An Analysis of the Application of Club Good Models to Determine Carrying Capacity of National Parks

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1 Illnos State Unversty ISU ReD: Research and edata Master's Theses - Economcs Economcs An Analyss of the Applcaton of Club Good Models to Determne Carryng Capacty of Natonal Parks Rachel Smth Illnos State Unversty Follow ths and addtonal works at: Part of the Economcs Commons Recommended Ctaton Smth, Rachel, "An Analyss of the Applcaton of Club Good Models to Determne Carryng Capacty of Natonal Parks" (007). Master's Theses - Economcs.. Ths Artcle s brought to you for free and open access by the Economcs at ISU ReD: Research and edata. It has been accepted for ncluson n Master's Theses - Economcs by an authorzed admnstrator of ISU ReD: Research and edata. For more nformaton, please contact ISUReD@lstu.edu.

2 Smth An Analyss of the Applcaton of Club Good Models to Determne Carryng Capacty of Natonal Parks Rachel Smth Master s Student Department of Economcs Illnos State Unversty Normal, IL Capstone Project Submtted to Illnos State Unversty n Partal Fulfllment of the Requrements for Master s Degree n Economcs Advsor: Dr. Lon Carlson May 007

3 Smth An Analyss of the Applcaton of Club Good Models to Determne Carryng Capacty of Natonal Parks The Natonal Parks and Recreaton Act of 978 requres that park managers develop and mplement a plan regardng vstor carryng capacty. In response, econometrcans have developed models that may be helpful to park management n regards to meetng ths goal. The focus of ths paper s to hghlght some of the earler work done by Buchanan (965) and Ng (973) n regards to modelng club goods and then to examne more recent attempts by Turner (000) and Prato (00) n applyng these models to help determne carryng capacty of natonal parks. Turner (000) and Prato s (00) models wll then be evaluated n regards to potental mplementaton proble ms.

4 Smth 3 An Analyss of the Applcaton of Club Good Models to Determne Carryng C a p a c t y o f N a t o n a l P a r k s I. Introducton The US Natonal Park Servce Organc Act of 96 requred that natonal parks must be managed such that scenery, natural and hstorc objects, and wldlfe are conserved. Ths act also mandated that the park managers should provde recreatonal opportunty for vstors and non-mparment of resources (Prato, 00). These two mportant goals have been dffcult to balance as natonal parks have experenced ncreased vstors and thus hgher levels of congeston. Subsequently, the Natonal Parks and Recreaton Act of 978 requred that park managers develop a plan to dentfy and mplement such a plan to address vstor carryng capacty (Prato, 00). II. Publc v. Prvate Goods Economsts have struggled to fnd a satsfactory treatment for those goods whch do not fall neatly nto one of the two categores of publc (collectve-consumpton) and prvate (ndvdual-consumpton) goods. Whle t may be more satsfyng (n terms of analyss) to dstngush between these two types of goods, n realty, a number of goods fall between these two polar oppostes. Wesbrod (964) ponts out that there s a sgnfcant number of prvate goods that have characterstcs of publc goods. Because the frequency of purchase of quas-publc goods s uncertan and the assocated costs of expandng producton once servces have been reduced, Wesbrod (964) felt that socal welfare s benefted by subsdzng the producton of these goods.

5 Smth 4 Usng Sequoa Natonal Park, Wesbrod (964) frst made the assumpton that even wth admsson fees t would be mpossble to cover total costs. Ths s due to the lack of tradtonal external consumpton or producton factors. Another hndrance s that the commodty s not storable and therefore cannot be purchased and then used at a later date. Wth total costs beng greater than total revenue, Marshallan analyss would dctate that the park be closed and that alternatve uses for the park s resources should be found. Of course, ths s only consderng allocatve effcency and gnores socal welfare factors. Ignored n ths case are the people who are wllng to pay for the opton to purchase ths commodty (vst the park) n the future. Ths opton value wll have lttle nfluence n the prvate market, however, because there s no practcal mechansm for calculatng user fees. Furthermore, f revenue s nsuffcent and the park s closed, the opton demand for future park usage wll not be taken nto account (Wesbrod, 964, 473). Wesbrod (964) then consders the case where user fees are adequate to cover total costs. Ths means that the opton demand of persons who [are] not current consumers would be satsfed at zero margnal cost (Wesbrod, 964, 473). That s to say, so long as the park s n operaton, the opton exsts as a pure publc good. A pure publc good s defned as a good that can be consumed smultaneously wthout detractng from the consumpton opportuntes for others. Ths means that the park can then be vewed as havng an external economy wth two outputs: servce to users and stand-by servces to non-users. The latter statement s dffcult to quantfy due to the fact that some of the standby users wll not become actual users. Asde from consderng the frequency of

6 Smth 5 purchase, another consderaton s the hgh costs of expanson or recommencement of producton n a short tme frame. Ths, n fact, may be an mpossble demand. Consder the case where a large secton of trees has been cut down. In Sequoa Natonal Forest, t would take centures for the forest area to be restored. Ths means that the occasonal user would fnd t dffcult, f not mpossble, to purchase the good. In ths case, the costs assocated wth recommencement of producton are too hgh (Wesbrod, 964). In ther book The Theory of Externaltes, Publc Goods and Club Goods, Rchard Cornes and Todd Sanders (996) outlne four dstnct characterstcs of club goods. The frst characterstc s that an ncrease n membershp sze, and thus ncreased congeston, wll lead to an ncrease n both costs and benefts. The addtonal costs are a result of the now ncreased congeston and the benefts are the result of cost reductons that occur due to the sharng of membershp expenses. Ths s n contrast to publc goods, where costs assocated wth ncreased membershp wll be zero. Second, club goods wll have a fnte membershp. Thrd, for club goods, nonmembers have the choce of jonng another club that offers the same club good, or they may choose not to jon a club. Fourth, toll fees requre that there exst some excluson mechansm that prevents nonmembers from usng the club good. III. General Theory of Clubs Buchanan (965) developed a general theory of clubs n order to brdge the gap between purely publc and purely prvate goods. In the case of pure prvate goods, consumpton by one ndvdual automatcally reduces the consumpton level of another

7 Smth 6 ndvdual. For pure publc goods, however, there s non-rvalry n consumpton of goods and so goods may be used smultaneously wth no effect on competng consumers. Whle pure publc goods can serve an nfnte number of consumers and pure prvate goods have only an ndvdual consumer, the typcal publc good usually falls somewhere between pure publc and prvate goods and wll have a fnte number of consumers greater than one. The central queston then becomes, what s the optmal number of consumers or the membershp margn, otherwse defned as the sze of the most desrable cost and consumpton sharng arrangement (Buchanan, 965, ). Usng neo-classcal models that consder the case of pure prvate consumpton only, the ndvdual utlty functon s wrtten, () U=U(X,X,,X n ) where each X represents the quanttes of pure prvate goods avalable to each ndvdual durng a specfed tme perod. Ths s then extended to nclude both pure publc and prvate goods, () U=U(X,X,,X n, X n+,x n+,,x n+m ) wth X n+,x n+,,x n+m representng the quantty of pure publc goods avalable to each ndvdual durng a specfed tme perod (Buchanan 965). Wth a non-pure good, however, an ndvdual s utlty s a functon of the number of other persons wth whom he must share ts benefts (Buchanan, 965, 3). Sharng here means that the ndvdual consumes a reduced quantty of the good. Consder a group of people sharng one har cut per month. Ths means that each person would receve /th harcut per month. Gven any quantty of fnal good, as defned n terms of the physcal unts of some standard qualty, the utlty that the

8 Smth 7 ndvdual receves from ths quantty wll be related functonally to the number of others wth whom he shares (Buchanan, 965, 3). The number of ndvduals who share the good, or club sze, s dsregarded n the study of pure prvate goods because the optmal level s unty. In the case of club goods, however, the club sze N wll need to be ncluded for each good. The club sze varable, N, therefore measures the number of persons who are to jon n the consumpton-utlzaton arrangements for good X over the relevant tme perod (Buchanan, 965, 4). Ths produces the rewrtten utlty functon, (3) U=U((X,N ),(X,N ),,(X n+m,n n+m )) From here, t s possble to derve the margnal condtons for Pareto optmalty. Frst, defne the producton functon as, (4) F=F ((X,N ),(X,N ),,(X n+m,n n+m )) The club-sze s a necessary part of ths functon because a relatonshp exsts between club-sze and cost and club-sze and quantty purchased. For example, a larger club-sze wll usually result n lower collected fees. As a negatve externalty, however, ths may result n reduced quantty of servce. A large golf club, for example, may mean t s more dffcult to schedule a tee tme (Buchanan, 965). The producton functon makes t possble to derve equatons for the necessary margnal condtons for Pareto optmalty wth respect to consumpton for two goods X j and X r. Because the margnal rate of substtuton for consumpton s equal to the margnal rate of substtuton for producton, (5) u j /u r =f j /f r and by ncorporatng club-sze, ths can be wrtten as,

9 Smth 8 (6) u Nj /u r =f Nj /f r Ths relatonshp says that equlbrum occurs when the margnal benefts of addng a new member to the club are equal to the margnal cost of addng a member to the club. We can then combne (5) and (6) to show, (7) u j /f j =u r /f r =u N /f N When (7) s satsfed, the ndvdual wll have an optmal quantty of X j and wll be optmally sharng ths good over a fnte group of ndvduals (Buchanan, 965). IV. Ng Model Begnnng wth Buchanan s equaton (6), Ng (973) beleves that the condtons obtaned are the equlbrum condtons for an ndvdual, gven hs market opportuntes and assumng he can choose hs preferred N j. [Therefore], for Pareto optmalty, we have to maxmze the utlty of an ndvdual, subject to the constrants that the level of utlty of each other ndvdual s held constant and that socety s producton possbltes are gven (Ng, 973, 9). Let there be s ndvduals, m collectve goods, and (n-m) prvate goods modeled by the followng utlty functon for each th ndvdual (N!) U U X, N, D,... X, N, D X,... X ) ( m m m, m where Xj and Nj represent the quantty of and the number of ndvduals consumng the n jth collectve good, X j s the amount of the jth prvate good consumed by the th ndvdual, and Dj= f ndvdual belongs to club j and 0 f not. Dvsblty n the quantty of all goods and contnuousness of Nj s also assumed (Ng, 973). The producton functon can then be wrtten

10 Smth 9 (N) F( X s,..., X m, X n ) 0 In order to derve the necessary condtons for Pareto optmalty, U must be maxmzed subject to the constrantu U (,..., s). Therefore, the Lagrangan functon can be wrtten, (N3) L U s ( U U ) F By takng the partal dervatves respectve to L the followng equaton are obtaned: (N4) s U Xj F ( j,..., m) (N5) F ( j m,..., n;,..., s) U Xj s (N6) U 0 ( j,..., m) Xj Next, by combnng equatons N4, N5, and N6 and usng X n as a numerare, (N7) s U Xj U Xn F Xj F Xn ( j,..., m) (N8) s U Xj U Xn 0 ( j,..., m) Utlzng the fact that U be wrtten as Xj U Nj 0 for ndvduals not consumng Xj, equaton N7 can (N9) Nj U Xj U Xn F Xj F Xn ( j,..., m) (N9 ) U Xj U Xn FXj FXn ( j,..., m) sj However, due to the fact that N j s a dscrete varable, t s more approprate to use

11 Smth 0 (N0) U j U Xn ( U k Nj U k Xn ) 0 f S ; 0 f S k whch can be wrtten n terms of the margnal rates of substtuton, (N0 ) 0 X j k k ( U Xj U Xn) dx j U Xj U Nn 0 f S j ; f S k Ths says that, for each collectve good, any ndvdual n the club must derve a total beneft from the consumpton of that good n excess of (or at least equal to) the aggregate margnal dsutlty mposed on all other consumers n the club (Ng, 973, 93). The reverse s also true for ndvduals not n the club. Equaton N9 says that aggregate margnal valuaton equals the margnal cost (ths s the Samuelson condton wth the excepton that the set of consumers does not need to equal the set of ndvduals n socety, or N j s. Ths dffers from Buchanan s analyss n that Buchanan s equlbrum equaton (6) s no longer necessary for Pareto optmalty. Ths s due to the fact that N j enters nto the utlty functon of a number of consumers smultaneously, and each consumer cannot vary at N j at wll. Hence the relevant condton for each N j s the aggregate margnal valuaton rather than the ndvdual margnal valuaton (Ng, 973, 93). V. Turner Model Vstors makng use of natonal parks enjoy a varety of actvtes, ncludng: hkng, bkng, fshng, boatng, swmmng, cross-country skng, horseback rdng, and n some parks snowmoblng. As the number of people makng use of park servces has rsen, park congeston has ncreased, dmnshng user benefts. Ths congeston creates a stuaton where natonal parks are not purely publc goods, but rather are club goods.

12 Smth Usng Glacer Natonal Park, Turner (000) developed a hypothetcal model for managng multple actvtes at a natonal park. In partcular, Turner s model consders entrance fees and other user fees (Turner, 000). Turner s analyss employs a varable-utlzaton mxed-club model. Ths method was chosen because the club (natonal parks) conssts of a group of members (park vstors) who have dverse tastes and therefore wll utlze the club dfferently. In ths case, the club s a sngle multproduct club wth unrestrcted membershp; the park s unque, t offers more than one actvty and admsson to the park s open to all (though there may be an entrance fee or other toll that some ndvduals choose not to pay) (Turner, 000, 475). In order to smplfy the model, vstors are restrcted to two actvtes, or two goods (Turner, 000). Turner defnes ndvdual utlty as a functon of a numerare good y, recreaton V, and wlderness W. Snce wlderness s a publc good, everyone consumes an equal amount. Therefore, an ndvdual s utlty can be wrtten as U=U(y,V,W). Recreatonal benefts can be defned by the number of vsts v and the ndex of enjoyment Φ. Therefore, V=vΦ. Now, let a and a be varables for the amount of tme spent engaged n each of the two actvtes. Next, let q j represent the qualty of the actvty such that for each ndvdual the qualty-adjusted amount of actvty j engaged n for each ndvdual s represented by α j =a j q j. Therefore, Φ=Φ(α,α ) represents the enjoyment per vst derved for each ndvdual (Turner, 000). Congeston, park sze, and wlderness wll affect vstor enjoyment, although to what degree depends upon vstor preferences. Therefore, qualty decreases by γ j for each addtonal unt of congeston and qualty ncreases n relaton to the sze of the park,

13 Smth Z, and wlderness area, W. None the less, t should be recognzed that an ncrease n wlderness area can ncrease congeston. Thus, qualty of actvty j by for each ndvdual s gven by q(γ j,z,w) (Turner, 000). Total congeston s a functon of the total amount of each actvty. Therefore, f A =Σva and A =Σva, then γ j (A,A,Z,W). Z and W are ncluded because the larger the sze of the park or the larger the wlderness area, the less lkely there wll be congeston cross-over effects that nterfere wth ndvdual enjoyment of the park. Smlarly, wlderness can be defned as a functon the two actvtes and park sze, or W=W(A,A,Z) (Turner, 000). Effcency Condtons The socally effcent allocaton of resources can then by found by maxmzng the Benthamte socal welfare functon ΣU wth respect to the resource constrant E Σy+Στv+C(Z,A,A ) where E s socety s endowment of the numerare, τ s each ndvdual s travel cost, and C( ) s the cost functon for the park. Therefore, the Lagrangan for the constraned optmzaton problem s: (T) L= ΣU(y,V,W)+μ(E- Σy+Στv+C(Z,A,A )) Where V= vφ(a q (γ (A,A,Z,W),Z,W),a q (γ (A,A,Z,W),Z,W)); A j =Σva j for j=,; W=W(A,A,Z) and μ s the Lagrangan multpler. The park manager/planner then chooses y, v, a, and a for each ndvdual and also chooses Z. Frst order condtons can then be manpulated to yeld,

14 Smth 3 (T) MRS ( C Vy ( P W A ) a A A W W ( C A )( W W A ) a A A a W A a ) (T3) (T4) MRS MRS Vy Vy q q C A ) a ( PW W )( WA a) A A W W C A ( PW W )( WA a ) A A W W (T5) Z ( PW W )( WZ ) C Z Z W W Z where MRS represents the margnal rate of substtuton; q j (T6) j MRSVyv a j j, j j whch represents the aggregate costs to vstors caused by margnal ncreases n congeston due to actvtes and ; P W =Σ j MRS Wy s a Samuelson summaton of margnal rates of substtuton. P W measures the aggregate beneft to socety of an ncrease n W. ε Z and ε W show the effect of park sze and wlderness on vstor enjoyment. Expresson T5 s the provsonal condton whereby the park s sze should by enlarged untl margnal socal beneft s greater than margnal socal cost. Havng a larger park s benefcal because t decreases congeston, ncreases wlderness, and thus leads to potentally greater rates of vstor enjoyment. Expressons T thru T4, represent toll (user fee) condtons (Turner, 000). Utlty Maxmzaton for Indvduals An ndvdual maxmzes utlty subject to the constrant that consumpton of the numerare plus the cost of vstaton, whch ncludes travel costs as well as a park

15 Smth 4 entrance fee F and tolls t for each actvty, must not exceed the ndvdual s endowment of the numerare E (Turner, 000, 477). The Lagrangan can be wrtten, (T7) L=U(y,vΦ(a q,a q ),W+λ(E-y-(τ+F-t a -t a )v) where varables y, v, a, and a are choce varables and λ s the Lagrange multpler. Assumng people do not consder congeston a deterrent to vstng the park yelds a set of frst order condtons whch can be manpulated to gve, (T8) MRS Vy = τ+f+t a +t a (T9) MRS Vy q =t and (T0) MRS Vy q =t Interpretaton of Toll Condtons Usng the ndvdual s optmzaton condtons T9 and T0, T3 and T4 mples that the planner can nfluence ndvduals to make socally effcent choces by mplementng a toll equal to (T) t j C Aj A j A j ) a ( PW W )( WA a ) j W W j where the frst term s the partal dervatve of the cost functon wth regard to each actvty, the second and thrd terms represent the ncreased tolls n response to an ncrease n congeston due to ncreased consumers for actvtes and, and the last term represents the ncrease n tolls as a result of dmnshng wlderness as a result of ncreased congeston. Whle the toll for each of the two actvtes should be dfferent, each ndvdual should pay the same toll. Some ndvduals may pay more because they consume a greater amount (Turner, 000).

16 Smth 5 These tolls should help to nternalze two types of externaltes. Frst, as congeston ncreases, tolls wll ncrease. Second, assumng the vstor actvtes reduce wlderness levels, ths wll rase tolls. Effcent actvty tolls wll mean that the resultng effcent entrance fee, F, s zero (Turner, 000). VI. Prato Model Conventonal defntons of carryng capacty were defned by the number of vstors an area can sustan wthout degradng natural resources and vstor experences (Prato, 00, 3). New defntons of carryng capacty, however, defne carryng capacty as the acceptablty of natural resources and human mpacts as measured by selected bophyscal resource and socal condtons, rather than the number of vstors (Prato, 00, 3). And whle much progress has been made n determnng carryng capacty, much of the prevous work has been non-quantatve, thus makng t dffcult for park managers to provde quanttatve proof that ther park s meetng establshed standards for bophyscal and socal carryng capacty (Prato, 00). Prato s model conssts of an ex post adaptve ecosystem management (AEM) model and the ex ante multple attrbute scorng test of capacty (MASTEC) method. The AEM model determnes whether the current state of an ecosystem s complant wth bophyscal and socal carryng capactes [by ncorporatng] adaptve management and ecosystem management prncples [that are] mplemented usng Bayes rule (Prato, 00, 3). The MASTEC method dentfes the best management acton for brngng an ncomplant ecosystem nto complance [by utlzng] a stochastc multple attrbute programmng model (Prato, 00, 3).

17 Smth 6 AEM Model To begn, assume each unt of the Natonal Park Servce falls nto one of four categores after evaluatng the unt s complance wth polcy concernng carng capacty: M, M, M 3, or M 4, where M s hghly complant, M s moderately complant, M 3 moderately ncomplant, and M 4 s hghly ncomplant. The pror probabltes are then p(m ), p(m ), p(m 3 ), and p(m 4 ) whch sum to one. Next, let R, R, R 3, and R 4 represent the characterstcs of a unt s resource/socal condtons. For example, let the percentage of natve speces and sutable endangered speces habtats represent the resource attrbute and let the level of congeston and wat-tme for publc transportaton n the park be the socal attrbute. R n ths case represents a sgnfcant loss n natve speces, hghly degraded endangered speces habtats, hgh levels of congeston, and very long wat-tmes for publc transportaton. R unts wll have moderate loss n natve speces, moderately degraded endangered speces habtats, moderately hgh levels of congeston, and long wat-tmes for publc transportaton. R 3 unts wll have most natve speces present, good habtat areas for endangered speces, low congeston, and short wat-tmes for publc transportaton. R 4 unts have abundant natve speces, excellent habtats for endangered speces, very lttle congeston, and very short wattmes for publc transportaton (Prato, 00). The AEM model uses Bayes rule n order to mnmze errors due to park managers msdentfyng the unt s carryng capacty. There are two types of errors that commonly occur. The frst occurs when the park manager dentfes a unt as beng complant wth carryng capacty condtons when t s not. The second occurs when the park manager decdes the unt s ncomplant wth carryng capacty condtons because

18 Smth 7 of resource/socal condtons when the park s actually complant wth carryng capacty condtons (Prato, 00). Usng the AEM model, (M R q ) s the outcome of a unt s carryng capacty and resource/socal condton where =,, I and q=,, Q, thus resultng n IQ possble outcomes. Pror probabltes of resource socal condton R q (outcomes are mutually exclusve) s, (P) p(r q )=p(m,r q )+ +p(m I R q ) where p(m R q ) s the jont probablty of (M R q ) (Prato, 00, 34). Bayes rule defnes the probablty that the ecosystem s n state M, gven the condton R q, s: (P) p(m R q )=p(m R q )/p(r q )=[p(r q M )p(m )]/[Σp(R q M )p(m )] where p(m R q ) s the posteror probablty, p(r q M ) s the lkelhood functon for R q, p(m ) s the pror probablty of M, and Σp(R q M )p(m ) s the expected value of the lkelhood functon (Prato, 00, 34). MASTEC Method If the AEM model ndcates that the unt s most lkely R 3 or R 4, than there s no need for the park manager to makes changes. However, f the AEM model ndcates that the unt s R or R the MASTEC method can be used to acheve a complant ecosystem state. The MASTEC method s an ex ante procedure [that helps] the manager select the best management acton for achevng complance wth carryng capactes (Prato, 00, 34). The MASTEC method ntegrates the Lmts of Acceptable Change and Vstor Impact Management carryng capacty methods. The Lmts of Acceptable Change method requres a manager to dentfy where and to what extent, changes n key bophyscal and socal processes are approprate and acceptable,

19 Smth 8 and to select a management acton that s most lkely to acheve conformance between observed condtons and establshed standards (Prato, 00, 34). A schematc of the MASTEC method s gven below n Fgure (Prato, 00, 35), Fgure Select Alternatve Management Actons Choose Attrbutes of Management Actons Choose Utlty Functon Determne Attrbute Weghts Establsh Carryng Capacty Constrants for all Attrbutes Determne Attrbute Values for Alternatve Management Actons Select Best Management Acton The best result for management wll maxmze the expected utlty functon E[U(z)] subject to the constrant z=a+e where z s a stochastc vector of attrbutes provded by a management acton, a s the determnstc component of z, whch gves the expected amounts of all attrbutes provded by the management acton, and e s the stochastc component of z, where E(e)=0 (Prato, 00, 33). By solvng the followng chance-constraned mathematcal programmng problem, management wll fnd the best soluton: Maxmze E[U(z*)]= E[U(a*+e*)] subject to:pr{ b * b ** } -α j for j=,,j, and Pr{ s * s ** } -β k for k=,,k k k j j

20 Smth 9 where * ndcates normalzed attrbute values. Ths s done to reduce management rankng bas created by dfferences n measurement unts and to convert negatve attrbutes (attrbutes that are negatvely related to utlty) to postve attrbutes. Thus, rather than less of an attrbute ncreasng utlty, more of an attrbute ncreases utlty. The normalzed attrbute falls between [0,]. The bophyscal attrbutes b j * are at least as great as the bophyscal standard b j ** wth relablty -α j where 0< α j < for all j bophyscal attrbutes. Smlarly, socal attrbutes s k * are at least as great as the socal standards s k ** wth relablty -β k where 0< β k < for all K socal attrbutes (Prato, 00). Specfyng that E[U(z*)] s addtve, meanng * * E[U(z*)]= E[ U( z )]... E[ UV ( zj K)], mples that the margnal utltes of each of the attrbutes are ndependent. Assumng the manager s rsk neutral, the expected utlty functon s, E[U(z*)]= J K wjb * jv wk s * kv j k where w j and w k are the weghts for the j th bophyscal attrbute and the k th socal attrbute, 0< w j <, 0< w k <, and J K w w k. If the manager has constant rsk averson, then j j k E[U(z*)]= J j j j j j K w [ a c ] w [ a c ] ; and f the manager has varable rsk k k k k k averson and the utlty subfunctons, U( z * ), then E[U(z*)]= J j j j j j K w [ U( a ) c ] w [ U( a ) c ] wth expected values a j and a k, k k k k k varances j and k, and postve scalng constants c j and c k (Prato, 00).

21 Smth 0 Usng a multple attrbute decson-makng framework to mplement the MASTEC method has the advantage of allowng more complex nformaton concernng management decsons to be collapsed nto a sngle number, t permts stakeholders wth dfferent attrbutes and/or values to rank and select management actons, t allows managers to dentfy the best method for complyng wth carryng capacty standards, and allows managers to evaluate the senstvty of a management acton to changes n attrbute weghts and values (Prato, 00). VII. Analyss and Evaluaton of the Four Models The ntal framework provded by Buchanan has served as a benchmark/pont of departure for each of the subsequent models. Ng s model s a modfcaton of Buchanan s that utlzes aggregate consumer margnal valuaton rather than ndvdual consumer margnal valuaton. Turner makes the choce to rewrte Buchanon s utlty functon n terms of a Benthamte socal welfare functon usng a numerare good, recreaton, and wlderness area. Turner then rewrtes the constrant n terms of socety s valuaton of the numerare, travel costs, and the cost functon of the park. In contrast, whle the prevously mentoned authors make use of the Lagrange method to maxmze utlty subject to a constrant, Prato takes a dfferent route by employng the more technology based MASTEC method. Whle Buchanan s and Ng s models help to formulate a model for general club goods, Turner and Prato s models specfcally focus on applcatons concernng natonal parks. Because these models have yet to be mplemented t s mportant that the models are evaluated and ther weaknesses addressed.

22 Smth Turner Turner s (000) model has several mplementaton problems. Frst, Turner s model uses ε Z and ε W to measure the mpact of wlderness area and park sze on vstor enjoyment. The potental problem wth ths s that both of these measures are nelastc. A park manager typcally does not have the opton of expandng the park when congeston levels are hgh. Nor does the park manager have the ablty to expand the number of trees n a short tme frame. Ths was one of the orgnal arguments gven by Wesbrod (964) concernng the dffculty n storng or quckly replacng lost resources. Data collecton s partcularly dffcult n regards to usng Turner s (000) model to estmate carryng capacty. Currently, the approprate data are not beng collected to use ths model. Turner s model requres the collecton of data concernng the levels of congeston for varous park actvtes and wlderness levels. Data also needs to be collected regardng park costs, vstor enjoyment, and publc valuaton of park servces. Further dffcultes exst n regard to formulatng an effectve survey, whch s often a dffcult and costly task that can result n based conclusons. Prato Whle Prato s (00) model may be the most dffcult to mplement, t may also prove to be the most useful. The most dffcult task s the development of a spatal decson support tool. The development of ths tool would provde numerous benefts to park management. Frst, t would make t easer to acqure and analyze techncal nformaton and publc nput. Second, the publc would become more nformed about the consequences of management decsons. The development of ths tool would enhance the manager s and publc s understandng of how dfferent attrbute weghts,

23 Smth attrbute standards and relablty levels for achevng standards nfluence the selecton of the best management acton (Prato 00, 39). The development of ths tool would also provde an analytc method for determnng park managers decsons. Fnally, ths tool would also help to allevate conflct and create a database that would be useful for solctng other fundng opportuntes. The aforementoned benefts of Prato s model not wthstandng, major mpedments to mplementng Prato s (00) model nclude budgetary restrctons, a lack of techncal expertse, hgh turnover of park management, and the long tme-frame requred to mplement the AEM model, although some of the budgetary problems may be overcome by solctng grant money. VIII. Concludng Remarks A szable weakness of each of the models s the assumpton that t s possble to exclude ndvduals who are not able and/or wllng to be a part of the club. Ths ncludes both the drect volatons as a result of vstors subvertng park rules by makng use of the park s servces wthout payng a fee and more ndrect volatons. For example, non-users beneft from the mantenance of natonal park areas regardless of whether they choose to make use of the park. Some of these benefts nclude cleaner ar, hgher property values, scenc vstas, and preservaton of wldlfe. So long as the possblty exsts for park users to make use of park servces wthout payng the assocated fees, there wll be a percentage of consumers who wll take advantage of the stuaton. Ths problem s further compounded by the dffculty and expense ncurred n montorng and fnng these free rders.

24 Smth 3 The ablty to dentfy carryng capacty thresholds s also a dffcult task for park managers. An ndvdual s percepton of envronmental damage s often a subjectve measure and therefore makes dentfyng a threshold level of damage extremely dffcult. Some would measure ths threshold as the pont where damage becomes notceable to consumers. At ths pont, demand for the good falls sharply and so the manager mght see carryng capacty as a functon of the number of vstors. Ths s not necessarly a consstent value, however, due to the fact that ncreased educaton and better management may lead to ncreased carryng capacty for the park (Davs, 00). Another concern s the transformaton of natonal parks nto a knd of amusement park. If actvtes fees are used, how wll ths change the way the park looks? How wll t change consumers experences? Do we charge hkers for each mle walked or do we restrct actvty fees to actvtes such as tours, boatng, etc.? These are all ssues that would need to be addressed by the park manager f user fees were mplemented. Fnally, any model ncorporatng a toll or user fee creates an ethcal dlemma regardng the excluson of the poor from publc property. When one consders that there are few places for low-ncome famles to enjoy recreatonal actvtes, some would argue that chargng fees potentally excludes low-ncome famles from a publc good. Addtonally, natonal parks are already subsdzed by federal dollars that are the result of taxaton. Ths means that some ndvduals may be payng for a good they are unable to use. Ths also rases a queston regardng whether ndvdual consumers of parks or all ndvduals who pay taxes should be responsble for mantanng park facltes.

25 Smth 4 Ultmately, a decson wll need to be made n regard to the mplementaton of user fees; s the goal to reduce subsdzaton, reduce congeston, or both?

26 Smth 5 References Buchanan, James M. (965). An Economc Theory of Clubs. Economca, 3(5): -4. Cornes, Rchard and Sandler, Todd (996). The Theory of Externaltes, Publc Goods and Club Goods. Cambrdge Unversty Press, New York, NY: Davs, Derrn and Tsdell, Clem (00). Recreatonal Scuba-Dvng and Carryng Capacty n Marne Protected Areas. Ocean & Coastal Management, 6(): Ng, Yew-Kwang (973). The Economc Theory of Clubs: Pareto Optmalty Condtons. Economca, 40(59): Prato, Tony (00). Modelng Carryng Capacty for Natonal Parks. Economcs, 39(3): Ecologcal Turner, Robert W. (000). Managng Multple Actvtes n a Natonal Park. Economcs, 76(3): Land Wesbrod, Burton (964). Collectve-Consumpton Servces of Indvdual- Consumpton Goods. The Quarterly Journal of Economcs, 78(3):