An insiuional perspecive on exernaliies. The Nordic wolf re-colonizaion Eivind Egeland Aronsen Aronsen Consuling N-7020 Trondheim, Norway Anders Skonhof Dep. of Economics Norwegian Universiy of Science and Technology N-7034 Trondheim, Norway Jan Tore Solsad Trondheim Business School, Sør-Trøndelag Universiy College N-7050 Trondheim, Norway Absrac The paper discusses and redefines he radiional concep of exernaliies. Inspired by J.R. Commons heory of insiuional evoluion we define exernaliies as policy relevan insiuional inerdependencies. Our concep of exernaliies is more general and reflecs insiuional failure raher han marke failure. We exemplify our insiuional concep of exernaliies by discussing he conflics associaed wih he re-colonizaion of wolves in Scandinavia. Pinpoining he conflic beween wolf managemen and sheep farming, we idenify exernaliies in he de jure propery righs o he pasures: As he wolf is supposed o live in muli-use landscapes, he grazing righ of he sheep farmers and he public righ o have a viable wolf populaion are muually exclusive. Compensaion paymens for sheep killed by wolves only redisribue benefis and coss beween he sheep farmers and he wildlife auhoriies (represening sociey a large), and do no reduce he conflic. One way o eliminae he exernaliies is o clarify he de jure propery righs and separae sheep and wolves. JEL code: Keywords: Q20 Exernaliy, Insiuions, wolf managemen, sheep farming
1. Inroducion The economic lieraure on exernaliies is enormous and i has been claimed o be one of he leas coheren and mos conenious areas of economic analysis (Bromley, 1991:67). The presen paper scruinizes he insiuional aspec of exernaliies. Our approach is inspired by J. R. Commons selecion heory of insiuional evoluion where a each momen of ime he prevailing insiuional srucure defines he opporuniy se for individual acion, and where one indivisual s righ is anoher s duy (Biddle, 1990; Bromley 1991). However, various de jure individual righs and correlaed duies may be muually exclusive, and hence in conflic wih each oher, so ha one individuals righ may affec he de faco individual righs of ohers. For example, he insiuion of having complee privae conrol of land may be in conflic wih he public righ of biodiversiy preservaion. Accordingly, when a privae landowner follows his narrow selfineress and, say, legally maximizes he ne benefis of his imber logging value, his will in general come in conflic wih he public righ of biodiversiy preservaion. Hence, he legal claims of he differen agens are muually exclusive, or in oher words, he prevailing assignmen of propery righs are inconsisen. In his aricle we will analyse such conflics from a concepual poin of view. The analysis will be exemplified wih a real life example, namely he much debaed conflics caused by he re-colonizaion of wolves in Scandinavia. Some few decades ago here were bounies for killing wolves in Norway (as well as in Sweden). However, in 1972 he bounies were replaced by a wolf preservaion policy. The proecion of he Scandinavian wolf was srenghened during he 1980s when Norway and Sweden became signaory members of he Bern-convenion. The insiuional change - opening up for he re-colonizaion of he wolf - refleced a change of preferences; raher han seeing he wolf as a mere nuisance, people began o appreciae he idea of having a viable wolf populaion in heir counry, i.e., wolves evenually generaed exisence value. The new preferences were opposed o he old insiuional seing of bounies and riggered insiuional change. In he presen paper we will redefine he erm exernaliy and undersand i as a driving force in he process of insiuional change. Our principal discussion sars in secion 2 wih a raher broad discussion abou he radiional concep of exernaliies. In secion 3, we discuss more closely he insiuional perspecive on exernaliies inspired by he work of J. R. Commons. In secion 4 we presen he Scandinavian wolf example, which in secion 5 is sudied more formally by consrucing a sylized bioeconomic model including wo agens wih conflicing 1
ineress; a group of sheep farmers and he wildlife auhoriy. The sheep farmers have he legal righ o graze heir sheep on public, as well as on privae, land during he summer oudoors season. The sheep farmers follow heir selfineres and maximize he economic benefi of heir sheep sock. However, because of predaion by he wolf his will come in conflic wih he public righ of keeping a viable wolf populaion. The managemen of he wolf populaion is assumed o be aken care of by he wildlife auhoriy, or The Direcorae of Naural Resource Managemen, wih he goal of maxmizing he wildlife benefi consising of he exisence value of wolf (Kruilla, 1967; Aldred, 1994; Afield, 1998)bu also accouning for he fac ha he wolf prey upon he sheep sock. The oucome of he model is discussed in secion 6 while secion 7 summarizes our findings. 2. On exernaliies Our discussion of exernaliies begin wih a look a he famous sag hun example by Rousseau (1974) 1. Five huners, wih a rudimenary abiliy o speak and o undersand each oher come ogeher a a ime when hey are all hungry. Since he hunger of each one of hem will be saisfied by a fifh par of a sag, hey agree o cooperae o rap one. Bu he hunger of any one of hem will also be saisfied by a hare, so as a hare comes wihin reach, one of hem grabs i, and by pursuing his individual self ineres in his manner permis he sag o escape. From his simple sory, he economis could make several observaions. 2 Firs, if we presume ha he uiliy funcions of he paricipans are of he sandard ype preferring more food o less, each of he individuals uiliy funcions are dependen on he ohers in he sense ha he sill hungry paricipans uiliy levels remain low because of a decision uni exernal o hemselves. Second, he resul is ineffecive wheher efficiency is defined in Pareo erms or in erms of maximizing oal producion: Assuming ha a hare and a fifh par of a sag are perfec subsiues, cooperaion will boh raise oal producion and he welfare of he ohers wihou compromizing ones own welfare. Third, as he sag huners agreed o cooperae, meaning ha he ransacion coss of informaion and negoiaion were manageable, he ransacion cos of enforcemen were apparenly no since cooperaion failed o maerialize. This poins o he imporance of ransacion coss in he undersanding of exernaliies. 1 Firs ediion 1762. 2 Kenneh Walz, 1959: Man, he Sae and War,provides a classical piece of poliical science discussing Rousseau s example in connecion wih inernaional relaions heory. 2
In line wih his, inerdependency of decision unis, inefficiency and ransacion coss are imporan facors when i comes o characerizing exernaliies. However, in he lieraure we find various exernaliy definiions along hese dimensions. Firs we have he view ha exernaliies as inerdependency should be confined o uninended concequences of inended individual acions. Among ohers, in he auhoriaive exbook, Baumol and Oaes (1988, p. 17), sae ha: An exernaliy is presen whenever some individual s (say A s) uiliy or producion relaionships include real (ha is, nonmoneary) variables, whose values are chosen by ohers (persons, corporaions, goverernmens) wihou paricular aenion o he effecs on A s welfare. The moivaion for his limiaion seems reasonably clear. If someone comes driving ino your garden and dumps his garbage, his is a differen social phenomena han if smoke from a facory makes your lawn wiher. The firs is inenional, he second o a cerain exen, bu only o a cerain exen, an uninended by-produc. I is only he second phenomena we should seek o address by exernaliy heory. However, problems wih his disincion arises when he heory is applied o he real world. In he exbook example of he polluing firm, he firm will, afer some ime, surely learn ha he smoke i emis has adverse effecs on he neighborhood. If he emission coninues, he exernaliy may be incidenal o he main business of he facory, bu no uninended (Schmid, 1987). Theoreically i is also highly problemaic o assume ha he engineers in profi maximising facories are generally unaware ha heir producion has some unforunae byproducs (Van and Bromley, 1997: 147). Therefore, i seems reasonable o assume ha he facory akes advanage of he opporuniies ha he insiuional seing provides, i.e, if abaemen is required or no, o which degree i is required, compensaion of affeced paries, and so on. Real world applicaions of a definiion including he uninended aspec may be furher hwared by uncerainy and/or asymmerical informaion. For a period i may be uncerain or even unknown if a cerain polluan is a healh hazard. There may be uncerainy regarding how much he facory emis, presumably wih he facory holding more informaion han he governmen, ec. For hese reasons i seems doubful if incorporaing he uninended aspec will be very helpful in policy prescripions. 3
Second, we may disinguish beween exernaliies as marke or non-marke inerdependency. This brings us o he differen sands of he Coase (1960) influenced bargaining model and he Pigovian influenced model of sae regulaion (Van, 2005). These models consider exernaliies as inefficiency, and hey do so quie differenly. We sar wih exploring he Coasean perspecive. Concepualizing exernaliies in Pareo-erms, Buchanan and Subblebine (1962) make a disincion beween Pareo-relevan and irrelevan exernaliies. If no gains can be obained by one pary wihou making he oher worse off, hen he exernaliy is Pareo-irrelevan. For an economy locaed on a Pareo-opimal poin, hen, here can be only Pareo-irrelevan exernaliies. These reflec marke inerdependency beween agens on a Pareo-efficien level. The meris of his disincion can be viewed in ligh of he classical example of he polluing firm causing damage o a downsream fishery. I is possible for he facory o abae he polluan raher han dumping i in he river, bu his will be cosly. Under he assumpion of zero ransacion coss, bargaining ensures ha we arrive a an efficien equilibrium, where marginal abaemen coss equal he marginal coss of polluion, wheher he firm is given he righ o pollue or he fishery is given he righ o an unpollued river. In so far as ransacion coss are zero, and all non-marke values are privaized, all non-marke inerdependency will be urned ino Pareo-efficien marke inerdependency hrough he process of bargaining. This resul is ofen referred o as he Coase Theorem: If only propery righs are clearly defined, efficiency will be obained irrespecive of who is given he propery righs. In equilibrium, he river will sill be pollued and exernaliies as marke inerdependency will be presen. Bu here will be no exernaliies as inefficiency - he level of polluion will be Pareo-efficien and he exernaliies will be Pareo-irrelevan. This reasoning of course presupposes he absence of income effecs (e.g., Bromley 1991). This needs a lile reflecion. In he sag-hun example above, he ransacion cos of enforcemen was he cause of he exernaliy. How meaningful is i hen o analyse exernaliies under he assumpion of zero ransacion coss? Indeed, Dahlman (1979:161) says ha wihou ransacion coss exernaliies would be of no consequence, and Bromley (1991: 63) saes ha in a world wihou ransacion coss here could be no exernaliies. 3 I 3 Some would also add ha wihou ransacion coss insiuions and rules will have no economic funcion, so here would be no insiuions eiher (Papandreou, 1994). 4
seems a lile bi peculiar o analyse exernaliies where he relevance of exernaliies are assumed away! This poins o he imporance of inegraing posiive ransacion coss in economic analyses (Coase, 1988). Now, if ransacion coss are posiive and fixed, bu less han he gain of eliminaing exernaliies as non-marke inerdependency hrough bargaining, nohing of subsance is changed and he Coase-heorem sill holds. However, if coss are fixed, bu larger han he gain, he locaion of efficiency depends on he iniial disribuion of propery righs (Van, 2005). In he above polluion example, efficiency will now be characerized by no abaemen if he facory has he righ o pollue and no polluion if he righ o an unpollued river is wih he fishery. Moreover, if we have posiive marginal ransacion coss, he marginal willingness o pay for abaemen and he marginal willingness o pay o omi abaemen will be affeced depending on he iniial disribuion of propery righs (Van, 2005). If he facory has he righ o pollue, he fishery has o iniiae increasingly cosly informaion gahering, conracing and enforcemen in order o reduce he level of polluans. Tha is, he fishery s willingness o pay for abaemen will be reduced, and efficiency occurs a a lower level of abaemen. In he opposie case, when he fishery has he righ o an unpollued river, he facory s willingness o pay for omiing abaemen will be reduced due o ransacion coss, and efficiency occurs a a higher level of abaemen. Surely, he locaion of efficiency depends on he naure of he ransacion coss and on he disribuion of propery righs, he laer deermining who has o bear he ransacion coss. The domain of he Coase heorem is hus severely limied. The Pigovian influenced sae regulaion model modifies he assumpions of he Coasean bargaining model in hree imporan ways. Firs, he propery righs srucure and disribuion are aken as given. In he presence of exernaliies, hen, who is he responsible pary and who is he vicim is clearly defined. Second, he Pareo-opimum as an efficiency crierion is replaced by he poenial Pareo improvemen es (Kaldor, 1939; Hicks, 1939). Here, efficiency is represened by maximizing ne welfare (ne producion value) and may hus be improved alhough represening coss o some. Third, as argued by Van (2005), o make he 5
model consisen, here mus be an implici assumpion of posiive ransacion coss, 4 and he ransacion coss of sae regulaion mus be lower han he ransacion coss of he bargaining process. 5 The role of he sae, hen, is o economize on ransacion coss by correcing for hese exernaliies. Due o he lower ransacion coss, more of he exernaliies will be Pareorelevan under sae regulaion as compared o he bargaining model. However, as far as here are posiive ransacion coss in sae regulaion, he locaion of he efficien resource allocaion will also here be a funcion of he insiuional seing. The Pigovian influenced sae regulaion model may be associaed wih he polluer pays principle. Considering he above example of he polluing facory, he sae should impose a uni ax on he facory s emission in order o equalize he facory s privae coss wih he social coss of emission, ha is, he coss imposed on he fishery (he vicim). In he presence of posiive ransacion coss, he locaion of efficiency will obviously depend on he normaive judgemen abou he propery righs disribuion. To sum up, wheher we consider he bargaining- or he sae regulaion model, he imporan poin is ha he economically efficien level of polluion depends on he insiuional seing when ransacion coss are posiive (Bromley, 1991: 77-78). Thus, here will be an efficien soluion for every insiuional seup, or pu differenly: Boh efficiency crieria are biased owards he saus quo. As Papandreous (1994) observes, economic lieraure on insiuions ends o conclude ha he exising is opimal. Thus, efficiency defined in Pareo or poenial Pareo erms is no an ehically neural concep as efficiency and disribuion canno be analysed independenly of each oher. Accordingly, i seems jusified o conclude like Marinez-Alier and O Connor (1999), ha all general equilibrium models presuming such independence are inaccurae a bes. 6 3. An insiuional perspecive of exernaliies Based on he above criicism we will apply an insiuional undersanding of he concep of exernaliy in he presen analysis. The approach is inspired by J.R. Commons arificial selecion heory of insiuional evoluion (see e.g. Biddle, 1990 for an accoun). A each 4 This is a prerequisie for having exernaliies as non-marke inerdependency and inefficiency in he firs place. 5 As he ransacion coss of he vicims in a bargaining siuaion is likely o be much higher han he ransacion coss of sae regulaion, his seems o be a reasonable assumpion (Van, 2005). 6 This problem is obviously accenuaed if differen insiuional seings canno be compared wih a single (e.g moneary) value. 6
momen in ime he prevailing insiuional srucure - which is a resul of prior collecive acion - guides individual acion. Wihin his srucure here will be insiuional inerdependency: An individual s righ is anoher s duy and an individual s privilege is anoher s absence of a righ (Bromley, 1991). For example, an individual s righ o sole access o a resource mus be backed by he correlaed duy of everybody else no o inerfere wih his righ. However, various individual righs and correlaed duies may be muually exclusive, ha is, in conflic wih each oher. The insiuion of having complee privae conrol of land may for example be in conflic wih he public righ of biodiversiy preservaion (cf. also he inroducory secion). Thus, raher han being backed by a correlaed duy he claim o privae propery of land is challenged by a conflicing claim o a public righ. Ulimaely, i is how individuals behave wih respec o he given insiuional srucure which deermines he naure of insiuional inerdependency. Looking a propery as a benefi sream, a propery righ is he capaciy o conrol curren and fuure appropriaion of he benefi sream (Bromley, 1991; Demsez, 1967). For a propery righ o have effec, oher individuals mus volunarily refrain from inerfering wih he propery righ or mus be compelled o do so by he sae. Effecive proecion of a propery righ is hus he correlaed duy of all ohers no o inerfere wih his righ, volunarily or forced (Bromley, 1991). 7 Wihin he given srucure of righs and correlaed duies, one individual s acion will in general affec he benefi and cos flow of ohers (Biddle, 1990). For insance, wihin he insiuion of open access, he harvesing behavior of an individual will affec he profi opporuniies of ohers hrough he sock-effec. This is insiuional inerdependency revealed: An individual s opporuniy field depends on he de jure insiuional srucure of righs, he enforcemen of hose righs and on he behavior of oher individuals. Some of he insiuional inerdependencies may comply wih he purpose of he prevailing insiuional srucure, meaning ha hey are approved by he collecive. Ohers, however, may be uninended consequences of collecive acion: As here are nohing like perfec foresigh in he collecive process of esablishing and reshaping insiuions, some individual 7 Enforcemen may be needed o ensure ha de jure righs and duies become de faco righs and duies. 7
acions wihin he prevailing insiuional srucure may affec oher individuals in ways ha are no anicipaed by he collecive (Biddle, 1990). In so far he uninended consequences are socially undesired, collecive acion and insiuional change will be riggered in order o reesablish compliance. Moreover, preferences may be endogenous (e.g., Bowles, 1998, Kahneman 2011, Ch. 27). This means ha he collecive purpose may change over ime. The insiuional srucure - being a produc of prior collecive acion and purpose - may hus fall ou of sep wih he resurgen collecive purpose. Tha is, some of he insiuional inerdependencies which were formerly approved by he collecive no longer are. Also in his case collecive acion and insiuional change will be riggered o re-esablish compliance beween he insiuional srucure and he prevailing collecive purpose. This means ha a each momen in ime some of he insiuional inerdependencies may be policy relevan and some may no. We sugges ha he erm exernaliy is used o denoe he case of policy relevan insiuional inerdependency. Being uninended and undesired consequences of collecive acion, exernaliies are hus insiuional inerdependency exernal o he prevailing collecive purpose. Raher han represening marke failure, hen, exernaliies are more general and represen insiuional failure. In his way exernaliies become driving forces of insiuional change. Caused by uninended consequences of collecive acion and changed preferences, exernaliies represen insiuional failures in he form of policy relevan insiuional inerdependencies. The economis s role in his should be o race such failures. This implies o analyse he srucure and enforcemen of he de jure individual righs and correlaed duies and how individuals behave wihin his insiuional srucure, ha is, o idenify he de faco opporuniy field of individuals. In he nex sep, he opporuniy field mus be evaluaed agains he prevailing collecive purpose. If he de faco funcioning of he insiuional srucure deviaes from he prevailing collecive purpose, here is insiuional failure as a resul of exernaliies. In his case a policy response (collecive acion) is required. 4. Insiuional changes and he benefi and cos flow of he Scandinavian wolf We now proceed o discuss he paricular example of he Scandinavian wolf re-colonizaion, he relaed insiuional changes and changes of he cos and benefi sreams conneced o he 8
mos relevan sakeholders. These sakeholders are he sheep farmers who bear he coss of he he wolf populaion hrough predaion loss, and he general public represened by he wildlife auhoriy. The raher poor Norwegians before he wenieh cenury probably had deeper worries han he survival of he scandinavian wolf. Considered as a hrea for boh livesock and people, he wolf was huned down locally wihou much resisance. In he absence of a sae or a significan group of people valuing he wolf posiively, here was no negaive exernaliy associaed wih wolf killings. Or, in he preceding erminology, he prevailing collecive purpose was negaive oward wolves. However, as wolf huning of one farmer reduced he coss of oher farmers in erms of reduced loss of livesock, here was sill an insiuional inerdependency presen: The collecive waned any farmer o have he righ o bring livesock o he pasures wihou any inerference from wolves, and wolf huning had o be inensified in order o secure ha righ. Accordingly, he sae esablished a bouny for killing wolves in 1845 (Søbye, 2000; Søbye, Judin and Rundom, 2000). Wolf huning herefore represened a posiive exernaliy in he form of a policy relevan insiuional inerdependency. However, in line wih he so-called pos-maerialism hypohesis by Inglehar (1971), which saes ha when basic maerial needs are me, individuals o a larger exen give prioriy o pos-maerial issues like caring for he environmen, culure and so forh, aiudes were changed more in favour of wolf exisence in he course of he 20 h cenury. The collecive purpose changed wih he new aiudes and he prevailing insiuional srucure - which was he produc of a ime when he wolf was considered a mere nuisance - fell ou of sep wih i. The formerly awarded killing of wolves evenually came o represen a negaive exernaliy. This riggered collecive acion and insiuional change. To avoid wolf exincion and loss of exisence value he wolf was preserved by he sae in 1972 and earlier huning pracises of wolves were banned. The ime had come for re-colonizing he scandinavian wolf in Norway. The exisence value of wolf was also insiuionalized hrough various inernaional convenions and legal provisions. Noably, Norway became a signaory o he Bern-convenion in 1986, which means ha he counry is commied o keep a viable populaion of wolf on Norwegian erriory. The overall wolf managemen objecive in 9
Norway is o secure a susainable populaion of he scandinavian wolf. 8 However, i is also declared ha wolf managemen mus ake place in a muli-use landscape (Inns.S. nr. 174, 2003-2004). As foresed and mounainous areas are imporan grazing resources, his means here will be conflicing ineress in he form of wolf preying on livesock. Thus, besides securing a criically hreaened wolf populaion, an imporan dimension of wolf managemen is o reduce he conflic associaed wih i ( 12 in O prp 9, 1980-1981; Inns O nr 50, 1980-1981). The old conflic beween sheep farming and he wolf reemerged wih he wolf re-colonizaion. To reduce he conflic, he sae esablished compensaion paymens for sheep killed by wolves. These coss are borne by he public. The negaive effecs of he re-colonized wolf don sop here. Wolf preying on moose and oher hunable wildlife species (like roe dear) consiue anoher wolf-relaed conflic in Scandinavia. Because wolves are few and pachily disribued he oal effec is raher small. Sill, some landowners and areas are seriously affeced (see, e.g., Skonhof, 2006 and he references herein). So far his is no compensaed by he governmen. Ye anoher imporan dimension in he conflic is fear. According o one sudy, only abou 23% would accep o live less han 10 km from wolf-areas, and 66% compleely or parly agree ha hey would worry abou he securiy of heir family when being oudoors in areas wih wolves (Linnell and Bjerke, 2002; see also Karlsson, 2007 for he Swedish case). This is he insiuional seing and he major benefi and cos flows associaed wih curren managemen of he wolf in Norway. We will now apply our insiuional perspecive on exernaliies o analyse he conflic associaed wih re-colonizing he Scandinavian wolf. We will formalize our discussion by consrucing a sylised bioeconomic model in he nex secion. 5. A bioeconomic model of wolf managemen and sheep farming The following analysis is resriced o highligh he sheep predaion problem. Hence, cos and benefi sreams relaed o he moose and oher harvesable wildlife populaions subjec o wolf predaion are no aken ino accoun, neiher is he fear experienced by people living close o 8 More specificly, he Norwegian wildlife auhoriy has esablished ha he managemen goal is o have hree successful wolf reproducions wihin he managemen area annually. While he goal was reached in 2004, only wo reproducions were documened in 2005 and 2006, and only one in 2007. (Wabakken e al, 2004; 2005; 2006; 2007). 10
he wolf. Accordingly, he wo agens considered in he model are a group of sheep farmers operaing in a cooperaive manner and assumed o ac as a single agen, and he wildlife auhoriy (The Direcorae for Naural Resource Managemen) represening he general public. We assume ha boh agens are raional and aim o maximize presen-value benefi over an infinie horizon, and where he wo agens play a dynamic Courno game. Only he open loop sraegy is considered; ha is, he group of sheep farmers and he wildlife auhoriy commi heir opimal managemen sraegy o each oher a 0over an infinie planning horizon, given he expecaion of he enire opimal sraegy of he oher player (Dockner a al. 2000). We focus on he seady sae oucome of his game. In Norway oday here are abou 15.000 sheep farms and here are more han wo million animals during he oudoors grazing season. Mos of he sheep farms are locaed in mounainand fores covered areas and oher sparsely populaed areas. The main produc is mea. Remaining income comes from wool as sheep milk producion is non-exisen. Housing and indoor feeding is required hroughou he winer because of snow and harsh weaher condiions. Lambs are born during lae winer o early spring. When weaher condiions allow, sheep are released ino rough grazing areas in he valleys and mounains, which are ypically communally owned. I is hence during he summer rough grazing period, he sheep flocks may be vulnerable o large predaors, such as he wolf (bu also lynx, wolverine and bear). Sheep farming is basically a conrolled biological process and, and possible excep for predaion, i is herefore no densiy dependen effecs regulaing populaion growh (more deails in e.g., Skonhof 2008). On he oher hand, he naural growh of he wolf populaion is assumed o be densiy regulaed. In wha follows, we consider a given area wih sheep farming and a wolf populaion. As he wolf migrae and dispearse over huge areas, he area is supposed o be raher large so ha inflows and ouflows of animals can be negleced. There are many sheep farmers wihin his area, bu as indicaed hey are supposed o operae as a single agen. Wih populaion size (in number of animals) a ime (year) and X as he sheep W as he size of he wolf populaion, also in number of animals, he sheep populaion growh is firs given as: (1) dx / d sx G( X, W ) h. 11
s 0 represens he fixed proporional naural growh, h 0 is he slaughering and G( X, W ) is he wolf predaion (funcional response). The predaion is assumed o be increasing in he wolf densiy, G( X, W ) / W G 0, as well as he number of sheep W G 0. Addiionally, he sheep predaion per wolf on he margin increases in he sheep X densiy, GXW 0. While predaion is deermined by he size of he wolf pack, ogeher wih he size of he sheep populaion, here may also be a feedback effec as he size of he sheep populaion may influence he wolf populaion growh. However, as he wolf has differen oher food sources like moose and roe deer (see also above), and ha hese food sources are he criical facors for he wolf populaion during he winer, any possible numerical response o variaions in he sheep populaion is negleced (see, e.g., Nielsen e al. 2005). Therefore, he wolf populaion growh simply reads: (2) dw / d F( W ) y, where FW ( ) represens naural growh and y 0 is he number of animals conrolled, or huned. The wolf naural growh is assumed o be densiy dependen and governed by a onepeaked value funcion in a sandard manner (see below). As already indicaed, he Norwegian sheep farmers ge heir income from mea and wool producion, and where he income from mea sale couns for abou 80 % of oal income. Wih p as he fixed per animal slaughering price, ph hence describes he yearly income when ignoring income from wool sale. The farmers are also currenly compensaed for he loss caused by wolf preying on sheep (see, e.g., Eksperuvalge 2011). Wih 0 k p as he per animal compensaion assumed o be fixed, he yearly compensaion benefi is kg( X, W ). On he cos side, we find ha he cos srucure of he farmers differs sharply beween he oudoors grazing season and he indoors feeding season, and where he indoors variable coss are subsanial higher. These coss include fodder, labour (as an opporuniy cos) and veerinarian coss, and is relaed o he size of he sock, CX ( ), wih C ' 0, C '' 0 and 12
C(0) 0. Therefore, when ignoring he oudoors coss and he fixed coss, he farmer ne curren benefi wries: (3) ph C( X ) kg( X, W ). 1 The problem of he group of farmers is o maximize ne presen value benefi d subjec o he populaion growh equaion (1), and he expeced wolf conrolling policy by he wildlife auhoriy. In addiion he iniial sheep sock size has o be known. 1 0 is he discoun ren of he farmers. The curren value Hamilonian of his problem reads H [ ph C( X ) kg( X, W )] [ sx G( X, W ) h ] where 0 is he sheep populaion shadow price. The firs order condiions are he conrol condiion H / h p 0 and he porfolio condiion H / X C '( X ) kgx ( X, W ) ( s GX ( X, W )) d / d 1. 0 e The inerpreaion of hese condiions is sraighforward. The sheep conrol condiion says ha sheep harvesing should ake place up o he poin where he marginal sheep slaughering value is equal o or below is cos refleced by he sheep shadow price. When i is below he shadow cos, here is no slaughering. I hence indicaes a bang-bang conrol or singular conrol as is expeced when he objecive funcion is linear in he conrol. The porfolio condiion seers he shadow price value. Essenially i indicaes ha he capial gain of he sheep populaion d / d plus he value of ne marginal sock effec [ ( s G ( X, W )) wg ( X, W ) C '( X )] mus be equal he marginal benefi of X X slaughering and puing he proceeds in he bank,. 1 Because he Hamilonian of he above problem is linear in he conrol, we find ha he sufficien condiion is ha he maximized Hamilonian is concave in he sock variable, i.e., he weak Arrow sufficiency condiion is saisfied (see Appendix) Afer some small manipulaions and dropping he ime subscrip, we find he seady sheep golden rule condiion as: (4) GX ( X, W ) p k C'( X) s 1. p p 13
In addiion, he sheep seady sae harves is governed by h sx G( X, W) while he profi reads psx ( p k) G( X, W) C( X ). Boh he sock size and he harves are coningen upon he degree of compensaion. Wih full compensaion ( k p) condiion (4) is reduced o s C '( X ) / p and he opimal long-erm sheep populaion is hence similar o a siuaion wihou predaion. The same is rue for he profi. While he regular slaugher income of he farmers is reduced hrough predaion, he slaugher income is mainained hrough predaion as an animal aken by he wolf has he same value for he farmer as supplied a he slaugherhouse. Wihou full compensaion and k p, however, he farmers will experience a negaive economic effec of predaion, and equaion (4) will yield a negaive relaionship in he X W diagram. If he size of he sheep populaion has negligible effec on he per head wolf consumpion and GX 0, he golden rule condiion will also be idenical o he siuaion wihou wolf. Tha is, he golden rule number of sheep will be similar wih and wihou wolf predaion. However, he opimal number of animals slaughered will be lower and so will he profi. The wolf populaion is managed by he wildlife auhoriy. In addiion o aaching a posiive exisence value o he wolf, here are also cerain oher cos and benefi componens included in he managemen. I is cosly o conrol he wolf populaion, bu i may under cerain condiions also represen a harvesing value. Addiionally, we have he compensaion coss. The curren ne benefi sream relaed o he wolf populaion may herefore be wrien as: (5) U qy B( W ) y A( W ) kg( X, W ), where q 0 is he harvesing value assumed o be fixed and independen of he number of wolves sho and BW ( ) is he per uni harvesing cos assumed o be non-increasing in he populaion size, i.e., B' 0, AW ( ) is he exisence value of wolf as appropriaed by he general public where A' 0, A'' 0 and A(0) 0. The problem of he wildlife auhoriy is o maximize he oal ne presen value wolf benefi 2 Ue d subjec o he populaion growh (2), he iniial size of he wolf populaion and he 0 expeced sheep slaughering policy by he farmers. 2 is he discoun ren of he wildlife 14
auhoriy which generally may differ from he discoun ren of he farmers. The curren value Hamilonian of his problem reads L [ qy B( W ) y A( W ) kg( X, W )] [ F( W ) y ], where is he wolf populaion shadow price. The conrol condiion is L / y q B( W ) 0 while he porfolio condiion reads L / W A( W ) B'( W ) y kg ( X, W ) F '( W ) / d when he possibiliy W 2 of exincion is ruled ou; ha is, i is always beneficial wih a posiive wolf populaion. The wolf conrol condiion says ha wolf harvesing should ake up o he poin where he ne marginal wolf harvesing value is equal o or below is cos refleced by he wolf shadow price. When i is below he shadow price i is beneficial wih no harvesing. Therefore, also for he wolf populaion we find a bang-bang conrol or singular conrol as he wildlife auhoriy objecive funcion is linear in he conrol variable. The shadow price is negaive for sure when he harvesing value is zero. The porfolio condiion saes ha he capial gain of he wolf populaion d / d plus he marginal value of ne sock effec [ A( W ) B'( W ) y kg ( X, W ) F '( W )] mus be equal he marginal benefi of harvesing W and puing he proceeds in he bank,. 2 The weak Arrow sufficiency condiion is given in he Appendix. The wolf golden rule condiion now reads: B'( W ) F( W ) A( W ) kgw ( X, W ) (6) F'( W) 2 q B( W ) In addiion, he wolf populaion equilibrium offake is given by y F( W). Wih zero compensaion and k 0 he sheep managemen has for obvious reasons no influence on he wolf managemen and hence equaion (6) alone deermines he size of he wolf populaion. Oherwise, wih compensaion and 0 k p, we find ha (6) yields a negaive relaionship beween he sheep populaion size and he number of wolves. Tha is, more sheep is only consisen wih a lower wolf populaion for he wildlife auhoriy. Noice ha while boh equaion (4) and equaion (6) are based on presen-value maximizaion wih a sraegic ineracion in an open-loop seing, hese equaions can be given a broader 15
inerpreaion. I can namely be shown ha wih zero discouning ( 1 0 ) condiion (4) yields he soluion of he problem of maximizing he sheep profi (3) in ecological equilibrium for a given size of he wolf populaion. Similarly, wih 2 0 equaion (6) yields he soluion of maximizing he curren ne wolf benefi (5) for a consan wolf populaion and aking he size of he sheep populaion as given. To obain some clear-cu resuls we specify he funcional forms. The sheep funcional response is given as G( W, X ) X W wih 0 indicaing ha he wolf per capia consumpion increases linearly wih he number of sheep. 9 Accordingly, we have GW X ogeher wihg X W and GXW. The wolf naural growh is specified o be logisic, F( W ) rw (1 W / K), wih r 0 as he inrinsic growh rae and K 0as he carrying 2 capaciy. The sheep indoors cos funcion is given by C ( c / 2) X wih c 0. For simpliciy, and no far from realiy as he wolf operaes in packs ( schooling ), we assume ha he wolf harves funcion is sock independen; ha is, B( W ) b wih b 0as he fixed uni huning/conrolling cos. Finally, he wolf exisence value funcion is specified as A( W ) W ( u vw ), wih u 0 and v 0, indicaing a decreasing marginal exisence value. This funcion is scaled so ha he wolf populaion never will be larger han u/2v. Thus, 2 0 A W u vw will always hold. See he Appendix for he weak Arrow sufficiency condiions for hese specified funcional forms, which implies ha (6 ) is downward sloping. For hese specific funcions, he sheep and wolf golden rule condiions now become: (4 ) W p k s cx / p, 1 p and (6 ) 2W k X u 2vW r 1 2, K ( q b) 9 A possibly more realisic assumpion is ha he wolf per capia consumpion increases a a decreasing rae, exemplified by he funcion G( X, W ) [ X / ( )] X W. 0 is a shape parameer and 0 is he maximum consumpion per animal. 16
respecively. Figure 1. The sheep golden rule condiion (4 ) and he wolf golden rule condiion (6 ) for various degree of sheep compensaion Figure 1 depics hese wo equaions for various values of per sheep compensaion value k. For all 0 k phe sheep equaion (4 ) will be downward sloping while i will be verical when he farmers are fully compensaed and k p. The wolf equaion (6 ) has a downward slope for all 0 k p, while i is horizonal when here is no compensaion and k 0. Therefore, a higher compensaion yields more sheep and less wolf, and vice versa. No surprisingly, we also find ha a higher marginal exisence value of he wolf yields more wolf and less sheep while a more valuable sheep producion hrough a higher slaugher price p leads in he opposie direcion. We find similar effecs wih smaller sheep farming coss c. Higher discouning of he wildlife auhoriy means ha he auhoriy will find i beneficial o keep fewer wolves. Therefore, he sheep farmers will increase he socking rae and he profiabiliy will be improved. A more myopic policy of he sheep farmers works in he opposie direcion. 6. Discussion As he above model demonsraes here is a muual inerdependency beween he wo agens when 0 k p; he wildlife auhoriy affecs he sheep socking rae and he profiabiliy of 17
he sheep farmers, and he sheep farmers affec he cos and benefi flows generaed by he wolf populaion. The compensaion paymen plays a key role in he model as i deermines he disribuion of benefi and cos flows beween he agens. I is no only a maer of redisribuion; i also affecs he allocaion of sheep and wolves in he considered area wih sheep farming coexising wih a wolf populaion. As shown in Figure 1 we have wo polar cases: A denoes he case wihou compensaion and amouns o graning he sole propery righ o The Direcorae for Naural Resource Managemen. On he oher hand, B denoes he case of full compensaion and amouns o graning he sole propery righ o he sheep farmers. Poin C exemplifies an inermediary case (less han full compensaion) wih where 0 kˆ p. k kˆ The curren official policy of Norway is o gran full compensaion o he sheep farmers for sheep killed by wolf (again, see Eksperuvalge 2011), corresponding o poin B in he figure. This amouns o giving he sheep farmers he sole propery righ o he grazing areas. Accordingly, having a viable populaion of wolf is de faco no so much a public righ as i is a public good ha mus be collecively paid for. On behalf of he general public he wildlife auhoriy responds by keeping a lower populaion of wolves. The curren policy is solely based on a judgmen concerning righful ownership - in erms of poenial Pareo improvemen here is no efficiency crierion involved. A Pigovian influenced sae regulaion model would also include he efficiency crierion. Based on maximizaion of he ypically equally weighed sum of he agens uiliy funcions, he opimal allocaion of sheep and wolves is derived. This akes place a he wolf populaion size where he marginal cos of he wolf in erms of killed sheep equals he marginal benefi in erms of he exisence value. In he figure his corresponds wih poin D which is he so-called social planner soluion of he model. Wih zero compensaion as he poin of deparure (A in he figure), he Pigovian influenced regulaion model would idenify he wildlife auhoriy as he responsible pary for imposing an exernaliy (in erms of wolves killing sheep) on he vicim, he group of sheep farmers. To inernalize he exernaliy he sae should impose a uni ax on he wildlife auhoriy given by p in order o reach he social opimal soluion a D. This complies wih he polluer pays principle where a uni ax on sheep killed by wolves is imposed on he general public. Wih 18
reference o oday s regime of full compensaion (A in he figure), he Pigovian influenced regulaion model would sugges ha he general public should sill pay for wolves killing sheep, bu he compensaion paymen o he sheep farmers should be wihdrawn. Thus, he responsible pary would be he sheep farmers imposing an exernaliy on he vicim, he general public, in erms of compensaion expenses. Now i is ime o inroduce our own concep of exernaliy as policy relevan insiuional inerdependency. Based on his, and given he full compensaion regime of oday, where do we idenify he exernaliy? Obviously, wheher sheep killed by wolves are fully compensaed ( k p), no compensaed ( k 0 ) or reaed in erms of he polluer pays principle where he general public is imposed a uni ax on sheep killed by wolves while he group of sheep farmers is no compensaed, one or boh of he agens will be negaively affeced by he oher. Keeping Coases s (1960) argumen in mind, saying ha i is no obvious who is he responsible pary when an exernaliy is presen, we mus go beyond he muual negaive effecs beween he agens in order o idenify he exernaliy. Raher, we mus urn o he poliical objecives of he sae. The poliical objecive is o have a susainable populaion of he Scandinavian wolf in Norway wihou resricing he grazing righs of sheep farmers in wolf areas (cf. he declaraion ha wolf managemen mus ake place in a muli-use landscape) a he same ime as conflic should be a a minimum. This is exacly where we find he policy relevan insiuional inerdependency: The de jure righs of he agens are muually exclusive. Given he curren insiuional seing, he grazing righ of he sheep farmers is in conflic wih he righ of he public o have a viable populaion of wolves in Norway. The prevailing assignmen of propery righs is inconsisen. To eliminae he exernaliy he de jure propery righs mus be clarified. An obvious policy response would be o assign propery righs which imply a separaion of sheep and wolves, eiher geographically or by he use of herdsmen. 6. Concluding remarks The presen paper offer a criical review of he radiional concep of exernaliies. Based on his, and inspired by Commons heory of insiuional evoluion, we redefine he radiional concep. Raher han reflecing marke failure, our undersanding of exernaliies is more general and reflec insiuional failure. In shor, we define an exernaliy o be policy relevan insiuional inerdependency. Insiuional inerdependencies originae from he srucure of 19
he de jure propery righs, he enforcemen of hose righs and on he behaviour of individuals. As an illusraion we discuss our insiuional undersanding of exernaliies in he conex of he conflic beween sheep farming and wolf managemen in Norway. Here we idenify exernaliies, i.e. policy relevan insiuional inerdependencies, in he de jure propery righs srucure: The sheep farmers and he wildlife auhoriies propery righs o he muli-use landscapes are muually exclusive. Compensaion paymens o sheep farmers only redisribue benefis and coss beween he agens and do no reduce he conflic. One way o eliminae he exernaliies would be o clarify he de jure propery righs and separae sheep and wolves. 20
Appendix Sheep farming The weak Arrow sufficiency condiion requires 2 H / X 2 ( k ) G C 0which wih XX singular conrol and p also reads 2 2 / ( ) XX 0. Wih convex sheep H X p k G C cos funcion ogeher wihgxx 0, we have 2 2 H/ X 0. Wildlife Auhoriy The weak Arrow sufficiency condiion is saisfied when 2 2 L / W A B'' y kgww F '' 0. Wih singular conrol q B( W) 2 2 L / W A B'' y kgww q B F '' 0. When '' 0, his also reads B, G 0 and F '' 0, we always find his condiion saisfied wih ( qb) 0. When ( qb) 0, as for no harvesing value q, A q B F '' and 0 mus hold o mee he sufficiency condiion. WW Specific funcional forms The weak Arrow sufficiency condiions wih he specified funcional forms for he sheep managemen problem and he wolf managemen problem read 2 2 H / X c 0 and 2 2 L / W 2 r( q b) / K 2v 0, respecively. The wolf managemen problem herefore demands r q b / K v 0. The geomeric inerpreaion of his condiion is ha equaion (6 ) for all 0 k p should be downward sloping in he X-W diagram (Figure 1). 21
Lieraure Aldred, J. 1994. Exisence Value, Welfare and Alruism. Environmenal Values 3: 381-402. Afield, R. 1998. Exisence Value and Inrinsic Value. Ecological Economics 24(2-3):163-68. Baumol, W. and W. Oaes 1988. The Theory of Environmenal Policy. Cambridge Universiy Press, Cambridge Biddle, J.E. 1990. Purpose and Evoluion in Commons Insiuionalism. Hisory of Poliical Economy 22 : 19 47. Bowles, S. 1998. Endogenous Preferences: The Culural Consequences of Markes and oher Economic Insiuions. Journal of Economic Lieraure XXXVI : 75-111. Bromley, D.W. 1991. Environmen and Economy: Propery Righs and Public Policy. Oxford, Cambridge, Massachuses: Basil Blackwell (inc/ld). Buchanan, J.M. and W.C. Subblebine 1962. Exernaliy. Economica 29: 371-384. Coase, R.H. 1960. The Problem of Social Cos. Journal of Law and Economics 3: 1-44. Coase, R. H. 1988. The New Insiuional Economics. The American Economic Review 88(2): 72-74. Dahlman, C.J. 1979. The Problem of Exernaliy. Journal of Law and Economics 22: 141-162. Demsez, H. 1967. Toward a heory of propery righs. The american economic review 57: 347-59. Ekins, P. 1997. The Kuznes curve for he environmen and economic growh: examining he evidence. Environmen & planning. A 29 (5): 805-30. Ersaningsuvalge 2011. Innsilling fra eksperuvalg vedrørende endringer I ersaningsordningen for rovvilskade på husdyr (in Norwegian). Direkorae for Naurforvalning, Trondheim Grossman, R. and A. Krueger 1995. Economic Growh and The Environmen. Quarerly Journal of Economics 110 (2): 353-77. Hicks, J.R. 1939. The Foundaions of Welfare Economics. Economic Journal 49(196): 696-712. Holz-Eakin, D. and T.M. Selden 1995. Soking he fires? CO 2 emissions and economic growh.. Journal of Public Economics 57: 85-101. Kaldor, Nicholas. 1939. Welfare Proposiions in Economics and Inerpersonal Comparisons of Uiliy. Economic Journal 49: 549 52. Kahneman 2011. Thinking fas and slow. Farrar, Sraus and Giroux: New York. 22
Karlsson, 2007 Kruilla, J.V. 1967. Conservaion reconsidered. American Economic review 57: 777-786. Linnell, J.D.C and T. Bjerke (eds) 2002. Fear of wolves: An Inerdisciplinary sudy. Trondheim: NINA Oppdragsmelding 722: 1-110. (In Norwegian wih an absrac in English). Marinez-Alier, J. and M. O Connor 1999. Disribuional Issues: An Overview, in J. Van den Bergh (ed.) Handbook of Environmenal and Resource Economics, pp. 380-392. Chelenham: Edward Elgar. Nilsen, E. e al. 2005. Moose harvesing in he presence of wolves. Journal of Applied Ecology 42: 389-99. Papandreou, A.A. 1994. Exernaliy and Insiuions. New York: Oxford Universiy Press. Rousseau, J-J. 1974. The Social Conrac. Penguin Classics, Penguin Books Ld: London. (firs ediion 1762). Schmid, A.A. 1987. Propery, Power, and Public Choice: An Inquiry ino Law and Economics, 2nd ed. Praeger, New York. Skonhof, A. 2006. The coss and benefis of animal predaion: An analysis of Scandinavian wolf re-colonizaion. Ecological Economics 58: 830-841. Skonhof, A. 2008. Sheep as capial and farmers as porfolio managers: A bioeconomic model of he Scandinavian sheep farming. Agriculural Economics 38: 193-200. Søbye, E. 2000. Ulvejak, mo og svindel, Saisisk senralbyrå, [02.04.2013]. hp://www.ssb.no/a/hissa/arikler/ar-2000-10-18-01.hml Søbye, E., M.I. Judin and T.O. Rundom 2000. Fra skuddpremier il fredning og irregulær avgang, [02.04.2013]. hp://www.ssb.no/jord-skog-jak-og-fiskeri/arikler-og-publikasjoner/fraskuddpremier-il-fredning-og-irregulaer-avgang Van, A. 2005. Insiuions and he Environmen. Edward Elgar, Chelenham, UK. Van, A. and D.W. Bromley 1997. Exernaliies A Marke Model Failure. Environmenal and Resource Economics 9: 135-151. Walz, K. 1959. Man, he Sae, and War. Columbia Universiy Press: New York. Wabakken, P e al. 2007. Ulv i Skandinavia: Sausrappor for vineren 2006-2007. Høgskolen i Hedmark Oppdragsrappor nr.3-2006. (In Norwegian wih absrac in English: The wolf in Scandinavia: Saus repor of he 2006-2007 winer). 23
Wabakken, P e al. 2006. Ulv i Skandinavia: Sausrappor for vineren 2005-2006. Høgskolen i Hedmark Oppdragsrappor nr.3-2006. (In Norwegian wih absrac in English: The wolf in Scandinavia: Saus repor of he 2005-2006 winer). Wabakken, P e al. 2005. Ulv i Skandinavia: Sausrappor for vineren 2004-2005. Høgskolen i Hedmark Oppdragsrappor nr.6-2005. (In Norwegian wih absrac in English: The wolf in Scandinavia: Saus repor of he 2004-2005 winer). Wabakken, P e al. 2004. Ulv i Skandinavia: Sausrappor for vineren 2003-2004. Høgskolen i Hedmark Oppdragsrappor nr.5-2004. (In Norwegian wih absrac in English: The wolf in Scandinavia: Saus repor of he 2003-2004 winer). 24