herding then U 02 = V2 ( w2 , G0 ) describes the indirect utility for the potential illegal hunter at Z'10. Illegal hunting changes the indirect utility function to V2 ( w2 − αFh, G0 − h ) , where h is the number of illegally hunted predators. The hunter's optimal level of h occurs when the marginal value of reducing the predator population
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with one more animal equals the expected fine when that animal is hunted. In Figure 7, this condition is fulfilled at allocation z'' for a low level of α and/or F. This means that the RH has an incentive to illegally hunt the predators as long as the predator population is larger than the one associated with z''. To keep the predator population at G0, the government must increase α, through the level of enforcement activity, or F, the penalty, resulting in further counter clock-wise movement, as indicated by the arrow in Figure 7, until no incentives for illegal hunting remains11. A problem with strict enforcement (or high penalties) is that it is likely to be very unpopular with the RH, since it indicates distrust. This means that the government is faced with a situation that is similar to "the Welfare Game", a well-known game theoretic problem, first described by Tullock (1983), see also Rasmusen (1994). The government has a choice between strict and lenient enforcement, where strict enforcement implies, not only that it is not in the interest of the individual RH to illegally hunt predators, but also that there will be bad relations with the community of RH, which is not in the interest of the government. The RH then has a choice between illegal hunting or not. This game is interesting, since it has no Nash equilibrium in pure strategies. Starting at the allocation Z', and with a lenient enforcement, the RH would illegally hunt predators. The government would then choose the strict enforcement as indicated by the arrow movement in Figure 7, and the RH would respond by ceasing to hunt illegally. However, if there is no illegal hunting the government has an incentive to reduce enforcement to the old level, which once again generates incentives for illegal hunting, and so on. Theoretically, this process should converge to a mixed strategy equilibrium, where the government imposes a "middle level" enforcement, and the RH illegally hunts when the predator population is so high that the marginal value of depleting the population is higher than the expected penalty. An alternative government strategy may be to use a differentiated penalty scheme. This is similar in spirit to the enforcement/penalty scheme which was suggested by Greenberg (1984), and further developed by Romstad (1990). This scheme may be used to theoretically divide the RH into three groups: those who have never illegally hunted predators (G1), those who have hunted illegally and been punished once (G2), and those who have hunted illegally and been punished two or more times (G3). Members of G2 may move back to G1 if, when controlled, they do not illegally hunt predators again. Members of G3 may, however, never be moved back to G2 or G1. One can then use a penalty for members of G3 severe enough to make it optimal for members of G2 never to hunt illegally again. G3 will then be an empty set. The penalty for G2 members can then be kept fairly low but still result in a lower level of illegal hunting than if such a low penalty was used uniformly. Note the correspondence between this system and the practice of suspended sentences, which is fairly common in Swedish legal practice. Such a differentiated penalty scheme would also be easier to accept for the RH than a uniform high penalty.
V. CONCLUDING REMARKS
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This paper has used the Kolm triangle to analyse the case when one agent is involuntarily contributing to a public good. The Kolm triangle shows itself to be a powerful tool to understand the intricacies of such a case. Even if the application in the paper has been to the reindeer - predator conflict in Scandinavia, the generality of the model should be emphasized. Involuntary contributions to environmental commodities are not an uncommon source of conflicts. It is frequently local people, sometimes in poor countries with a rich biodiversity, who bear the social cost when habitats are set aside for conservation. The benefits, in terms of existence values, of such conservation often accrue to the more affluent citizens of the Western world. African elephants, which evoke positive sentiments for most westerners, but which often cause considerable problems for local farmers when they forage on private farmland, are a case in point (see Vredin 1995). Another example might be the spotted owl protected in the United States under the present Endangered Species Act (ESA). Since the ESA prohibits "takings", i.e. any action that might reduce the owl population, and since the spotted owl requires a large habitat of old-growth forests, considerable areas have to be set aside for conservation purposes, affecting forestry companies and consequently the local population (e.g. Montgomery, Brown and Adams 1994; Hagen, Vincent and Welle 1992). In both of these conflict areas the Kolm triangle could profitably be used as an analytical instrument. Furthermore, as is shown in the paper, the Kolm triangle framework can also easily handle cases where the relative size between two groups of agents differs. The restriction that both types of agents must have Gorman-form utility functions is necessary for the representative consumer model to hold (Varian 1992). However, it is not too restrictive as the Gorman-form is fairly general and, for instance, contains both the homothetic and the quasilinear utility functions as special cases. On the other hand, the assumption of linearity in the predation effects on reindeer is, perhaps, more restrictive. Linearity is a necessary assumption for the Kolm triangle depiction to hold, otherwise, if the reindeer herder's budget line is non-linear, the consumption possibilites of the non-reindeer herders are directly affected (i.e. without reallocations) as the predator population increases12. This is a result which is both unintuitive and inconsistent with the theoretical model. Nevertheless, non-linearities may occur, in the context of this paper, if a pack-forming predator becomes common, starts forming large packs, and thereby becomes a more efficient hunter. Of the "four big" predators in the Swedish fauna, the wolf is the only one that hunts in packs, and is, thus, most likely to cause nonlinearities. It is hard to judge the importance of this problem, more than to say that it increases with the size of the predator populations, i.e. at allocations in the upper part of the Kolm triangle.
ACKNOWLEDGEMENTS
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This paper is based on research that was made possible by financial support from the Faculty of Forestry, Swedish University of Agricultural Sciences (SUAS), the Swedish National Council for Forestry and Agricultural Research (SJFR), and from the Helge Ax:son Johnson foundation. The paper also relates to the planning of a MISTRA-project on natural resources in the Swedish mountain region. The author would like to thank (without implicating) Mattias Boman, Leif Mattsson, Peichen Gong, and Peter Lohmander, all at SUAS, Eirik Romstad, Agricultural University of Norway, and two anonomous reviewers for comments on earlier versions of the paper. REFERENCES Ahlén, I. and M. Tjernberg (1996) Rödlistade ryggradsdjur i Sverige - Artfakta (Redlisted Vertbrates in Sweden - Species Facts). Uppsala: Swedish Threatened Species Unit, Swedish University of Agricultural Sciences. Andersson, T., A. Bjärvall and M. Blomberg (1977) Inställningen till varg i Sverige En intervjuundersökning (Attitudes towards wolf in Sweden - A survey). Stockholm: Statens Naturvårdsverk, PM 850. Baumol, W. J. and W. E. Oates (1988) The Theory of Environmental Policy. Cambridge: Cambridge University Press. Bjärvall, A., R. Franzén, M. Nordkvist and G. Åhman (1990) Renar och rovdjur (Reindeers and Predators). Stockhom: Naturvårdsverket Förlag. Bohlin, J. (1996) Rovdjur - ersättning för rovdjursrivna renar (Predators Compensations for Predator-killed Reindeer). Umeå: Memo from the Swedish Sami Confederation (SSR). Boitani, L. (1992), 'Wolf Research and Conservation in Italy'. Biological Conservation 61, 125-132. Boman, M. (1993) Kostnader för de "fyra stora" rovdjuren i svensk fauna - En samhällsekonomisk studie (Costs for the "Four Big" Predators in the Swedish Fauna - An Economic Study). Umeå: Working Report No. 165, Dept. of Forest Economics, Swedish University of Agricultural Sciences. Boman, M. (1995), 'Estimating Costs and Genetic Benefits of Various Sizes of Predator Populations: The Case of Bear, Wolf, Wolverine and Lynx in Sweden'. Journal of Environmental Management 43, 349-357. Boman, M. and G. Bostedt (1994) Wildlife Valuation - Estimating the Benefits of the Wolf in Sweden. Umeå: Working Report No. 198, Dept. of Forest Economics, Swedish University of Agricultural Sciences. Boman, M. and G. Bostedt (1997), 'Valuing the Wolf in Sweden: Are Benefits
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Contingent upon the Supply?', in Boman, M., R. Brännlund and B. Kriström, eds., Topics in Environmental Economics. Amsterdam: Kluwer Academic Press. Coase, R. (1960), 'The Problem of Social Cost'. Journal of Law and Economics 3, 1- 44. Cornes, R. and T. Sandler (1986) The Theory of Externalities, Public Goods, and Club Goods. Cambridge: Cambridge University Press. Dahle, L., B. Solberg and D. P. Sødal (1987) Haldningar til og betalingsvillighet for bjørn, jerv og ulv i Noreg (Attitudes to and Willingness to Pay for Bear, Wolverine and Wolf in Norway). Ås: Report No. 5/1987, Dept. of Forest Economics, Agricultural University of Norway. Greenberg, J. (1984), 'Avoiding Tax Avoidance: A (Repeated) Game-Theoretic Approach'. Journal of Economic Theory 32, 1-13. Hagen, D. A., J. W. Vincent and P. G. Welle (1992), 'Benefits of Preserving OldGrowth Forests and the Spotted Owl'. Contemporary Policy Issues 10, 13-26. Kolm, S.-C. (1970) L'É tat et Le Système des Prix. Paris: Dunod-C.N.R-S. Ley, E. (1993) On the Private Provision of Public Goods: A Diagrammatic Exposition. Ann Arbor: Working Paper No. 93-27, Center for Research on Economic and Social Theory, University of Michigan. Ley, E. (1996) On the Private Provision of Public Goods: A Diagrammatic Exposition. Investigaciones Economicas 20, 105-123. Montgomery, C., G. M. Brown and D. M. Adams (1994), 'The Marginal Cost of Species Preservation: The Northern Spotted Owl'. Journal of Environmental Economics & Management 26, 111-128. Norling, I., C. Jagnert and B. Lindahl (1981) Vilt och jakt, sociala och ekonomiska värden: Viltet och allmänheten (Game and Hunting, Social and Economic Values: The Game and the General Public). Stockholm: Report No. 5, Ministry of Agriculture. Rasmusen, E. (1994) Games and Information: An introduction to Game Theory. Oxford: Blackwell. Romstad, E. (1990) Pollution Control Mechanisms when Abatement Costs are Private Knowledge. Ph.D. Thesis, Corwallis: Dept. of Agricultural and Resource Economics, Oregon State University. Sametinget (1996) Samerna och rovdjursfrågan (The Sami and the Predator Issue). WWW-document on URL: http://www.sametinget.se/st/aktrovd.html. Schlesinger, H. (1989), 'On the Analytics of Pure Public Good Provision'. Public
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Finance 44, 102-109. SOU, Statens Offentliga Utredningar (Swedish Government Reports), 1983:67 Rennäringens ekonomi (The Economy of the Reindeer Industry). Stockholm: Allmänna Förlaget. Statistics Sweden (1997) Statistical Abstract of Sweden. Stockholm: Allmänna Förlaget. Tullock, G. (1983) Economics of Income Redistribution. Boston: Kluwer-Nuhuff. Varian, H. R. (1992) Microeconomic Analysis. New York: Norton. Varian, H. R. (1993) Intermediate Microeconomics. New York: Norton. Vredin, M. (1995) Values of the African Elephant in relation to Conservation and Exploitation, Umeå: Umeå Economic Studies, No. 390, University of Umeå. NOTES 1
Italy, with a human population density ten times that of Sweden, has a wolf population of about 200300 animals (Boitani 1992) 2
It is important to note that at the time of the survey there were virtually no wolves in Sweden.
3
Note that since the sample was unstratified the likelihood that it would include any reindeer herders was small. As it turned out, no reindeer herders were included in the realised sample. 4
A search made on the March 1996 EconLit CD-ROM (produced by the American Economic Association) for entries containing "Kolm" and "triangle" returned only Schlesinger (1989) and Ley (1993), the latter being an older version of Ley (1996). 5
The reindeer herder organisations are naturally much too diplomatic to articulate such threats bluntly, but they can be read between the lines in statements. For instance, in a recent letter to the Swedish government a reindeer herder organisation argued that inadequate compensation indirectly means that the Swedish parliament is "determining the number of predators that may exist in the reindeer herding area (author's translation)" (Sametinget 1996). Note that the predator population associated with z' is the highest population that can be reached by negotiation. The realized population of a negotiation process could be much lower. 6
7
One way to formally incorporate this in the reindeer herders' utility function is to include the reindeer stock as a nonconsumptive good. 8
It can be discussed whether or not the present Swedish government policy amounts to a full income compensation. The reindeer herders feel that it is inadequate and based on weak ground regarding the size of the predator populations (Bohlin 1996). 9
Hunting in Sweden is regulated in the Hunting Act of 1987, the Hunting Decree of 1987, and the Environmental Management Act of 1964, which all state that all wildlife for which there is no general
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hunting period is protected and belongs to the crown (i.e. the Swedish nation). Should an offence be considered to be serious, e.g. if the game is a rare species, the penalty can be prison for up to one year. The first term in the indirect utility function should really be w2 − G0 + ∆x , but since an income-loss compensation implies that ∆x = G , it can be reduced to w2 .
10
It should be noted that penalties very seldom change, which means that the enforcement policy, α, is more likely to change than the penalty, F. 11
To see this, try bending the line segment AB in, for instance, Figure 4, and compare the consumption possibilities of the non-reindeer herder in A and in B. 12
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