WORKING PAPER 2006-03 Resource Economics and Policy Analysis (REPA) Research Group Deparmen of Economics Universiy of Vicoria A Dynamic Bioeconomic Model of Ivory Trade: Deails and Exended Resuls G. Cornelis van Kooen July 2006
REPA Working Papers: 2003-01 Compensaion for Wildlife Damage: Habia Conversion, Species Preservaion and Local Welfare (Rondeau & Bule) 2003-02 Demand for Wildlife Huning in Briish Columbia (Sun, van Kooen, & Voss) 2003-03 Does Inclusion of Landowners Non-Marke Values Lower Coss of Creaing Carbon Fores Sinks? (Shaikh, Suchánek, Sun, and van Kooen) 2003-04 Smoke and Mirrors: The Kyoo Proocol and Beyond (van Kooen) 2003-05 Creaing Carbon Offses in Agriculure hrough No-Till Culivaion: A Mea-Analysis of Coss and Carbon Benefis (Manley, van Kooen, Moelner, and Johnson) 2003-06 Climae Change and Fores Ecosysem Sinks: Economic Analysis (van Kooen and Eagle) 2003-07 Resolving Range Conflic in Nevada? The Poenial for Compensaion via Moneary Payous and Grazing Alernaives (Hobby and van Kooen) 2003-08 Social Dilemmas and Public Range Managemen: Resuls from he Nevada Ranch Survey (van Kooen, Thomsen, Hobby, and Eagle) 2004-01 How Cosly are Carbon Offses? A Mea-Analysis of Fores Carbon Sinks (van Kooen, Eagle, Manley, and Smolak) 2004-02 Managing Foress for Muliple Tradeoffs: Compromising on Timber, Carbon and Biodiversiy Objecives (Krcmar, van Kooen, and Verinsky) 2004-03 Tess of he EKC Hypohesis using CO2 Panel Daa (Shi) 2004-04 Are Log Markes Compeiive? Empirical Evidence and Implicaions for Canada-U.S. Trade in Sofwood Lumber (Niquide and van Kooen) 2004-05 Conservaion Paymens under Risk: A Sochasic Dominance Approach (Beníez, Kuosmanen, Olschewski and van Kooen) 2004-06 Modeling Alernaive Zoning Sraegies in Fores Managemen (Krcmar, Verinsky, and van Kooen) 2004-07 Anoher Look a he Income Elasiciy of Non-Poin Source Air Polluans: A Semiparameric Approach (Roy and van Kooen) 2004-08 Anhropogenic and Naural Deerminans of he Populaion of a Sensiive Species: Sage Grouse in Nevada (van Kooen, Eagle, and Eiswerh) 2004-09 Demand for Wildlife Huning in Briish Columbia (Sun, van Kooen, and Voss) 2004-10 Viabiliy of Carbon Offse Generaing Projecs in Boreal Onario (Biggs and Laaksonen- Craig) 2004-11 Economics of Fores and Agriculural Carbon Sinks (van Kooen) 2004-12 Economic Dynamics of Tree Planing for Carbon Upake on Marginal Agriculural Lands (van Kooen) (Copy of paper published in he Canadian Journal of Agriculural Economics 48(March): 51-65.) 2004-13 Decoupling Farm Paymens: Experience in he US, Canada, and Europe (Ogg & van Kooen) 2004 14 Afforesaion Generaed Kyoo Complian Carbon Offses: A Case Sudy in Norheasern Onario (Jeff Biggs) 2005 01 Uiliy-scale Wind Power: Impacs of Increased Peneraion (Pi, van Kooen, Love and Djilali) 2005 02 Inegraing Wind Power in Elecriciy Grids: An Economic Analysis (Liu, van Kooen and Pi) ii
2005 03 Resolving Canada-U.S. Trade Dispues in Agriculure and Foresry: Lessons from Lumber (Biggs, Laaksonen-Craig, Niquide and van Kooen) 2005 04 Can Fores Managemen Sraegies Susain The Developmen Needs Of The Lile Red River Cree Firs Naion? (Krcmar, Nelson, van Kooen, Verinsky and Webb) 2005 05 Economics of Fores and Agriculural Carbon Sinks (van Kooen) 2005 06 Divergence Beween WTA & WTP Revisied: Livesock Grazing on Public Range (Sun, van Kooen and Voss) 2005 07 Dynamic Programming and Learning Models for Managemen of a Nonnaive Species (Eiswerh, van Kooen, Lines and Eagle) 2005 08 Canada-US Sofwood Lumber Trade Revisied: Examining he Role of Subsiuion Bias in he Conex of a Spaial Price Equilibrium Framework (Mogus, Sennes and van Kooen) 2005 09 Are Agriculural Values a Reliable Guide in Deermining Landowners Decisions o Creae Carbon Fores Sinks?* (Shaikh, Sun and van Kooen) *Updaed version of Working Paper 2003-03 2005 10 Carbon Sinks and Reservoirs: The Value of Permanence and Role of Discouning (Beniez and van Kooen) 2005 11 Fuzzy Logic and Preference Uncerainy in Non-Marke Valuaion (Sun and van Kooen) 2005 12 Fores Managemen Zone Design wih a Tabu Search Algorihm (Krcmar, Mirovic- Minic, van Kooen and Verinsky) 2005 13 Resolving Range Conflic in Nevada? Buyous and Oher Compensaion Alernaives (van Kooen, Thomsen and Hobby) *Updaed version of Working Paper 2003-07 2005 14 Conservaion Paymens Under Risk: A Sochasic Dominance Approach (Beníez, Kuosmanen, Olschewski and van Kooen) *Updaed version of Working Paper 2004-05 2005 15 The Effec of Uncerainy on Coningen Valuaion Esimaes: A Comparison (Shaikh, Sun and van Kooen) 2005 16 Land Degradaion in Ehiopia: Wha do Soves Have o do wih i? (Gebreegziabher, van Kooen and.van Soes) 2005 17 The Opimal Lengh of an Agriculural Carbon Conrac (Gulai and Vercammen) 2006 01 Economic Impacs of Yellow Sarhisle on California (Eagle, Eiswerh, Johnson, Schoenig and van Kooen) 2006 02 The Economics of Wind Power wih Energy Sorage (Beniez, Dragulescu and van Kooen) 2006 03 A Dynamic Bioeconomic Model of Ivory Trade: Deails and Exended Resuls (van Kooen) iii
For copies of his or oher REPA working papers conac: REPA Research Group Deparmen of Economics Universiy of Vicoria PO Box 1700 STN CSC Vicoria, BC V8W 2Y2 CANADA Ph: 250.472.4415 Fax: 250.721.6214 hp://repa.econ.uvic.ca This working paper is made available by he Resource Economics and Policy Analysis (REPA) Research Group a he Universiy of Vicoria. REPA working papers have no been peer reviewed and conain preliminary research findings. They shall no be cied wihou he expressed wrien consen of he auhor(s). iv
A Dynamic Bioeconomic Model of Ivory Trade: Deails and Exended Resuls G. Cornelis van Kooen Deparmen of Economics Universiy of Vicoria, Canada Draf: May 25, 2006 COMMENTS WELCOME ABSTRACT Trade in ivory is banned under CITES in an effor o proec he African elephan. The rade ban is suppored by some range saes, mos noably Kenya, because hey see he ban as an effecive means for proecing a flagship species, one ha aracs ouriss and foreign aid. I is opposed by some saes, mainly in souhern Africa, because heir elephan populaions are exceeding he capaciy of local ecosysems wih culling and oher sources have resuled in he accumulaion of large socks of ivory. They argue ha ivory rade will benefi elephan populaions. The quesion of wheher an ivory rade ban will proec elephan populaions is addressed in his paper using a dynamic parial-equilibrium model ha consiss of four ivory exporing regions and a single demand region. Resuls indicae ha a rade ban migh no be successful in mainaining elephan populaions, even if i leads o a sigma effec ha reduces demand and increases he marginal coss of markeing ivory. The modeling resuls sugges ha he species will survive only if he non-marke value of elephans is aken ino accoun. If rich counries compensae African range saes according o marginal willingness o pay for elephans, opimal populaions are lower han under an average paymen, and, perhaps surprisingly, he ineracion beween ourism benefis and marginal compensaion can lead o he demise of elephans in some regions where his would no occur oherwise. Finally, elephan populaions are even projeced o crash if range saes can operae an effecive quoa scheme, even one ha excludes poaching. Free rade in ivory and effecive insiuions ha ranslae numbers of elephans ino moneary paymens may be he bes hope for he elephan. Key Words: economics of elephan conservaion; economics of ivory rade; rade bans; carels and quoa I. BACKGROUND Ivory has been a raded commodiy since a leas Old Tesamen imes King Solomon s ships brough back ivory from Africa (I Kings 10:22) and his palace was inlaid wih ivory (I Kings 22:39). Ivory was commercially exploied by he Romans in ancien imes and laer by Arab raders and Europeans.... Beween 1890 and 1900, nearly 3.7 million kg of ivory were raded in he London marke alone,... and some 60,000 elephans
reached European markes every year during ha period (Blanc e al. 2002, p.15). Ivory expors from Africa had increased by 400% beween 1850 and 1875, bu losses in Wes Africa were paricularly high, wih he region dubbed he ivory coas for good reason (Fischer 2005). As human populaion expanded during he 20 h Cenury, elephans were increasingly confined o proeced areas. 1 Beginning someime in he 1960s or early 1970s, speculaion grew ha a complex combinaion of commercial rade and human-elephan ineracions were causing a serious decline in elephan numbers. In Ivory Coas, for example, here were an esimaed 1790 savanna and 3050 fores elephans in 41 isolaed groups in 1984, bu his declined o approximaely 270 oal elephans in perhaps 20 isolaed groups by he early 2000s; numbers were repored o be declining a a rae of 300 poached and 90 legally killed elephans per year beween 1976 and 1984, wih poaching coninuing o he presen (Fischer 2005). 2 Iain Douglas-Hamilon was he firs o compile daa on elephan range, numbers and rends in he 1970s and 1980s (Burrill and Douglas-Hamilon 1987; Douglas-Hamilon 1977-1979, 1993), bu he firs coninen-wide populaion esimaes became available in 1987 and are repored in Table 1 as 1989 esimaes (see ITRG 1989). 3 A comparison of firs and subsequen esimaes suggess ha elephan populaions in some areas may have fallen by half beween 1981 and 1987 (Said e al. 1995, p.1); researchers speculae ha he African elephan (Laxadona africana) declined in populaion from 1.2 million o 600,000 elephans in one decade, alhough he supporing evidence for his is sparse (Barnes e al. 1999; Blanc e al. 2002). The magniude of he esimaed drop in numbers is difficul o believe because of he large scale of killings his would have enailed. Trade in ivory became regulaed under he 1973 Unied Naions Convenion on Inernaional Trade in Endangered Species of Wild Fauna and Flora (CITES). CITES regulaes commercial rade in endangered species using a ranking scheme: Appendix I conains species banned from inernaional commercial rade; Appendix II liss species ha may be raded bu for which expor permis are needed (issued a he discreion of he exporing sae); and Appendix III includes species ha are hreaened and could become endangered in he fuure. Imporing counries agree no o rade in species (or pars of or producs from species) lised in Appendix I, and ensure ha proper expor permis accompany impors of species lised under Appendix II. Saes can apply sancions on species lised under Appendix III a heir discreion. Several modificaions have been made o CITES ha have had an impac on he saus of he African elephan. In 1981, a provision was added a New Delhi (Conference 1 Elephans appear o know he boundaries beween huning zones and proeced areas, having been observed o dash o and from waering holes locaed in he huning zone and visibly relaxing again once inside he park boundary (Scully 2002, p.87). 2 Fischer quoes daa from Roh and Douglas-Hamilon (1991) and Barnes (1999) among ohers. 3 These are likely an updae of he 1987 values. Ineresingly, funding for his research was provided primarily by he U.S. Fish and Wildlife Service. 2
Resoluion 3.15) ha would permi ransfer of cerain populaions from Appendix I (no rade) o Appendix II (limied rade) for he purposes of susainable resource managemen, a provision ha became known as he ranching crierion. In 1985, Resoluion 5.21 provided for he sysemaic re-lising of species from Appendix I o II in cases where counries of origin could agree on a quoa sysem ha would enable counries o manage species susainably. There was no provision for exernal (hird-pary) verificaion/conrol as quoa was o be deermined solely by paricipaing saes. A he same ime, under Resoluion 5.12, a Managemen Quoa Sysem (MQS) was creaed for he African elephan. The MQS relied solely on managemen decisions aken by he producing counries, wih consuming (second-pary) saes agreeing o prohibi impors of ivory (and oher elephan producs) from hese counries unless accompanied by an MQS permi. There were no exernally enforced incenives for susainable use, wih mos saes basing heir quoas on expeced confiscaions of poached ivory. Since consumer saes could obain ivory from non-msq saes wihou quesion, and due o lack of border conrols on illegal ivory, public confidence in he MQS failed and, in 1989, he elephan was moved o Appendix I saus despie a populaion of around 600,000 elephans (Table 1), well above wha migh be considered a minimum viable populaion for survival of he species. 4 Five souhern African elephan range saes Zimbabwe, Namibia, Boswana, Malawi and Souh Africa have generally opposed he Appendix I lising, because hey have relaively large elephan socks and elephans have become a nuisance in some Parks. These counries lobbied unsuccessfully in 1990 and 1994 o down-lis heir populaions and re-open (limied) rade in ivory and oher elephan producs. While lifing he resricions on rade is unlikely o happen in he shor run, lobbying by he five souhern African counries resuled in a decision in June 1997 (based on Resoluions 3.15 and 5.21), o permi Boswana, Namibia and Zimbabwe o sell off nearly 50 ons of sockpiled ivory on a one-ime basis. This consiued less han 60% of he ivory ha hese counries had accumulaed as a resul of confiscaions from poachers, naural moraliy, culling and desrucion of problem animals. The ivory was sold o Japan in 1999 a a price of US$103 per kg. 5 A COP12, in 2002, anoher one-off sale by Boswana, Namibia and Souh Africa was approved, bu ha sale had no ye been compleed by he end of 2004. These one-off sales have re-opened debaes abou how he African elephan is o be susainably managed, 4 Soulé (1987) suggess ha 2000 animals are adequae o ensure survival of a large mammal species (alhough wih grea expense a species can recover even from small populaions), while Konoleon and Swanson (2003) use a minimum viable populaion of 500 for he Gian Panda. 5 Ciing Milliken (African Elephans and he Elevenh Meeing of he Conference of he Paries o CITES, TRAFFIC Nework Briefing Doc., www.raffic.org/briefings/elephans-11hmeeing.hml), Bule, Horan and Shogren (2001) indicae ha COP10 agreed o permi non-commercial donors o buy ivory from sockpiles o enable range saes o reduce heir financial and securiy liabiliies associaed wih he sockpiles, under he proviso ha none of he ivory purchased in his way ges re-sold in any form a any fuure dae. Oher han he Japanese purchase, we know of no oher purchases ha have aken place. 3
and wha role rade will play. Populaion daa presened in Table 1 sugges ha he ivory rade ban has had a leas some success. The rapid decline in elephan abundance ha is hough o have occurred prior o and during he 1980s appears o have been haled, and indeed may even have been reversed. However, he underlying daa for any such conclusion are no very good esimaes of elephan populaions are conenious a bes; few reliable esimaes are available before 1989, and even hose in Table 1 are caegorized according o wheher esimaes are definie, probable, possible or speculaive. Furher, he area surveyed in each of he four years varied, being lowes for he 1998 populaion esimaes. Thus, populaion rends are indicaive a bes. The ivory rade ban remains conroversial. Criics of he ban allege ha endangered species migh be placed a risk by he perverse incenives ha a rade ban generaes. Banning rade makes elephan conservaion a less aracive aciviy, inadverenly promoing conversion of elephan habia o oher uses. In addiion, by reducing or enirely eliminaing revenues from elephan managemen and exploiaion, a rade ban migh undermine he incenive o manage he sock carefully and enforce propery righs o elephans and/or heir habia (see Bule, van Kooen and Swanson 2003). Conversely, supporers of he rade ban argue ha enforcing propery righs and susainable harvesing regimes in (semi-) open access habias is difficul and expensive. Hence, rade may simulae illegal harvesing. In addiion, i is suggesed ha he legal rade may faciliae he laundering of illegal ivory producs. The purpose in his paper is o invesigae he effecs of he ivory rade ban on elephan socks compared o he siuaion where rade is permied. As long as rens from elephan exploiaion remain in place (so he marginal benefis of harvesing elephans and markeing ivory exceed he marginal coss), a rade ban is unable o preven some harves of elephans and he sale of ivory in inernaional markes. Inernaional poaching gangs will be able o capure some of he ren and marke ivory hrough a variey of channels. However, he marginal coss of providing ivory will likely be higher under a rade ban han under legal rade, while demand will be reduced because some poenial buyers will have a sigma agains purchases of ivory (Fischer 2004). Under legal rade, he marginal coss of providing ivory will be lower, while he sigma facor will no longer apply as buyers assume elephan populaions are being managed susainably. We develop a dynamic bioeconomic mahemaical programming model of ivory rade wih four African exporing regions and one global imporing region. Africa is divided ino four regions because of differences in he size of heir elephan populaions, he insiuional and biological challenges o proecing elephan socks, he exen of poaching, and he imporance of elephans in aracing ouriss. The model is used in his paper o sudy he impacs of various insiuional arrangemens on economic well being and elephan numbers. In paricular, if propery righs o elephans can be clearly defined, here may be alernaive insiuional arrangemens ha lead o larger elephan numbers and a 4
lower chance ha he African elephan becomes exinc. One possibiliy is a quoa regime, such as he MQS, bu wih sronger enforcemen. A regime ha permis sales of ivory bu also pays elephan owners according o he acual size of he elephan sock in a counry may lead o greaer holdings of elephans while providing owners wih revenues o police elephan herds agains poachers. Differen regimes are invesigaed o deermine wheher he rade ban is indeed he bes means o proec elephans. Resuls indicae ha neiher free rade nor a quoa sysem can effecively proec he elephan unless accompanied by conservaion paymens from rich counries o range saes or recogniion ha elephans provide imporan ourism benefis, or boh. Since conservaion paymens are unlikely a his ime, a rade ban appears o be he mos effecive policy for mainaining elephan herds in African range saes where ourism is of lile imporance or he link beween elephans and ourism benefis is no properly recognized. A heoreical model of ivory rade is presened in he nex secion, while he mahemaical programming formulaions are described in secion III. How he programming model is parameerized is he subjec of secion IV, while resuls of alernaive policy opions and views abou he effec of rade on demand and (legal and illegal) supply are provided in secion V. The conclusions ensue. II. IVORY TRADE MODEL We begin by posulaing a simple, saic spaial price equilibrium ivory rade model. The model is described wih he aid of Figure 1 he inernaional marke for ivory. The African coninen is he inernaional source of ivory, as producs from Asian elephans (Elephas maximus) are assumed o be sold only in he Asian marke and usually wihin he counry in which hey are found and (illegally) harvesed. Since he domesic African marke for ivory is small wih any ivory worked in Africa simply sold abroad (or sold domesically and smuggled abroad), ivory rade is assumed ake place beween Africa as he excess supplier and he res of he world. The African excess supply funcion is denoed p S in Figure 1, while he inernaional excess demand for ivory (denoed p D ) is he demand lef over afer local ivory supply (from Asian elephans) is aken ino accoun. The excess supply funcion under free rade equals he horizonal sum of he legal and illegal excess supply funcions. (An indicaor variable I is used o denoe he effec of he rade ban on supply and demand, wih I=0 indicaing free rade and I=1 a rade ban.) Under free rade, an amoun q* is raded a price P*. As a resul of poached ivory, marke equilibrium occurs a poin v raher han poin u (Figure 1), wih q* q L amoun of illegal African ivory sold inernaionally. The global benefis of ivory rade are given by he sum of he consumer and producer surpluses area kvp* under he demand funcion p D (I=0), plus area xzp* above he p S (I=0) legal funcion. Assuming open access, he poachers supply curve, p S (I=0) illegal, is no equivalen o a marginal cos funcion; hence, poachers receive no rens. (An alernaive assumpion is considered in he rade ban siuaion.) Illegal (poached) ivory masquerades as legal ivory when here is free rade. Bu an 5
P P ivory rade ban does no hal all rade in ivory, alhough i does have wo effecs: Firs, he poachers supply funcion shifs upwards as he ransacion coss of markeing ivory increase. While poachers always incur coss associaed wih illegal aciviies (e.g., avoiding ani-poaching parols), coss of illegal aciviies increase as he coss of finding buyers and avoiding ban-imposed cusom conrols rise. Second, a rade ban shifs he (excess) demand funcion inwards because he ban creaes a sigma associaed wih he purchase of hings made from ivory (Fischer 2004). Under a rade ban compeiive equilibrium occurs a w, alhough i would occur a y if here were no sigma effec or added markeing coss for poachers. Wha worries many environmenal groups is ha removal of rade resricions will reduce he sigma of buying and owning ivory, implying greaer numbers of elephans being harvesed (a equilibrium v raher han w). An alernaive o a rade ban is a quoa. As already noed, a quoa was in place prior o he ivory rade ban, bu i was no conrolled in any sense by he paries hemselves or by ouside paries. The quoa can be illusraed wih he aid of Figure 2. In he absence of poaching, an effecive quoa reduces ivory sales o he quoa level Q, bu poached ivory increases sales from Q o Q+, reducing he marke price o Q+ PP from P Q. The illegal sales reduce he quoa (scarciy) rens earned by African elephan saes by PPQ+ nrp Q (from area cdrp Q o cdnp Q+ ). Noneheless, he quoa resuls in lower harvess of elephans compared wih compeiive free rade (q*) and may even lead o lower levels of elephan harves han under he rade ban if quoa revenue is used o police illegal harves. If policing increases he coss o poachers sufficienly, so ha he inercep s of p S (I=0) Illegal is shifed upward so i lies above P Q, no illegal ivory will reach he marke, effecively haling poaching. One obsacle o implemening a quoa sysem is ha African saes mus form an effecive ivory rade carel, somehow allocaing quoa among member saes. Logically, his is bes accomplished by allocaing quoa on he basis of exising elephan numbers. Quoa rading will ensure ha harvess are allocaed in he mos efficien fashion. The allocaion mechanism will deermine he disribuion of rens and will need o be acceped by all paries o preven cheaing. Furher, i is necessary o have in place insiuions o enable a quoa scheme o operae, namely, assignmen and proecion of propery righs o elephans and heir habia, and monioring and enforcemen of elephan harvesing and ivory sales. I also requires policing of poaching hroughou all range saes. I is unlikely ha proper monioring and enforcemen will be in place, bu perhaps a porion of he revenues generaed by he quoa could be used o finance hese aspecs of he scheme. The discussion has hus far ignored dynamic aspecs of elephan populaions and he poenial o sore ivory, a non-perishable commodiy, from one period o he nex. This means ha usks confiscaed from poachers, or obained from animals ha died of naural causes or were culled, ener sorage. Given ha ivory has value and ha here are coss o wildlife programs, saes wih significan quaniies of sored ivory, such as range saes in souhern Africa, will lobby o permi hem o sell socks, which is why CITES has permied some one-off sales. The exisence of socks complicaes he models discussed in Figures 1 and 2. Along wih he fac ha elephans grow and reproduce, an analysis ha includes 6
ivory socks is necessarily dynamic (since user coss of curren harvess on fuure populaions and harvess mus be aken ino accoun). Hence, a dynamic mahemaical programming approach is used. Anoher aspec no considered in he spaial price equilibrium model is he non-marke componen o ivory rade, namely, he elephan s role as a flagship species for aracing ouriss and he willingness of he inernaional communiy o proec elephans in siu, which is one reason for he ban on ivory rade. The ivory rade model needs o incorporae poenial paymens by rich (European and Norh American) counries o African saes on he basis of he numbers of elephans ha are reained in siu. To be effecive, however, paymens mus be made o hose wih propery righs o elephans and/or heir habia. I is he owners, wheher saes, individuals or communiies, ha need o have appropriae incenives o harves or proec elephans. Paymens o proec elephans will increase numbers beyond wha hey are currenly, or a leas possibly prevening elephans from being added o he lis of endangered species. III. MODEL FORMULATION Consider firs an idealized dynamic bioeconomic model in which he global ne benefis from ivory rade and elephan conservaion are maximized over ime. There is one ne consuming region and several regions ha produce elephans (range saes) and marke ivory. Iniially here is no poaching, and insiuions are such ha paymens from rich counries o range saes for elephan conservaion have he desired conservaion effec. The model is modified o include poaching and hen expanded o examine he failure of conservaion paymens, he poenial of a quoa regime, and he coss and benefis of an ivory rade ban. Compared o Fischer (2004), he advanage of he curren approach is ha i permis richer deail, alhough many of her resuls are confirmed. The model also permis counries (bu no poachers) o sore ivory, which hey will do under free rade as long as he expeced increase in price exceeds he coss of holding socks. Under a rade ban, sock holding is non-volunary. Kremer and Morcom (2000), and Bule, Horan and Shogren (2001), also consider he inerplay beween elephan harvess and ivory socks. They poin ou ha: (1) governmens can use sockpiled ivory as a hrea agains poachers hreaening o release ivory and drive prices low enough o sop poaching; and (2) i migh be possible for an agen o hoard sufficien socks o make i worhwhile for he agen o drive elephans o exincion. These researchers provide no evidence ha eiher of hese oucomes is likely, bu exincion of elephans dominaes conservaion in all he realisic scenarios hey examine and i never appears o pay for an agen o hoard ivory. Our objecive is o maximize he discouned ne global benefis of selling ivory and conserving elephans over some planning horizon. I is given by he sum of consumer and producer surpluses from markeing and selling ivory, ivory sorage coss, elephan harves coss, he spillover coss elephans impose on he ecosysem (here aken o be landowners), benefis from ourism, and he off-sie preservaion benefis of keeping elephans in siu: 7
q T j, N q j, Max N (1) [ ]. = = = d β p ( I, q) dq c( I, a) da + R( x ) k( I) h ss D( x ) + (1 I) B( x ) q, h 1 0 j 1 0 j 1 Here p d (I, q) is he inverse (excess) demand funcion for ivory; q is he quaniy of ivory a ime made available for sale on he inernaional marke by region j (of which here are N); I is an indicaor variable se equal o 1 when rade is prohibied and 0 oherwise; and c(i, a), where a is an inegraion variable, is he marginal cos funcion associaed wih he producion and markeing of ivory once elephans (denoed by x) have been harvesed (denoed h). Thus, he firs wo erms in expression (1) are he consumer surplus plus he quasi-ren accruing o ivory sellers. Noe ha he marginal cos funcion is no quie he same as he supply funcion, p S (I) in Figure 1, because i does no include elephan harvesing and opporuniy coss ha are aken ino accoun by he oher erms in (1). In expression (1), k(i) is he per uni cos of harvesing animals and s is a fixed cos of holding ivory socks (S). Given he imporance of elephans in aracing ouriss, which is of greaer relevance in some regions of Africa han ohers, R(x ) is a funcion linking elephan numbers o a region s ourism benefis. D(x ) is a measure of he damage elephans impose on he ecosysem, and B(x ) is conservaion or in siu benefis ha elephans provide a ime, wih x = N x j, j= 1. The cos of harvesing elephans is no densiy dependen as elephans are quie large and assumed o be easily racked, bu he cos is higher when rade is banned and poaching occurs. The facor β=1/(1+δ), where δ is he social rae of discoun, is used o discoun fuure reurns. A any ime, he sock of ivory in a given region, S, will depend on he sock in he preceding period plus addiions o he sock from elephan harvess minus any sales of ivory. For convenience, i is assumed ha no socks of ivory are held ouside of he elephan range saes. Elephan harvess may be he resul of decisions o eliminae roublesome animals, cull animals because here are oo many for he paricular ecosysem, or simply harves animals for sale of ivory, as well as incidenal ake due o naural moraliy or confiscaions of illegal ivory. The sock equaion is given by: (2) S +1 = S + γh q, j, =1,..., T 1 (Ivory sock holding dynamics) where γ is a parameer ha convers elephans o ivory. Counries can sell ivory or hold i unil a laer period, bu sales of ivory canno exceed available socks in any period: (3) q S,. (Sales of ivory canno exceed available sock) In addiion o a sock consrain, an equaion is needed o describe he growh and harves of elephan populaions: 8
(4) x +1 x = g(x ) h, j, =1,..., T 1 (Elephan populaion dynamics) where g(x ) is he elephan growh funcion ha migh exhibi logisic or depensaional growh (van Kooen and Bule 2000, pp.184-189). I is discussed in greaer deail below. For each region, iniial (opening) socks of ivory and elephans need o be idenified: (5) S 0 = S j, x 0 = x j, j. (Iniial condiions) In addiion, non-negaiviy consrains need o be imposed: (6) q, S, x, h 0,. (Non-negaiviy) Lasly, i is possible o specify opional susainabiliy condiions. Susainabiliy can be specified, for example, as an endpoin consrain on elephan socks in each region, or as a requiremen ha elephan numbers remain a or above some minimum viable populaion level ( m ): (7) x T xˆ, j or x m,. (Susainabiliy crierion) j The susainabiliy consrain is mean primarily o saisfy inernaional demands ha elephan socks be mainained. Less resricive versions of (7) migh require ha he oal of elephan socks across all range saes exceed some specified value a =T, or ha his oal exceed some minimum value in each period. Alernaive susainabiliy requiremens can be invesigaed, bu he African elephan could also be allowed o go exinc. Susainabiliy is difficul o enforce and his aspec is lef o fuure research. The forgoing expressions form he basis of several models ha can be used o invesigae he effecs of poaching and differen insiuional arrangemens on wellbeing and elephan conservaion. They can be used o deermine which policies and perspecives are likely o be he mos effecive in proecing elephans. Global Wellbeing wih No Poaching The firs quesion of ineres is: Wha are he consequences of free rade when here is no poaching? The following mahemaical program is used o examine he consequences for elephan conservaion of maximizing global welfare in his case: 6 6 In P1, as in laer formulaions, an opional susainabiliy consrain can be included. 9
P1: q Max, h q = D( x ) + B( x ) T j, N j, N d β p (0, q) dq c(0, a) da + [ R( x ) k(0) h ss ] q = 1 0 j 1 0 j= 1 Subjec o: (2), (3), (4), (5), and (6). Global Wellbeing wih Poaching Nex, consider he real-world case where elephan poaching and illegal ivory sales occur. I is assumed ha he decision maker maximizes benefis as before, aking ino accoun he supply funcion of poachers, alhough i can affec his supply hrough ani-poaching monioring and enforcemen (Bule and van Kooen 1999). The supply of illegal ivory from region j a ime is assumed o be a funcion of he inernaional price p d p and ani-poaching effor E: =fj(e, p d ), where q p denoes sales of illegal ivory from q j, poached elephans (wih poached elephans o be denoed h p in wha follows). While E is a poenial decision variable, i is lef as a subjec for fuure research, alhough i migh be possible o use simulaion analysis o examine he role of enforcemen (which is no done here). Raher, i is simply assumed ha illegal ivory is confiscaed a a consan rae (ξ) as a resul of fixed-cos ani-poaching programs. The mahemaical bioeconomic modeling program can now be wrien as: P2: T Q N q j, Max N [ ] = = = d β p (0, q) dq c(0, a) da + R( x ) k(0) h ss D( x ) + B( x ) q, h 1 0 j 1 0 j 1 Subjec o: (3) and (5), plus: p (2 ) S +1 = S + γh q + ξ j, =1,..., T 1 q j, (Ivory sock holding) p q j, (4 ) x +1 x = g(x ) h, γ j, =1,..., T 1 (Elephan dynamics) p p (6 ) q, S, x, h,, 0, q j, h j, (Non-negaiviy) p p p (8) q h ξ q, j j, γ, (Sales of poached ivory canno exceed ivory from poached elephans minus confiscaions) N p (9) Q = ( q + q ), j= 1 (Adding up) p d (10) q = f ( E, p (0, Q )), j j, j, (Supply of illegal ivory from each region) 10
Consrain (8) is required so ha sales of illegal ivory canno exceed ivory available from poached elephans; i is assumed ha illegal ivory is sold in he same period he poached elephans are killed and ha poachers do no sockpile ivory (alhough some of he poached ivory is confiscaed). Relaxaion of his assumpion is a opic for fuure research. Consrains (9) and (10) deermine he global price of ivory and he amouns of illegal ivory sold by each region. 7 The las erm in (4 ) indicaes he number of elephans ha poachers would harves. I is also assumed ha poachers do no hold ivory socks bu ha confiscaed ivory eners socks. African Welfare wih Compeiive Selling and Poaching Now consider he case where only he wellbeing of African elephan range saes is imporan. In ha case, we eliminae as a consideraion he wellbeing of ivory buyers. Furher, conservaion paymens for elephans held in siu are rarely if ever made, and cerainly no on he basis of oal willingness o pay (WTP). One alernaive is ha conservaion paymens are paid (if a all) on he basis of he conribuion ha he las elephan on he coninen makes o preservaion benefis, ha is, on he basis of marginal WTP. In ha case, he modified program is: P3 q Max, h q T N j, = = c(0, a) da + R( x ) + B '( x ) x k(0) h ss D( x ) 1 j 1 0 d β q p (0, Q ) Subjec o he same consrains as in P2. In his case, because hey face a downward sloping WTP funcion, he range saes would maximize he revenue from conservaion paymens by significanly reducing elephan socks. To avoid his, rich counries could simply declare ha hey would pay range saes a fixed amoun per elephan so ha B'(x)=B 0 0, where B 0 is a consan ha is zero if no conservaion paymens are made. An Ivory Carel wih Poaching Suppose ha he African range saes could form an ivory carel, maximizing heir overall wellbeing from sales of ivory, while somehow allocaing elephan harvess and ivory expors in a manner accepable o all counries. In ha case, an addiional efficiency condiion requires ha marginal coss of harvesing elephans and markeing ivory are he same in each region and equal o marginal revenue. Damage from elephans is ignored in his marginaliy condiion, bu no he marginal cos of harvesing elephans for heir ivory. The carel deermines how much ivory is sold on he marke in each period from each of he N regions, as well as how many elephans are o be harvesed in each region for heir ivory. 7 Given he assumpion underlying consrain (8), his implies ha illegal sellers have some noion or forecas of he price. Furher research is required ino alernaive formulaions, perhaps ones ha involve holding of illegal socks. 11
The opimizaion program is: P4: q Max, h q T N j, = = c(0, a) da + R( x ) + B '( x ) x k(0) h ss D( x ) 1 j 1 0 d β q p (0, Q ) Subjec o he same consrains as in P2 plus: k(0) p (0, Q ) d (11) c( 0, q j, ) + Q + p (0, Q), γ Q d (Marginaliy condiion: MC j MR) Ivory Trade Ban wih Poaching Finally, consider he case of he ivory rade ban (I=1). In order o sudy he effec on elephan herds in he various African regions, we ake he perspecive of he criminal gangs ha sell ivory illegally in inernaional markes. I is assumed ha hey maximize quasi-rens (producer surplus) from markeing ivory, bu ha hey canno form a carel. If hey were somehow able o exer marke power, hen less ivory will be sold han under he assumpions of program P5 and even less elephans will be killed. Hence, he rade ban case considered here migh be regarded as a worse-case, rade-ban scenario. Any susainabiliy consrain ha migh be imposed also falls away since poachers are no concerned abou mainaining elephans over ime. P5: q Max p, h p T N β q = 1 j= 1 p p q j, d p p (1, Q ) f (1, a) da k(1) h j 0 Subjec o: (4) and (8), wih (8) replacing (3), plus p (4 ) x +1 x = g(x ) j, =1,..., T 1 h j, (Modified elephan dynamics) (5 ) x 0 = x j, j (Iniial condiion on elephan numbers only) p p (6 ) q, x, 0, h j, (Modified non-negaiviy) N p (9 ) Q = q (Modified adding up) j=1 Model P5 implies ha elephans are no ruly an open access resource, bu a derived demand. Illegal killing of elephans may sill occur under open access, however, if usks are illegally sockpiled, elephans are killed for bush mea and/or hides, or illegal killing is done by peasans simply o ge rid of roublesome animals. While socks of ivory are considered immaerial in P5, since only governmens are assumed o sockpile ivory, fuure research 12
migh be able o separae illegal and legal sock holding, hereby enabling criminals o hold ivory socks as a hedge agains unforeseen fuure price changes, for example. IV. DATA AND MODEL PARAMETERIZATION A major problem in implemening he forgoing models concerns he availabiliy of daa. Few daa are available and much of ha is based on local observaions in range saes (e.g., Menon 2002). The IUCN Species Survival Commission has racked elephan numbers for he pas decade and a half (ITGR 1989; Said e al. 1995; Barnes e al. 1999; Blanc e al. 2003), while he inernaional communiy has implemened Monioring he Illegal Kill of Elephans (MIKE) and he Elephan Trade Informaion Sysem (ETIS) o keep an eye on illegal aciviies exacerbaed by he rade ban. MIKE sared in Ocober 2001 and is managed by he CITES Secrearia hrough a Cenral Coordinaing Uni headed by a Direcor based in Nairobi, while ETIS is managed by TRAFFIC (hp://www.raffic.org/) a join program of he World Wildlife Fund and he World Conservaion Union (IUCN). MIKE represens an effor o monior illegal elephan killing in elephan saes by developing he capaciy of wildlife agencies o use heir ani-poaching parols and oher mehods for deecing carcasses, recording wha hey find and enering informaion ino a sandardized daabase. The agencies also underake o conduc populaion surveys on a wo o hree year cycle. ETIS is an inernaional monioring sysem o rack illegal rade in elephan producs (mainly ivory), bu i relies on individual counries o repor seizures. While ETIS has published ime series of seizure daa by counry ha could provide a saring poin for an analysis of he impac of species lising and rade on seizures (see Figure 3) (Milliken e al. 2004), progress on MIKE has been more limied because i is aking ime o ge he sysem up and running (Huner, Marin and Milliken 2004). A deailed specificaion of he consumer and producer surplus componens of he objecive funcion (1) as employed in he mahemaical programming model is provided in Appendix A. There is insufficien informaion o deermine he pre-ban and pos-ban demand funcions, p d (0, q) and p d (1, q), respecively. Fischer (2004) repors ha ivory was rading for abou $150 per kg in he pre-ban period, wih price peaking a over $1,200 per kg shorly afer he ban s imposiion and hen seling a some $450/kg hereafer. 8 The only informaion abou quaniies raded perains o repored seizures of elephan producs. The firs year for which hese are repored is 1989, he year of he rade ban. From Table 2, he average number of annual seizures of illegal elephan producs (as hey crossed inernaional borders) increased by 120% afer 1989, alhough, as indicaed in Figure 3, here is no real discernable rend in he amoun of illegal ivory sold in he years following he rade ban, a leas based on repored seizures. I appears ha illegal aciviy coninues unabaed. Huner, Marin and Milliken (2004) use observaions on ivory carvers 8 In comparison, Kremer and Morcom (2000) cie Simmons and Kreuer (1989) for prices of uncarved elephan usks: $7/lb ($9.20/kg) in 1969, $52/lb ($114.40/kg) in 1978, and $66/lb ($145.20/kg) in 1989 (wih 2.2 lb = 1 kg). 13
in various regions of Africa and Asia o esimae ha beween 6,433 and 16,185 African elephans (and 123 o 349 Asian elephans) are sill supplied illegally o he marke each year (Table 2). This implies ha beween 44.4 and 111.7 onnes of illegal ivory from African elephans sill ener he marke annually, or abou one-enh of wha was markeed (legally and illegally) under free rade. Given a dearh of addiional informaion, we simply assume ha he excess demand funcion in Figure 1 can be wrien as: 9 (12) p d (I=0) = 720 0.0005 q. According o (12), a a real pre-ban price of $150/kg, some 1140 onnes of ivory would be raded. Wha would be sold under a rade ban assuming he demand curve changes due o a sigma effec? If he pre-ban demand funcion (12) coninued o describe he siuaion, he marke price of he ivory would be $664-$698 per kg. As noed, however, i is repored o be nearer $450 per kg. We assume ha he inercep on he pos-ban excess demand curve has shifed down by his difference, or by abou $220 (=$670 $450), so ha he no-rade excess demand funcion can be described by: (13) p d (I=1) = 500 0.0005 q. A a price of $450 per kg, only 100 onnes of African ivory would be sold inernaionally, well wihin he range esimaed by Huner, Marin and Milliken (2004) and indicaed above. 10 On he supply side, he African coninen is divided ino four regions ha represen differen elephan subspecies he savanna elephan (Laxodona africana africana) and he fores elephan (Laxodona africana cyclois) and elephan economics. The fores elephan is difficul o view and is found primarily in Wes and Cenral Africa, wih populaions in Wes Africa raher small and insignifican in coninenal erms (Table 1). The savanna elephan is an imporan flagship species for he ourism indusry. While imporan in all saes of Eas and Souhern Africa, populaions in he laer region have hreaened he ecosysem carrying capaciy, so elephans have been culled and ivory sockpiled. Thus, while Kenya is concerned abou he adverse impacs of ivory rade, saes in Souhern Africa have lobbied o sell ivory. 9 Based on seven pre-ban observaions on price and presumed ivory sales from various CITES sources, deflaed prices (2000 US$ per kg) were regressed on quaniy (kg of ivory) and ime (wih 1960=1 and 1989=29) o obain: P = 220.025 0.00046 q + 16.581, R 2 = 0.883 F=7.059* (1.83) ( 2.37) * (3.73) ** where he -saisics are provided in parenheses, ** indicaes saisical significance a he 1% level or beer and * indicaes significance a he 5% level. Assuming his regression resul is a demand funcion (ignoring idenificaion and oher problems) and aking =30 gives resul (12). 10 Based on he calculaions provided here, he price paid by Japan in 1999 ($103/kg) is likely low. 14
I is assumed ha, in addiion o he coss of harvesing elephans (see equaion (1)), here is a fixed cos plus a per uni cos of aking ivory ou of socks and bringing i o marke. The fixed cos represens he ransporaion and search coss (finding markes). Boh fixed and per uni coss are higher when a rade ban is in place as ransacions are illegal. To deermine he supply funcions in each region, we begin by assuming ha under a rade ban, 100,000 kg of ivory would sell for $450/kg. To deermine he regional illegal supply funcions, we furher assume ha 60% of he illegal supply (or 60,000 kg) comes from Cenral Africa, since Huner, Marin and Milliken (2004) argue ha much of he illegal supply originaes in his region. The amouns coming from he oher regions are indicaed in Table 3. If we assume linear supply funcions and guessimaes of he inerceps, i is hen possible o deermine he slopes of he supply curves based on he share of he oal quaniy of illegal ivory ha each region conribues o he marke. The inercep and slope parameers for he illegal supply (marginal cos) funcions under a rade ban are provided in Table 3. In order o consruc he legal and illegal supply funcions, a number of assumpions need o be made. Under free-rade, 1140 onnes of ivory are raded a a price of $150/kg. A ha price, regions are assumed o supply legal ivory o he marke according he proporions indicaed in Table 3 (roughly based on he proporions in Table 1). However, no all of he ivory sold is from legal socks. Under a ban, 100 onnes of ivory are assumed o be supplied illegally (as noed above); wih free rade, we assume ha 200 onnes are provided illegally wih he proporion of he illegal supply from each region he same as under he ban. Thus, 780 onnes per annum are supplied legally. We assume ha he illegal supply funcions are flaer and have shifed down compared o he rade-ban case, because rade reduces ani-poaching effor and makes i easier o launder poached ivory. The legal supply funcions are assumed o have a lower ordinae inercep and o be flaer han he illegal supply curves, as marginal coss of supplying ivory o he inernaional marke mus be lower for legal suppliers han illegal ones. The inercep and slope parameers for he illegal and legal supply funcions in he case of rade are also provided in Table 3. Ani-poaching effor can affec he supply of illegal ivory. Unforunaely, here is lile informaion abou he effec ha law enforcemen has on he illegal supply of ivory. Milliken e al. (2004) provide wo measures of law enforcemen effor he Corrupion Percepion Index score (which for a region would be he average of he counry scores) and an index of enforcemen given by he oal number of in-counry seizures divided by he oal number of seizures (p.23). Arguably, he World Bank s (2005) Governance and Ani-corrupion indicaors are a beer indicaor of enforcemen abiliy han he Corrupion Percepion Index. Thus, raher han a single index for each region, four indexes are provided for each of he regions in he model (see Table 4). Furher, Milliken e al. s index of enforcemen, bu hen adjused for elephan populaions and normalized for Africa, is also provided in Table 4 for each region. Wes and Cenral Africa have he wors scores, respecively, in erms of enforcing he ivory rade ban, and hese low scores accord wih he World Bank s low measures of performance relaed o governmen effeciveness, rule of law and corrupion. Eas Africa performs jus as poorly on he World Bank s indicaors, bu does 15
relaively beer in he enforcemen of he ivory rade ban, perhaps because of he imporance of he elephan o he economies of Eas African saes. Saes in Souhern Africa are more prone o enforce ivory rade laws and are generally beer performers on oher measures as well, bu all saes in Africa lag well behind saes in Asia ha purchase elephans and counries of Europe and Norh America (see Bule, van Kooen and Swanson 2004). As par of he analysis, i is assumed ha African range saes can do beer in he enforcemen of illegal killing of elephans and rade in elephan pars. To describe he fecundiy, moraliy and growh characerisics of elephans, we specify he following simple linear funcion: 11 (14) x +1 = (1+r) x, wih x K j, where r is he growh rae in elephan socks and K j is he elephan carrying capaciy for ecosysems in region j. Se r=0.067 (Milner-Gulland and Leader-Williams 1992) and iniial elephan populaions equal o he elephan oals for each region in 2002 (Table 1). The carrying capaciy of each region is deermined from informaion abou elephan range and he proporion of elephan range ha is proeced. For he fores elephan, i is assumed ha unproeced elephan range has a carrying capaciy of 0.15 elephans per km 2, while i is 0.25 elephans per km 2 for proeced range. The carrying capaciy of open range is higher, so i is assumed o be 0.20 per km 2 for unproeced and 0.35 for proeced range in he case of he savanna elephan. Background informaion and carrying capaciies are provided in Table 5. The esimaed coninenal carrying capaciy of abou 974,000 elephans is lower han numbers exising in he early 1970s (some 1.2 million), bu elephan range has also decreased significanly since hen due o rising human populaions and encroachmen. Ivory socks are largely unknown, alhough Milliken (1997) esimaes ha here are some 462.5 onnes of verifiable and legiimaely held socks of ivory in Africa, and anoher 243 onnes of undeclared (perhaps illegal) ivory, or a oal of 705.5 onnes. This amoun is allocaed across regions in proporion o each region s number of elephans. One esimae of exan socks is o add o hese esimaes he increase in sockpiled ivory over he period 1997-2004 relying on informaion repored by Milliken e al. (2004). Average seizures by region are provided in Table 2 for he period 1990-2003, while he raw ivory equivalen weigh of an average seizure over he period 1989-2004 was 0.498 kg. Assume ha seized ivory accouned for half of he increase in ivory socks, wih he remainder coming from culling, killings of roublesome animals, and, in some regions, legal huning for moneary gain. Using his informaion o deermine he increase in socks since 1996 gives he esimaes provided in he nex o las row of Table 5. One could also argue ha, using 11 An alernaive is o employ he sandard logisics growh funcion: x +1 x = r x (1 x /K), where r is he inrinsic growh rae in elephan socks and K is he ecosysem s elephan carrying capaciy. However, for his discree form and he parameers used in his model, i leads o an immediae reducion in elephan numbers by half even wihou harvess. 16
Milliken s (1997) esimae of 1996 socks, an average of 88.2 onnes of ivory were added o socks each year. If his coninued up o 2004, here would be some 1300 onnes of sockpiled ivory. As he exac number is unknown, we assume 900 onnes of socks allocaed as indicaed in he las row of Table 5. Furher, we assume a consan rae of confiscaions of 5%, so ξ =0.05. Milner-Gulland and Leader-Williams (1992) esimae poaching coss o be abou $180 per elephan. Thus, i is assumed ha c(i=1)=$180; arbirarily choose one-hird of his amoun o be legal harvesing coss, c(i=0)=$60. While Kenya and Mozambique, for example, do no permi huning of elephans, huning is allowed in some saes. Noneheless, Scully (2002, pp.47, 86, 122) repors ha, in 1999, Safari Club Inernaional members could pay some $10,000 for he privilege of huning an elephan (likely in souhern Africa and specifically Zimbabwe). Alhough lef o fuure research, for souhern Africa a leas, we could consider elephan harvess yielding a benefi of $10,000. The coss of holding ivory socks consis of he forgone opporuniy cos (given by he discoun raes) and a physical cos of holding ivory, which is assumed o be small, s=$0.50/kg each period. Average usk weigh has dropped significanly since 1970, probably because older animals wih larger usks were killed firs, so curren socks of elephans end o be much younger. Scully (2004, p.123) poins ou ha i ook 55 elephans o obain 1 onne of ivory in 1979, compared o 113 elephans around 1990 (p.123) a decline from 18.18 o 8.85 kg of ivory per animal. 12 No only is usk size (and he age of elephans) declining, bu more are born wihou usks. Yacob e al. (2004) measured 31 usks of elephans in Erirea and found an average usk weigh of 8.7 kg, while Huner, Marin and Milliken (2004) repor ha, based on 7800 ivory seizures, he average usk weighs 3.68 kg hey use his informaion o conver esimaes of ivory being carved ino number of elephans killed illegally. Boh male and female African elephans grow usks (while only male Asian elephans have usks), bu for whaever reason he average number of usks per African elephan is 1.88. Thus, he above values conver o 16.4 kg and 6.9 kg of ivory per elephan. Because of he dispariy in esimaes and ha weighs have declined over ime, we choose γ=7.5 kg of ivory per elephan. Bule and van Kooen (1996) assume a linear damage funcion, D(x)=dx, wih he consan cos imposed by elephans on he ecosysem, d, deermined by he amoun of forage ha an elephan consumes annually (which is equivalen o he consumpion of 4.7 12 Scully quoes David Chadwick. Scully (2002, pp.69-71) also repors ha, afer making donaions o several local Mozambique causes (including a hospial), hree members of he Safari Club Inernaional killed, among oher animals, hree elephans in July 1998, despie an unambiguous 1990 law prohibiing elephan huning in Mozambique. The larges of he elephans had usks weighing an incredible 92 lbs (41.8 kg) each! 17