Welfare and Biodiversity Tradeoffs in Urban Open Space Protection

Transcription

1 Welfre nd Biodiversity Trdeoffs in Urbn Open Spe Protetion Liil Tibev Deprtment of Applied Eonomis University of Minnesot St. Pul, MN Emil: Robert G. Hight USDA Forest Servie, Northern Reserh Sttion 992 Folwell Ave. St. Pul, MN Emil: Stephen Polsky Deprtment of Applied Eonomis University of Minnesot St. Pul, MN Emil: Seleted Pper prepred for presenttion t the Agriulturl & Applied Eonomis Assoition s 204 AAEA Annul Meeting, Minnepolis, MN, uly 27-29, 204. Copyright 204 by L. Tibev, R. Hight, nd S. Polsky. All rights reserved. Reders my mke verbtim opies of this doument for non-ommeril purposes by ny mens, provided this opyright notie ppers on ll suh opies.

2 Abstrt: In this pper, we nlyze the optiml sptil pttern of open spe nd residentil development in n urbn model tht inludes provision of both lol nd globl publi goods. In our model, households hoose where to live bsed on lnd pries, proximity to employment, nd menity vlues tht inlude ess to open spe (lol publi good). Open spe lso provides hbitt for biodiversity (globl publi good). We pplied the model in the Twin Cities Metropolitn Are nd inlude endogenous lnd pries, lnd txes tht finne the purhse of open spe, heterogeneous lnd qulity, multiple employment lotions, nd pre-existing sptil fetures, suh s institutionl nd environmentl menities. Bsed on this pplition we develop n effiieny frontier tht shows trdeoffs between mximum welfre of households, whih inludes provision of lol publi goods, nd provision of hbitt for biodiversity, whih is ssumed to not ffet household welfre. We show there is the potentil for lrge inrese in biodiversity onservtion with only modest redutions in welfre when strting from sptil pttern of development tht mximizes household welfre. Biodiversity onservtion n be improved by hnging the sptil onfigurtion of open spe towrds higher qulity hbitt nd ggregting proteted res to inrese ontiguity. 2

3 . Introdution More thn eighty perent of the U.S. popultion lives in urbn res (U.S. Census 2009), nd in mny of those res the rtes of lnd onversion from open spe to developed uses fr exeed rtes of popultion growth (Fulton et l. 200). Between 982 nd 997, the mount of urbnized lnd in the U.S. inresed by 47 perent, from pproximtely 5 million res in 982 to pproximtely 76 million res in 997. During this sme period, the ntion s popultion grew by only 7 perent (Fulton et l. 200). Two onsequenes of lnd onversion from inresed development re the lol nd globl loss of vluble eosystem servies from open spe. Open spe provides benefits to lol residents in the form of estheti menities, reretionl opportunities, filtrtion of pollution tht my improve wter nd ir qulity, mong others. Open spe lso provides benefits tht rue more brodly (ntionlly or globlly) suh s rbon sequestrtion nd hbitt for biodiversity. Empiril evidene from hedoni property prie models hs shown tht urbn residents vlue nerby open spe (Geoghgen 2002, Hobden et l. 2004, Irwin 2002, Lutzenhiser nd Netuil 200, Mhn et l. 2000, Thorsnes 2002, Tyrvinen nd Miettinen 2000, Wu et l. 2004). Hedoni property prie studies in the Twin Cities Metropolitn Are in Minnesot hve found positive vlues of open spe on nerby property vlues, with few exeptions. Snder nd Polsky (2009) found tht home sle pries inresed with loser proximity to prks, trils, lkes, nd strems. Home sle pries lso inresed with the rel extent of views nd the mount of wter nd grssy lnd overs in views. Both Anderson nd West (2006) nd Kliber nd Phneuf (200) found positive vlue of open spe on property vlues on verge, though eh found onsiderble heterogeneity of effets depending on type of open spe nd neighborhood ontext. Doss nd Tff (996) found strong positive effets on property vlues from hving view of lke, s well s being in loser proximity to lkes nd some types of wetlnds (though not forested wetlnds). Finlly, Snder et l. (200) found n inrese in property vlues from n inrese in neighborhood tree over. Conerns of lol itizens bout loss of open spe nd the lol menities they provide hs led stte nd lol governments to rise publi funds in support of lnd onservtion (Kothen nd Powers 2006, Nelson et l. 2007, Ruliffson et l. 2002). Sine 996, stte nd lol governments pssed n verge of 9 bllot mesures per yer rising n verge of $2.2 billion dollrs to quire nd protet open spe (Trust for Publi Lnd 204). Loss of open spe n lso led to the loss of eosystem servies with more widespred benefits inluding loss of rbon sequestrtion, nd the loss of hbitt tht supports biodiversity. Ewing et l. (2005) found tht 60% of the ntion s rrest nd most imperiled speies re found within designted metropolitn res (p. viii) with mny endngered speies loted in rpidly urbnizing res experiening the gretest loss of open spe. Under the U.S. Endngered Speies At, development n be urtiled if it would use hbitt loss tht would hrm listed speies. Conflits between development nd endngered speies onservtion hve ourred in the Sn Frniso By Are over the Mission Blue Butterfly (Betley 992), in Ornge County ust south of Los Angeles over the Cliforni gntther (Zink et l. 2000), est of Los Angeles in Sn Berndino County over the Cohell Vlley fringe-toed lizrd (Betley 992), ner Austin, Texs over the blk-pped vireo nd other speies (Tylor 994), mong others. Conerns bout the loss of eosystem servies with ntionl or globl benefits, suh s the loss of hbitt nd hrm to endngered speies, my or my not lign with welfre onsidertions of lol 3

4 residents. For exmple, restritions on development to onserve endngered speies, might led to redutions in ggregte lol welfre, both in terms of limits on development nd the pttern or open spe nd the menities it provides to lol residents (Innes et l. 998, List et l. 2006). Mking good deisions bout urbn lnd use requires onsidertion on how lnd use ffets the provision of both lol publi goods s well s provision of more globl publi goods. The weight pled on eh of these different types of publi goods will ffet the optiml lnd use within n urbn re, where the weight represents the reltive importne of lol versus globl publi goods. We ddress the optiml mount nd lotion of open spe in n urbn re tking ount of the provision of lol nd globl publi goods nd estimte the potentil trdeoffs between lol publi gols tht ffet household welfre nd globl publi goods relted to biodiversity protetion. To do this we nlyze disrete spe urbn model with endogenous hoie of the lotion of open spe nd development. Households hoose neighborhood of their residene bsed on its proximity to employment opportunities, proximity to open spe, nd the size of housing plot nd onsumption tht they n fford given their inome nd rel estte pries in tht neighborhood. Inresing the mount of open spe inreses environmentl menities but lso onstrits the mount of lnd vilble for housing. We nlyze n open ity model where popultion dusts in wy to keep household utility onstnt. Though household utility is onstnt, rel estte pries re not. Lnd rents re determined endogenously in the model nd rise nd fll with the overll ttrtiveness of the ity. In the model, expenditures on housing re ptured in the household s hoie problem but we do not pture lnd rents. Assuming tht lnd rents rue to some individuls in soiety then mximizing welfre is equivlent to mximizing lnd rents in n open ity model. We nlyze the optiml mount nd lotion of open spe given the dul obetive of mximizing welfre s well s biodiversity onservtion. This mximiztion is onstrined by lnd vilbility nd property tx revenue, whih finnes provision of open spe. Biodiversity onservtion is funtion of heterogeneous qulity, sptil proximity, nd size of nturl res proteted s open spe. We show how the optiml pttern of open spe nd development vries with different weights on open spe menity vlues nd biodiversity onservtion. Solving the model for different weights illustrtes the trdeoffs between household utility nd onservtion obetives. The existing literture in urbn nd environmentl eonomis hs not ddressed the question of the optiml provision of open spe with dul obetives of mximizing household welfre nd biodiversity onservtion. Severl studies hve nlyzed the equilibrium effets of speifi open spe onfigurtions using struturl eonomi models of household lotion hoie (see Irwin et l. 2009, Irwin 200 for reviews). Most of these models extend the urbn eonomis models developed by Alonso (964), Mills (967, 972), nd Muth (969) nd inlude n exogenously determined entrl business distrit (CBD), popultion of households with identil inomes nd preferenes, trvel osts tht depend on the distne between residene nd CBD, nd household utility tht depends in prt on proximity to open spe menities. Two-dimensionl urbn models with pre-determined lotions of open spe hve been nlyzed to determine the lotion of ity boundries nd onditions tht led to sprwl (i.e., res of development tht re disoint from the existing developed res) (Wu nd Plnting 2003, Wu 2006). These models show tht publi open spe my use lepfrog development when pled outside the ity nd trvel ost to the CBD is suffiiently low. Further, open spe provision n inrese or derese the ity s popultion nd re depending on the size nd lotion of the open spe. For instne, if reltively lrge open spe with low menity vlue is loted ner the CBD, it n redue the ity s popultion by eliminting desirble sites for development (Wu nd Plnting 2003). Finlly, if the menity benefit of n open spe prel is 4

5 enoyed by households throughout the ity in ddition to households lose by, then ity size, lnd rent, nd household welfre re ll greter (Kovs nd Lrson 2007). While nlyses of urbn models provide insight into the effets of speifi open spe onfigurtions, most of those studies do not ddress questions bout the optiml provision of open spe. Lee nd Fuit (997) nlyze the effets of greenbelts tht form ring of open spe round the entrl business distrit nd determine the optiml plement of greenbelt. Yng nd Fuit (983) solve for the optiml pttern of open spe in one-dimensionl formultion nd show tht the optiml density of open spe is uniform proportion of re independent of distne from the CBD when environmentl menities re purely lol (i.e., no menity spillover effets). They briefly onsider the se with menity spillover in one-dimensionl disrete-spe model with five neighborhoods. Tibev et l. (2008) use disrete-spe urbn model bsed on Yng nd Fuit (983) to determine the optiml pttern of open spe, housing, nd lnd vlue given relisti fetures suh s multiple business enters, existing open spe menities, nd menity vlues of griulturl lnd. In ontrst to ontinuous-spe urbn models, the disrete-spe model ssumes distint neighborhoods in whih developble lnd is homogeneous within neighborhood but heterogeneous ross neighborhoods. Open spe provides environmentl menities within the neighborhood it is loted nd my provide menities in other neighborhoods (menity spillover). The presene of menity spillover hs strong effet on the results. When open spe is lol publi good tht ffets only the immedite neighborhood, it is optiml to provide the sme mount of open spe in ll neighborhoods. With menity spillover effets, optiml open spe provision differs ross neighborhoods, depending on the trnsporttion ost. With high trnsporttion ost, it is optiml to provide open spe in greenbelt t the edge of the ity with housing onentrted ner the ity enter. Lnd use ptterns lso determine hbitt provision for biodiversity. The field of onservtion plnning hs developed sptil metris of biodiversity onservtion nd omputtionl tools to determine reserve designs tht mximize those metris (see Moilnen et l nd Billionnet 203 for reviews). For exmple, site seletion models hve been developed to mximize speies representtion within reserves (Cmm et l. 996, Churh et l. 996), ount for probbilisti speies ourrene (Hight et l. 2000, Cmm et l. 2002), nd ount for speies hbitt preferenes, re requirements, nd dispersl bilities (Polsky et l. 2008), subet to eonomi onstrints relted to site purhse nd mngement. Although site seletion models re beginning to inlude endogenous effets of lnd protetion on development, lnd pries, nd subsequent protetion osts (Armsworth et l. 2006, Toth et l. 20, Dissnyke nd Onl 20, Butsi et l. 203), none ount for the effets of open spe on household lotion hoie nd welfre. We pply our model to nlyze the effets of vrious ptterns of open spe on both welfre nd biodiversity using dt from the Twin Cities Metropolitn Are. When the gol is to mximize welfre (i.e., mximize the vlue of lnd rents in the ity), the optiml provision of open spe is hevily skewed towrds the urbn boundry nerly forming ring round the ity. When the gol slightly shifts to mximizing biodiversity, the optiml lotion of open spe beomes more lustered nd shifts wy from the urbn boundry nd towrds res with higher hbitt qulity or loser to existing prks. Our results suggest tht proteting open spe to ttin biodiversity onservtion hs reltively little impt on household welfre. However, even minor shifting of optimiztion priorities from mximizing lnd rents to mximizing the effetive hbitt ontinuity results in very different optiml lndspe ptterns. 5

6 The pper is orgnized s follows. In Setion 2, we develop disrete-spe urbn model of optiml provision of open spe. Setion 3 desribes the eonomi nd lnd-use dt from the Twin Cities Metropolitn Are (Minnepolis St. Pul, MN, USA) nd prmeterizes the model. Setion 4 solves the model numerilly to nlyze how different priorities between the eonomi nd biodiversity obetives ffet the optiml size nd lotion of open spe, household welfre, biodiversity onservtion, nd sptil pttern of residentil development nd lnd vlues. We inlude onluding omments in Setion The model We onsider disrete spe ity tht onsists of neighborhoods. Neighborhoods ontin lnd tht n be lloted to residentil development or open spe. In ddition, neighborhoods lso ontin preexisting ommeril nd industril development s well s nturl nd institutionl menities. Let l be the totl re vilble for residentil nd open spe lnd use in neighborhood. Eh household hooses neighborhood in whih to reside. Three min ftors determine hoie over neighborhoods. The first ftor is the mount of onsumption good,, nd the mount of residentil lnd, h, tht household n fford while residing in neighborhood. The ffordbility is ffeted by housing prie in neighborhood, whih is denoted by p, property tx τ levied by the government on residentil lnd, nd household's inome v. The prie of the onsumption good is normlized to one. The seond ftor is the ommuting ost between the neighborhood of residene nd the nerest employment lotion b. Neighborhoods with ommeril lnd use provide employment opportunities. Beuse different neighborhoods throughout the ity use lnd for ommeril purposes, there exist multiple employment lotions b =, 2,, B. Let d B min d be the ommuting distne from b b neighborhood to the nerest employment lotion b. Then the ost of ommuting to nd from work is f. d funtion of distne The third ftor is the environmentl nd institutionl menities in the neighborhood of residene s well s in the nerby neighborhoods. Let A denote ll menities ruing to households in neighborhood. A is funtion of open spe, nd distne k k zk, preexisting menities k d from the neighborhood of residene to the neighborhood of menities k, suh tht d k k k > 0 for ll k nd d k = 0 for k. The households hve identil inome v nd preferenes u, h ; A over onsumption, residentil lnd, nd menities. In the numeril pplition below we ssume the utility funtion to be Cobb- Dougls: (2.) u, h ; A h A, where,, 0,, α + β + γ =, nd Preexisting institutionl menities inlude, but re not limited to, existing religious, edutionl, soil, ulturl, governmentl, or mor helth re filities. 6

7 (2.2) A,..., k z zk exp d d k k Eqution (2.2) revised for proportion of re insted of totl re (2.2 proportion),, exp is the funtion of open spe nd preexisting menities deresing in distne where δ's re prmeters ssoited with menities nd distnes. For eh neighborhood, household mximizes its preferenes (2.) subet to its budget onstrint: (2.3) p h f d v, p where p is the mrket prie nd property tx τ levied on the residentil lnd use. We onsider the se of n open ity, where no rbitrge ross lotions holds for ll neighborhoods u, h, A for ll neighborhoods. In order for household to mintin utility level implying tht u u, household estblishes the mximum prie tht it is willing to py to reside in eh neighborhood. This mximum prie is the bid-rent funtion, given s: (2.4) F h, A,...,, u v h, A,...,, u f d, where h, A u is the inverse funtion of u h, A u, lndowners who ollet ll lnd rents. h,. For simpliity, we designte bsentee The ity government provides open spe by prtiipting in the lnd mrket. To finne its provision of open spe the government levies tx τ on residentil lnd use. The government hs blned budget nd equtes its open spe expenditure to tx revenue from residentil development (2.5) p l p. The ity government solves for the optiml provision of open spe,, residentil lnd use, h, nd number of households, n, in eh neighborhood for ll =,2,...,. In doing so, it onsiders both the eonomi omponents, suh s endogenous pries nd households' welfre, nd the biodiversity implitions. In the following we develop biodiversity sore nd then speify the problem of optiml provision of open spe. 2.. Biodiversity sore Our biodiversity sore is funtion of the size nd ggregtion of nturl res proteted s open spe. Let φ be n ggregtion sore bsed on the mount of proteted open spe nd its proximity to 7

8 other open spe in the region. Letting d k be the distne between neighborhoods nd k, the proximity sore for eh neighborhood is: k (2.6),..., exp d, k k where σ is non-negtive weight tthed to the distne between neighborhoods. The ggregtion sore for eh neighborhood disounts open spe tht is frther wy. In this se, neighborhoods with more open spe proteted lose by hve higher ggregtion sores. The effetive hbitt ontiguity sore is the sum of proteted res weighted by ggregtion sores: (2.7) B,..., Optiml provision of open spe The optiml provision of open spe,, residentil lnd, h, nd popultion density, n, for ll neighborhoods =,..., mximizes the weighted dul obetive of the bid-rent funtion net of opportunity ost of n lterntive lnd use pttern nd the effetive hbitt ontinuity sore: (2.8) h g g mx F h, A,...,,,..., u p n h p B,, n subet ton h l for ll,...,, where p g F h A u,, nd B() re s defined in equtions (2.4) nd (2.7) respetively. Reognizing tht ity plnners tth different priorities to the gols of mximizing household net benefit nd mximizing biodiversity onservtion, we onsider different weights from primrily eonomi onsidertions, of µ =, to primrily biologil onsidertions, of µ = 0, nd onstrut the entire spetrum of solutions for 0,. We then nlyze the resulting trdeoff in the optiml provision of open spe. is griulturl lnd prie nd funtions Sine the household's preferenes re stritly inresing in housing, the totl lnd onstrint holds with equlity nd we n substitute l - from the lnd onstrint into the obetive funtion for n h. After the substitution we n obtin the optiml housing llotion s funtion of menities, distne, nd utility level by mximizing the bid-rent funtion in eqution (2.4) over housing. With these two substitutions nd using the utility funtion from eqution (2.), the optimiztion problem (2.8) n be restted s follows: (2.9) mx A v d g l p l u is liner funtion for the ost of ommuting to work funtion (i.e., d where nd A is funtion of,..., s defined in eqution (2.2)., f in eqution 2.3) d 8

9 Tx onstrined optiml provision of open spe So fr we hve been onsidering the optiml provision of open spe onstrined by physil vilbility of spe. One the optiml open spe pttern * tht solves problem (2.8) is estblished, we n find orresponding ompetitive equilibrium prie for eh neighborhood (see Appendix A for derivtion of ompetitive equilibrium llotion nd pries): (2.0) d f v u A p,...,. Using this prie (2.0) nd the government s budget eqution (2.5), we n find the tx rte tht supports this optiml provision of open spe in ompetitive equilibrium. In prtie, muniipl government is onstrined not only by the physil vilbility of spe but lso by the publily eptble lnd tx. When there is n upper bound on the eptble tx rte, tx onstrined or seond best llotion of open spe ˆ solves the following problem: (2.) given, 0,,,...,,...,,,..., for ll subet to :,...,,,...,, mx,, g g n h p l p l h n B p h n p u A h F where p is the ompetitive equilibrium prie s funtion of,, in eqution (2.0). Substituting eqution (2.0) for pries into the government s budget eqution (2.5) s well s using the sme substitutions s when deriving eqution (2.9) we n restte onstrined optimiztion problem (2.) s follows: (2.2). subet to: mx g d f v A l d f v A l p l u d v A In the following setions we solve the model by pplying it to the se of the Twin Cities. We first prmeterize the model nd then nlyze the optiml onfigurtions of open spe nd residentil development nd the ssoited optiml lndspe ptterns nd welfre implitions 3. Dt nd prmeter vlues We pply our model of optiml provision of open spe to the seven-ounty metropolitn re surrounding Minnepolis nd St. Pul, Minnesot, USA, (Figure ). The study re is divided into 689 neighborhoods, where eh neighborhood is defined s n existing U.S. ensus blok vrying in size

10 from 0.2 km 2 to 222 km 2, overing totl of 7704 km 2. The lotion nd boundries of eh neighborhood re determined by their ltitude nd longitude oordintes. For eh neighborhood, we ssemble the re in existing ommeril development, prks, institutionl menities, wter, nd residentil nd undeveloped lnd (Tble ) using the 2000 Generlized Lnd Use dt set for the region (Metropolitn Counil 2007). Ares of existing ommeril development (462 km 2 ) re fixed t their urrent vlues. Ares of existing prks (660 km 2 ), institutionl menities (32 km 2 ), nd wter (500 km 2 ) re treted s menities nd re lso fixed t their urrent vlues. Preexisting menities for i w eh neighborhood onsist of prks, z, institutionl menities, z, nd open wter bodies, z, suh i w tht z z z z. In the numeril pplition we dd preexisting prks to new open spe to determine the open spe ggregtion sore, restting eqution (2.6) s,..., k zk exp d k. k Ares of existing residentil development (42 km 2 ) nd undeveloped lnd (4538 km 2 ) re ombined into one undeveloped lnd bse (5950 km 2 ) tht represents lnd vilble for residentil development or protetion s open spe. We identify two neighborhoods representing downtown Minnepolis nd St. Pul s employment enters (Figure ) nd ompute the vetor of the distnes between eh neighborhood nd the nerest downtown. We lso ompute the mtrix of distnes between eh neighborhood nd ll other neighborhoods in the ity. The biodiversity sore is bsed on the mount, heterogeneous qulity, nd ggregtion of proteted open spe. The Metropolitn Counil hs identified regionlly signifint nturl resoure res in the seven-ounty Twin Cities metropolitn region (Metropolitn Counil 2007). The nturl res over 892 km 2 (2% of 7704 km 2 ) nd inlude forest, grsslnd, nd wetlnd hbitt. Eh nturl re is rted s moderte, high, or outstnding qulity bsed on its size, shpe, over-type diversity nd dent lnd use. Throughout the study re, there re, 2, nd 670 km 2 of moderte, high, outstnding qulity nturl res. We overly the mps of nturl res nd ensus bloks nd ompute the totl nturl re overge by qulity lss in eh neighborhood. Nturl res our in 25 neighborhoods (3% of 689 bloks) nd over km 2 of those neighborhoods (Figure ). Within eh neighborhood, we ssume tht nturl res our only within the undeveloped lnd lss. To embody this heterogeneity of existing nd newly proteted open spe into the biodiversity sore (Eqs. 2.6 nd 2.7), let q =,,4 represent the qulity of open spe, where q = represents open spe tht is not designted s nturl re nd q = 2, 3, 4 represent nturl res with moderte, high, nd q outstnding qulities, respetively. Then,, for ll nd q is deision vrible for the re of q q neighborhood tht is proteted open spe of type q, where, the upper bound on the re of neighborhood tht n be proteted s open spe type q. Let ω q mesure the effetiveness of reting hbitt for biodiversity on lnd of qulity type q =,,4. Then, effetive hbitt re in neighborhood k is funtion of the re of existing prks z k nd re of newly proteted open spe of 4 q q different hbitt qulities: ( z k k ) q 2 k, where the re of existing prk, z p k, is open spe tht is not designted s nturl re (i.e., hbitt of qulity type ). We ssume tht the effetiveness prmeter ω q inreses with the qulity of nturl res: ω = 0., ω 2 = 0.6, ω 3 = 0.8, nd ω 4 =.0. The prmeter vlues of the optimiztion models re summrized in Tble 2. Annul household inome is $45,700 for Minnepolis St. Pul in 2009 (Bureu of Eonomi Anlysis, 200). We 0

11 librte the reservtion utility level to 0.2 to mth the Twin Cities urrent (2009) size of.4 million households. We bse the prie of griulturl lnd on the verge vlue of $6428 per h ($2602 per re). We ssume the onsumption, housing, nd menity shres in the utility funtion (2.) to be equl to 0.56, 0.36, nd 0.08, respetively. Annul trnsporttion ost for ommuting to work is $43 per km. To ompute nnul trnsporttion ost, we ssume trvel speed of 40 km/h, wge of $23.78 per h (hourly wge in Minnepolis St. Pul in 2009; Minnesot Deprtment of Employment nd Eonomi Development, 2009), fuel nd vehile mintenne osts of $0.20 per km, nd 520 one-wy ommutes per yer (5 round trips per week for 52 weeks). We ssume tht the distne prmeter in the menity funtion is equl to 0.0 so tht open spe in one neighborhood ontributes to the utility of people in surrounding neighborhoods t level tht deys slowly with distne. We perform sensitivity nlysis to determine the effets of inresing this distne dey prmeter from 0.0 to.0. The distne prmeter in the ggregtion sore of the biodiversity funtion is 0.0. We ssume tht existing menities enter the menity funtion in the sme fshion s open spe. 4. Results This setion disusses the min findings of this pper nd nlyzes optiml sptil onfigurtion of open spe nd residentil development. We find tht even minor shifting of optimiztion priorities from mximizing lnd rents to mximizing the biodiversity mesure results in very different optiml lndspe ptterns nd welfre implitions. 4.. Benhmrk se or lnd use urrently on the lndspe We strt with benhmrk se where open spe is limited to the existing prks nd no new lnd quisition designted s open spe. Given this existing open spe onfigurtion we solve for the mrket equilibrium pries, residentil development, nd popultion density with no property tx. This benhmrk se is illustrted in Figure 2. Higher housing densities nd lnd pries re onentrted ner downtown Minnepolis nd St. Pul nd dent to prks long the Mississippi River nd the lkes loted entrlly s well s in ounties West of Minnepolis nd North of St Pul. This residentil development solution throughout the ity fits losely with the tul residentil development urrently on the lndspe (Figure ). This mth of our model generted solution to tul sptil pttern lso reflets the menity vlues tht households ple on urbn open spe. The benhmrk biodiversity sore is normlized to 00 nd is bsed solely on existing prks nd wter bodies (Tble 3, olumn ). Net benefit per household, whih we define s the mximum willingness to py net of opportunity ost, is equl to $8,568 (equl to totl net benefit of $2.23 billion divided by.4 million households) Mximizing lnd rents Given the benhmrk se desribed bove, we now introdue property tx levied on residentil lnd use. Tx revenue finnes quisition of new open spe. The pttern of new open spe nd residentil development s well s optiml txtion depend on the muniipl obetives tht rnge from primrily mximizing lnd rents to primrily mximizing biodiversity nd nywhere on the obetives spetrum between these two extremes. First, onsider the se when the primry gol is to mximize lnd rents. In this se, we find tht the optiml onfigurtion of open spe is hevily skewed towrds the urbn boundry nerly forming ring round the ity (Figure 3, row ). This result is onsistent with erlier findings by Yng nd Fuit (983) nd Tibev et l (2008). Lrge res of lnd in the

12 peripherl neighborhoods with the lowest property vlues nd loted furthest from the employment enters re designted s new open spe while high density housing is onentrted ner downtown Minnepolis nd St. Pul. Compred to the benhmrk se, the mount of open spe nerly doubles, dding 53 km 2 of newly proteted open spe to the lredy existing 660 km 2 in prks. Of these totl new quisitions 4% of new open spe is loted on Regionlly Signifint Nturl Ares with higher lnd qulity. As result, the biodiversity sore doubles to 209 ompred to the benhmrk se of 00 (Tble 3, olumn 2). In this se the optiml property tx is 6%. Beuse of the inrese in menities ssoited with new open spe, the ity beomes more ttrtive nd the number of households inreses slightly from.4 to.5 million. While new open spe pulls more people into the ity, it lso restrits the mount of lnd vilble for residentil development. As result, the inresed popultion density long with higher pries serve s push effet. Despite the introdution of 6% tx the net benefit per household inreses by % ompred to the benhmrk se with no property tx nd no new open spe. It ppers tht the optiml expnsion of open spe in the urbn re more thn ompenstes the introdution of optiml txes, higher popultion density, nd higher pries Wht if biodiversity mtters: shifting priorities towrd biodiversity mximiztion while keeping txes fixed So fr we disussed the se when the primry obetive ws to mximize lnd rents. In this setion we expnd our nlysis by putting more emphsis on biodiversity mximiztion. Shifting optimiztion priority wy from lnd rent nd towrds the biodiversity obetive hnges the size, lotion, nd qulity of new open spe (Figure 3). The lotion of new open spe shifts wy from the periphery to neighborhoods tht hve higher hbitt qulity nd re loser to existing prks nd the ity enters. Compred to the se of mximizing lnd rents, the totl re of new open spe dereses but is more lustered. For exmple, shifting the priority towrds biodiversity preservtion from μ = 0.99 to μ = 0.90 dereses protetion of low qulity res by 30% from 30 km 2 to 0 km 2 nd inreses protetion of the outstnding nturl res by 70% from 52 km 2 to 258 km 2 (Tble 3). As result, the biodiversity sore more thn doubles ompred to the mximizing lnd rents se inresing from 209 to 47 nd qudruples ompred to the benhmrk se with no txes. Beuse higher qulity nturl res re loted in neighborhoods with higher property vlues, the improvement in biodiversity omes t the expense of.07% net loss of the lnd rent inome (from $2.55 to $2.32 billion) nd 43% redution of the totl proteted re (from 53 km 2 to 29 km 2 ). The lnd use pttern emerging from prioritizing biodiversity emphsizes protetion of high qulity nturl res tht re more lustered together in neighborhoods loted loser to the urbn enter s opposed to more spred out peripherl open spe proteted in the mximum lnd rent pproh. As result of proteting less open spe the ity ttrts fewer households ( redution from.5 to.3 million households). However, while the overll popultion slightly dereses, popultion density in neighborhoods surrounding the ity enters nd open spe lusters inreses. When open spe is more lustered nd entrlly loted, popultion density is higher in entrl neighborhoods nd lower in peripherl neighborhoods thn in the se when open spe is spred round the periphery. Similr pttern pplies to property vlues tht re lower on verge but re higher in entrl res. Reltive to the benhmrk se, prioritizing biodiversity obetives with fixed tx results in higher bid rent, lower popultion density, nd more open spe, but higher property vlues. We find tht introduing of biodiversity obetives with moderte tx leds to overll improvement ompred to the benhmrk. 2

13 These results suggest tht the biodiversity mesure n improve by hnging the sptil onfigurtion of open spe towrds lnds with higher qulity nturl res with slight redutions in household net benefit nd popultion density but with lrger plot res. We nlyze the full spetrum of the trdeoff between totl lnd rent nd biodiversity obetives given 6% tx rte (Figure 4) (We explore the solution with optiml txes in the next setion.). The biodiversity sore n be inresed by ftor of 2.3 (from 209 to 48 %) with redution of totl lnd rent by only 2% (from $2.55 to $2.22 billion) Prioritizing biodiversity with optiml txes Up to this point, we solved for the optiml tx for lnd rent mximiztion nd kept tx fixed t this optiml rte while hnging the priorities wy from lnd rent mximiztion nd towrds the biodiversity onservtion obetive. We now relx this ssumption nd llow txes to hnge solving for the optiml tx for different priorities for the two obetives. As we ontinuously prioritize the biodiversity onservtion obetive (i.e., µ gets smller), the totl re of new open spe, optiml tx rte, nd biodiversity sore inrese (Tble 4). With more open spe proteted to improve the biodiversity sore, there is less lnd vilble for residentil development resulting in higher lnd pries, lower popultion, nd lower totl lnd rent. Consider the trdeoff between lnd rents nd biodiversity with optiml txes, even t 9% property tx the metro re hieves most of the biodiversity benefits tht orrespond to n inrese in biodiversity mesure to 825 from 00 in the benhmrk se with no txes (Figure 4b). This eight-fold inrese in biodiversity omes t the expense of 0.9% redution in lnd rents ompred to the benh mrk se. At 9 to 20 perent tx rte the trdeoff ure hieves golden point. Up to 20% tx there re high returns to biodiversity t low ost (very steep trdeoff urve). However, bove 20%, tx beomes burden on the metro re resulting in lrge redutions in lnd rents nd only mrginl improvements in biodiversity (flt trdeoff urve). Consistently prioritizing the biodiversity obetive lso hnges the pttern of open spe protetion. In omprison with the mximum lnd rent solution (µ = 0.99), insted of only putting new open spe in the periphery, the optiml solution with µ = 0.90 positions new open spe throughout the ity, long the Mississippi river, nd onentrtion in the northern suburbs where lrge nturl res re loted (Figure 5). New open spe is lso loted in neighborhoods with nturl res tht re loser to the entrl business distrits. Households re onentrted ner the entrl business distrits, nd housing density is lower ner the periphery. Lnd pries re higher ner the entrl business distrits, nd higher thn those for the mximum lnd rent solution Spillover effet So fr in our nlysis we ssumed tht households my benefit from open spe menities throughout the ity s whole with only moderte redution of benefits in distne from the neighborhood of residene. We now ondut sensitivity nlysis nd exmine the effets of reduing menity spillover effet so tht the benefits of environmentl menities strt to rpidly derese with distne nd households benefit primrily from open spe menities in their own nd nerby neighborhoods. We find tht s spillover effet dereses the ity beomes less ttrtive nd fewer people wnt to reside in the metro re. As result lnd rents beome lower. We lso find tht low spillover effet hs negtive impt on biodiversity. When the primry gol is to mximize lnd rents, we find tht new open spe is mostly loted in neighborhoods ner the urbn boundry where there re few existing prks (Figure 6, row ); however, 3

14 the mp of new nd existing open spe shows reltively uniform distribution ross the ity. Beuse open spe menities outside neighborhood no longer ontribute to household utility, the menity vrible in the household utility funtion is lower nd households need more residentil spe nd more open spe within their neighborhood to reh the fixed utility level. As result, while most neighborhoods hve open spe, there re fewer households nd lower lnd vlues. Compred with the mximum lnd-rent solution with high menity spillover (Tble 3), the solution with low menity spillover (Tble 5) hs slightly less new open spe (50 km 2 ) but more Regionlly Signifint Nturl Ares (267 km 2 ) resulting in higher biodiversity sore (275). Further, the solution with low menity spillover hs fewer households (0.72 million) nd lower net benefit per household ($7,908). The tx rte neessry to support the optiml provision of new open spe is 8%. Similr to the ses with high menity spillover, shifting optimiztion priority wy from lnd rent nd towrds the biodiversity obetive hnges the lotions of new open spe to neighborhoods tht hve higher hbitt qulity nd re loser to existing prks nd the ity enters (Figure 6). Shifting the priority towrds biodiversity preservtion from μ = 0.99 to μ = 0.60 dereses non-nturl res in the proteted res from 235 km 2 to 0 km 2 nd inreses the outstnding nturl res from 99 km 2 to 282 km 2 (Tble 5). As result, the biodiversity sore inreses from 275 to 559. Beuse higher qulity nturl res re loted in neighborhoods with higher property vlues, the improvement in biodiversity omes t the expense of 3% net loss of the lnd rent inome (from $2.93 to $2.50 billion) nd 30% redution of the totl proteted re (from 50 km 2 to 352 km 2 ). As result of proteting less open spe nd shifting proteted lnd to neighborhoods with higher qulity nturl res, the ity ttrts fewer households ( redution from 0.72 to 0.68 million households) nd lower verge lnd vlue ( redution from $6,823/h to $5,978/h) Are the lotion nd size of existing prks optiml? We sk the question of whether the lotion nd size of the existing prks in the Twin Cities metro re re optiml. To nswer this question, we exmine the optiml onfigurtion of open spe nd residentil development when there is no existing open spe. We find tht the optiml llotion tht prioritizes biodiversity gols nd levies moderte lnd vlue tx resembles the losest the urrent Twin Cities lndspe (μ = 0.6 nd τ = 5%). It is interesting to note tht this finding is onsistent with vrious ntionl rnkings pling the Twin Cities metro re mong the top US ities (Rnked st mong Ameri s Top 20 Helthiest Cities Forbes; rnked 4 th mong Top 0 Helthiest, Hppiest Cities in Ameri ABC news). This sptil onfigurtion indites reveled preferenes in the Twin Cities metro re for the urbn plnning obetives tht prioritize biodiversity (i.e. μ = 0.6 insted of μ = ). Compred to the sptil onfigurtion with existing prks (660 km 2 ), the optiml sptil onfigurtion tht mximizes lnd rent hs 500 km 2 of new open spe loted mostly on the periphery of the ity (Figure 2b). The totl lnd rent nd lnd pries re lower beuse there is no endowment of existing prks providing open spe menities (Tble 6). With the biodiversity obetive, 889 km 2 of new open spe re loted primrily in neighborhoods with nturl res, whih re onentrted long the Mississippi river nd on the northern fringe of the ity (Figure 2b). As result, the biodiversity sore is muh higher thn the solution with existing open spe while the number of households nd lnd vlues re bout the sme (Tble 6). The solution tht mximizes biodiversity (Figure 2b) is losest to the existing open spe onfigurtion (Figure 2) to the extent tht existing prks re loted in neighborhoods with nturl res. However, there re mny existing prks in neighborhoods lose to the ity enter, whih re not present in either of the optiml solutions, suggesting tht n optiml solution with low spillover effet, whih tends to spred out open spe ross the ity, might be loser to the existing onfigurtion. 4

15 5. Conlusion Urbn eonomi models tht nlyze the sptil pttern of housing development s funtion of the size nd lotion of open spe n be extended for use in onservtion plnning. Disrete spe models, suh s the one we present for the Twin Cities, n be used to determine optiml sptil ptterns of open spe nd housing subet to physil onstrints on lnd vilbility nd prtil onstrints on tx rte given plnner s obetives of mximizing household welfre nd biodiversity. Anlysis of the impts of the plnner s preferenes for the obetives llows determintion of the trdeoffs mong lterntive open spe quisition strtegies. Results from the Twin Cities pplition suggest tht plnners n protet dditionl open spe for onservtion without muh loss in household welfre, nd these gins n be obtined with resonbly low property tx rte. Conservtion plnning, i.e., pplying systemti pprohes to biodiversity onservtion, is reltively new field (Mrgules nd Pressey 2000, Moilnen et l. 2009). For exmple, Armsworth et l. (2006) ombined eonomi nlysis of lnd mrkets with onservtion plnning to show how buying lnd for onservtion my inrese lnd pries, hnge the pttern of development, nd redue onservtion metris. Toth et l. (20) used this frmework in n integer progrmming model to selet reserve sites over time to mximize biodiversity protetion while ounting for lnd-prie feedbks tht rise from open-spe menity premiums nd shifts in mrket equilibriums. This pper expnds the existing frmework by embedding model of residentil lotion hoie, whih depends on lnd vlue, ommuting ost, nd open spe menities, within ity plnner s problem of determining the optiml provision of open spe nd residentil lnd use. Doing so llows nlysis of the effets of inresing biodiversity onservtion on endogenous lnd pries, housing density, nd household welfre. Further, our model ounts for importnt sptil linkges mong lnd units, either for eologil or for eonomi resons. For exmple, the onservtion vlue of setting side lnd prel my depend on the mount of onserved lnd nerby. The vlue of lnd for development my be enhned by being dent to onservtion lnd beuse households prefer the menities of nerby open spe. There re dditionl questions tht remin for future reserh. We emphsize tht our pplition is stylized in the sense tht we determine optiml housing pttern for developble lnd bse tht inludes existing housing. Work is needed to onstrut more relisti model in whih existing housing is ounted for in open spe nd development deisions. Perhps of greter importne is the expliit inorportion of timing. Conservtion lnd purhses, s well s development, do not hppen instntneously but unfold with time. One pproh to dynmi nlysis of open spe provision is to develop n eonomi gent-bsed model of lnd use, whih llows for the trking of the trnsitionl dynmis of development, both over spe nd time s the urbn re grows (e.g., Mglio et l. 202). A dynmi model will llow onsidertion of mny dditionl issues beyond those ptured in stti nlysis. 5

16 6 Appendix A. Open-ity equilibrium Given n open spe llotion, preexisting menities z, property tx τ, griulturl rentl pries g p, lotion of business enters B s s b, nd uniform utility level u in n open ity, define ompetitive equilibrium llotion n h,, nd prie p suh tht:. Households mximize their preferenes (eqution 2.) subet to their budget onstrint (2.3). The solution to this household s onstrined utility mximiztion problem re demnd funtions for onsumption, d f v, nd housing, p d f v h. 2. Utility level is equl to u for ll neighborhoods =,,. 3. A neighborhood is inluded into the ity boundry when g p p for ll neighborhoods =,,. 4. The government blnes its budget eqution (2.5). 5. The lnd mrket n h + l lers for ll neighborhoods =,,. 6. The totl ity popultion is the sum of households in eh neighborhood,. N n The following re ompetitive equilibrium llotion nd prie tht stisfy onditions through 6. d f v, A d f v u h, u A d f v l n, d f v u A p.

17 Referenes ABC News Top 0 Helthiest, Hppiest Cities in Ameri, Alonso, W Lotion nd Lnd Use. Hrvrd University Press. Armsworth, P.R., C.D. Dily, P. Kreiv nd.n. Snhirio Lnd mrket feedbks n undermine biodiversity onservtion. Proeedings of the Ntionl Ademy of Sienes 03(4): Anderson, S.T. nd S.E. West Open spe, residentil property vlues, nd ontext. Regionl Siene nd Urbn Eonomis 36: Betley, T Blning urbn development nd endngered speies: The 7 Cohell vlley hbitt onservtion pln. Environmentl Mngement 6 (): 7-9. Billionnet, A Mthemtil optimiztion ides for biodiversity onservtion. Europen ournl of Opertionl Reserh 23: Bureu of Eonomi Anlysis Regionl Eonomi Aounts, Per Cpit Personl Inome in Butsi, V., D.. Lewis, nd V.C. Rdeloff Reserve seletion with lnd mrket feedbks. ournl of Environmentl Mngement 4: Cmm,.D., S. Polsky, A. Solow, nd B. Csuti A note on optiml lgorithms for reserve site seletion. Biologil Conservtion, 78: Cmm,.D., S.K. Normn, S. Polsky, nd A.R. Solow Nture reserve site seletion to mximize expeted speies overed. Opertions Reserh 50(6): Churh, R.L., Stoms, D.M., nd F.W. Dvis Reserve seletion s mximl overing lotion problem. Biologil Conservtion 76, Dissnyke, S.T.M. nd H. Onl. 20. Amenity driven prie effets nd onservtion reserve site seletion: A dynmi liner integer progrmming pproh. Eologil Eonomis 70: Doss, C.R. nd S.. Tff The influene of wetlnd type nd wetlnd proximity on residentil property vlues. ournl of Agriulturl nd Resoure Eonomis 2(): Ewing, R.,. Kostyk, D. Chen. B. Stein, nd M. Ernst Endngered by Sprwl: How Runwy Development Thretens Ameri s Wildlife. Wshington, DC: Ntionl Wildlife Federtion, Smrt Growth Ameri, nd NtureServe. 7

18 Forbes Ameri s Top 20 Helthiest Cities, minnepolis-minn/ Fulton, W., R. Pendll, M. Nguyen, nd A. Hrrison Who sprwls most? How growth ptterns differ ross the US. The Brookings Institution Center on Urbn nd Metropolitn Poliy, Wshington, DC. Geoghegn, The vlue of open spes in residentil lnd use. Lnd Use Poliy 9 () Hight, R.G., C.S. ReVelle, nd S.A. Snyder An integer optimiztion pproh to probbilisti reserve site seletion problem. Opertions Reserh 48(5): Hobden, D.W., G.E. Lughton, nd K.E. Morgn Green spe borders tngible benefit? Evidene from four neighbourhoods in Surrey, British Columbi, Lnd Use Poliy 2(2): Innes, R., S. Polsky nd. Tshirhrt Tkings, ompenstion nd endngered speies protetion on privte lnd. ournl of Eonomi Perspetives 2(3): Irwin, E.G The effets of open spe on residentil property vlues. Lnd Eonomis 78 (4): Irwin, E.G New diretions for urbn eonomi models of lnd use hnge: inorporting sptil heterogeneity nd trnsitionl dynmis. ournl of Regionl Siene 50(): Irwin, E.G., K.P. Bell, N.E. Bokstel, D.A. Newburn, M.D. Prtridge, nd. Wu The eonomis of urbn-rurl spe. Annul Reviews of Resoure Eonomis : Kliber, H.A. nd D.. Phneuf Vluing open spe in residentil sorting model of the Twin Cities. ournl of Environmentl Eonomis nd Mngement 60: Kothen, M.. nd S. Powers Explining the pperne nd suess of voter referend for open-spe onservtion. ournl of Environmentl Eonomis nd Mngement 52: Kovs, K.F. nd D.M. Lrson The influene of reretion nd menity benefits of open spe on residentil development ptterns. Lnd Eonomis 83(4): Lee, C.M., nd Fuit, M Effiient onfigurtion of greenbelt: theoretil modeling of greenbelt menity. Environment nd Plnning A 29 (), List,.A., M. Mrgolis, nd D.E. Osgood Is the Endngered Speies At endngering speies? NBER Working Pper No Lutzenhiser, M., nd N.R. Netusil The effet of open spes on home s sle prie. Contemporry Eonomi Poliy 9 (3):

19 Mglio, N., V. MConnell, M. Wlls, nd E. Sfirov Zoning on the urbn fringe: Results from new pproh to modeling lnd nd housing mrkets. Regionl Siene nd Urbn Eonomis 42: Mhn, B.L., S. Polsky, nd R.M. Adms Vluing urbn wetlnds: A property prie pproh. Lnd Eonomis 76 (): Mrgules, C.R. nd R.L. Pressey Systemti onservtion plnning. Nture 405: Metropolitn Counil Mills, E.S An ggregtive model of resoure llotion in metropolitn re. Amerin Eonomi Review 57: Mills, E.S Studies in the Struture of the Urbn Eonomy. ohns Hopkins Press. Minnesot Deprtment of Employment nd Eonomi Development Ouptionl Employment Sttistis Progrm. Moilnen, A., K.A. Wilson, nd H.P. Possinghm, editors Sptil Conservtion Prioritiztion: Quntittive Methods & Computtionl Tools. New York: Oxford University Press. Muth. R.F Cities nd Housing. University of Chigo Press. Nelson, E.., M. Uwsu, nd S. Polsky Explining ommunity demnd for publily provided open spe. Eologil Eonomis 62: Polsky, S., E. Nelson,. Cmm, B. Csuti, P. Fkler, E. Lonsdorf, C. Montgomery, D. White,. Arthur, B. Grber-Yonts, R. Hight,. Kgn, A. Strfield, nd C. Toblske Where to put things? Sptil lnd mngement to sustin biodiversity nd eonomi returns. Biologil Conservtion 4: Ruliffson,.A., P.H. Gobster, R.G. Hight, nd F.R. Homns Nihes in the urbn forest: Orgniztions nd their role in quiring metropolitn open spe. ournl of Forestry 00(6): September issue Snder, H.A., nd S. Polsky The vlue of views nd open spe: Estimtes from hedoni priing model for Rmsey County, Minnesot, USA. Lnd Use Poliy 26: Snder, H.A., R.G. Hight, nd S. Polsky 200. Eologil Eonomis Tibev, L., R. G. Hight, S. Polsky A disrete spe urbn model with environmentl menities. Resoure nd Energy Eonomis 30: Tylor, M.E Promoting reovery or hedging bet ginst extintion: Austin, Texs s risky pproh to ensuring endngered speies survivl in the Texs Hill Country. Environmentl Lw 24:

20 Thorsnes, P The vlue of suburbn forest preserve: estimtes from sles of vnt residentil building lots. Lnd Eonomis 78(3): Toth, S., R.G. Hight, nd L. Rogers. 20. Dynmi reserve seletion: Optiml lnd retention with lnd prie feedbks. Opertions Reserh 59(5): Trust for Publi Lnd LndVote. Online dtbse: Tyrvinen, L. nd A. Miettinen Property pries nd urbn forest menities. ournl of Environmentl Eonomis nd Mngement 39 (2): U.S. Census Tble. Popultion nd perent distribution by ore bsed sttistil re (CBSA) sttus for the United Sttes nd Divisions, nd for Purto Rio: 2000 nd 2008 (CBSA- EST2008-). Soure: U.S. Census Bureu, Popultion Division. Relese Dte: Mrh 9, Wu, Environmentl menities, urbn sprwl, nd ommunity hrteristis. ournl of Environmentl Eonomis nd Mngement 52: Wu,. nd A.. Plnting The influene of publi open spe on urbn sptil struture. ournl of Environmentl Eonomis nd Mngement 46: Wu,., R.M. Adms, nd A.. Plnting Amenities in n urbn equilibrium model: residentil development in Portlnd, Oregon. Lnd Eonomis 80 (): Yng, C.H., Fuit, M., 983. Urbn sptil struture with open spe. Environment nd Plnning A 5: Zink, R.M., G. F. Brrowlough,.A. Atwood, nd R.C. Blkwell-Rgo Genetis, txonomy, nd the onservtion of the thretened Cliforni gntther. Conservtion Biology 4(5):

21 Tble. Lnd re Lnd type Are (km 2 ) Lnd totl 7,704 Commeril development 462 Prks 660 Institutionl menities 32 Wter 500 Undeveloped lnd 5,950 Nturl re totl 892 Moderte High 2 Outstnding 670 Tble 2. Prmeter vlues. Prmeter Nottion Vlue Consumption good shre α 0.56 Housing shre β 0.36 Amenity shre γ 0.08 Inome ($000 per yer) v Utility level in n open ity 0.2 Amenity vlue for unit of open spe δ.00 Amenity vlue for unit of pre-existing feture δ z.00 Distne weight for menity funtion δ d 0.0 Distne weight for frgmenttion sore σ 0.0 Prie of griulturl lnd ($000 per h) p g 6.43 Trnsporttion ost ($000 per km per yer) θ 0.4 2

22 Tble 3. Optiml solutions with no tx, with the optiml tx (6%) when priority is given to mximizing lnd rent (μ = 0.99), nd with tx fixed t 6% nd deresing priority, μ, for the mximum lnd rent obetive. These ses ssume lrge spillover effet, δ d = 0., for open spe menities. Optiml tx (6%) Tx fixed t 6% nd deresing No Tx Vribles priority, μ Benhmrk μ = 0.99 μ = 0.90 μ = 0.60 Totl net bid rent ($billion) Biodiversity sore Averge prie ($/h) 25,294 27,022 26,500 26,330 Number of households,43,332,5,34,34,4,26,896 Averge household re (h) Popultion density (hhs/km 2 ) Totl new open spe (km 2 ) Non-nturl re (km 2 ) Nturl re: Moderte (km 2 ) Nturl re: High (km 2 ) Nturl re: Outstnding (km 2 ) Tble 4. Optiml solutions with the optiml tx rtes for deresing priorities, μ, given to the mximum lnd rent obetive. These ses ssume lrge spillover effet, δ d = 0., for open spe menities. Vrible Optiml txes nd deresing priority, µ μ = 0.99 μ = 0.90 μ = 0.60 Totl net bid rent ($billion) Biodiversity sore ,32 Optiml tx Averge prie ($/h) 27,022 28,706 3,705 Number of households,5,34,077, ,276 Averge household re (h) Popultion density (hhs/km 2 ) Totl new open spe (km 2 ) Non-nturl re (km 2 ) Nturl re: Moderte (km 2 ) Nturl re: High (km 2 ) Nturl re: Outstnding (km 2 )

23 Tble 5. Optiml solutions with smll menity spillover (δ d = 0.5): no tx, the optiml tx (8%) when priority is given to mximizing lnd rent (μ = 0.99), nd tx fixed t 8% nd deresing priority, μ, for the mximum lnd rent obetive. Vrible No Tx Optiml tx (8%) Tx fixed t 8% nd deresing priority µ Benhmrk μ = 0.99 μ = 0.90 μ = 0.60 Totl net bid rent ($billion) Biodiversity sore Averge prie ($/h) 4,946 6,823 6,279 5,978 Number of households 685,8 722, , ,586 Averge household re (h) Popultion density (hhs/km 2 ) Totl new open spe (km 2 ) Non-nturl re (km 2 ) Nturl re: Moderte (km 2 ) Nturl re: High (km 2 ) Nturl re: Outstnding (km 2 ) Tble 6. Optiml re-prking solutions with 6% nd 5% tx rtes, different priorities, μ, nd lrge spillover effet, δ d = 0.. Vrible With Existing Open Spe No Existing Open Spe No Tx No Tx 6% Tx 5% Tx μ = 0.99 μ = 0.60 μ = 0.99 μ = 0.60 Totl net bid rent ($billion) Biodiversity sore Averge prie ($/h) 25,294 2,537 24,277 23,563 26,326 25,755 Number of households,43,332,03,563,72,458,42,886,70,586,46,582 Averge household re (h) Popultion density (hhs/km 2 ) Existing prks (km 2 ) Totl re new prks (km 2 ) Non-nturl re (km 2 ) Nturl re: moderte (km 2 ) Nturl re: high (km 2 ) Nturl re: outstnding (km 2 )

24 Residentil Institutionl menities Prks Commeril, industril, nd trnsporttion Wter Minnepolis St. Pul Figure. Existing lnd use nd eologil rnking of sites in the seven-ounty metropolitn re surrounding Minnepolis nd St. Pul, Minnesot, USA. 24

25 Residentil lnd use (households per km2) 2 Existing open spe (%) Prie ($ per h) μ τ 0% Figure 2: Mrket pries nd residentil lnd use given existing prks nd no new open spe Residentil lnd use (households per km2) 2b New open spe (%) Prie ($ per h) μ τ 6% μ 0.6 τ 6% μ 0.6 τ 5% Figure 2b. Optiml residentil nd open spe lnd use nd mrket pries ssuming there is no existing open spe. 25

26 Residentil lnd use (households per km2) New open spe (%) New nd existing open spe (%) Lnd vlue ($ per h) μ 0.99 τ 6% μ 0.60 τ 6% Figure 3. Optiml residentil nd open spe lnd use nd mrket pries when the obetive is to mximize: () lnd rents (μ = 0.99) nd (b) biodiversity onservtion (μ = 0.60). Tx rte τ = 6%. Lrge menities spillover effet δd =

27 Biodiversity sore Fixed tx of 6% Biodiversity sore Biodiversity sore Vrible tx Both: fixed nd vrible tx on one hrt Net bid rent in billions $ Net bid rent in billions $ Net bid rent in billions $ () (b) Figure 4. Trdeoff between biodiversity nd lnd rents with fixed tx () nd optiml tx (b). 27

28 Residentil lnd use (households per km2) New open spe (% vilble re) New nd existing open spe (% vilble re) Lnd vlue ($ per h) μ 0.99 τ 6% μ 0.90 τ 20% Figure 5. Optiml distribution of households, open spe, nd lnd vlue for solutions with priority given to the lnd rent obetive (μ = 0.99) nd priority given to the biodiversity onservtion obetive (μ = 0.90) nd the minimum tx rte, τ, tht supports it. These ses ssume lrge spillover effet, δd = 0., for open spe menities. 28

29 Residentil lnd use (households per km2) New open spe (% vilble re) New nd existing open spe (% vilble re) Lnd vlue ($ per h) μ 0.99 τ 8% μ 0.60 τ 8% Figure 6. Optiml solutions with smll menity spillover (δd = 0.5): Optiml distribution of households, open spe, nd lnd vlue for solutions with priority given to the lnd rent obetive (μ = 0.99) nd priority given to the biodiversity onservtion obetive (μ = 0.90) nd tx rte, τ = 8%. 29