Environmental Regulation and the Optimal Location of the Firm under Uncertainty. Murat Isik

Transcription

1 Envronmental Regulaton and te Optmal Locaton of te Frm under Uncertanty Murat Isk Center for Agrcultural and Rural Development Iowa State Unversty 57 eady all Ames, IA 500 Tel: 55) Fax: 55) E-mal: May 3, 003 Paper prepared for presentaton at te Amercan Agrcultural Economcs Assocaton Annual Meetng, Montreal, Canada, July 7-30, 003 Copyrgt 003 by Murat Isk. All rgts reserved. Readers may make verbatm copes of ts document for non-commercal purposes by any means, provded tat ts copyrgt notce appears on all suc copes.

2 Envronmental Regulaton and te Optmal Locaton of te Frm under Uncertanty Abstract Ts paper examnes te optmal locaton of a compettve frm n response to envronmental costs mposed by te abatement nvestment and taxes wen te cost of te envronmental regulaton vares spatally under uncertanty. It contrbutes to te lterature by ncorporatng te spatal settng nto a rsk-averse frm s locaton decsons n te presence of envronmental regulaton uncertanty. An ncrease n te cost of te envronmental regulaton moves a rskaverse frm closer to te output market. An augmented nput or emsson tax causes te rskaverse frm to locate closer to te output market. Uncertanty about envronmental regulatons n te form of te abatement nvestment and taxes also leads a rsk-averse frm to locate closer to te output market, wle t does not affect a rsk-neutral frm s locaton decsons. Te results ave mplcatons for te desgn and mplementatons of envronmental and oter developmentrelated polces. Key ords: rsk averson, uncertanty, regulaton, market-based polces. JEL Classfcaton: D8, R38, Q8.

3 . Introducton Te locaton coce of frms as mportant mplcatons for te future development of varous ndustres n agrculture and manufacturng sectors. Knowng te possble trends n te frm locaton mproves our ablty to formulate publc polces affectng te ndustry development as well as to effectvely respond to te envronmental problems of concentratons of frms on certan areas. Terefore, t s mportant to examne ow varous polces would mpact frms locaton decsons. Envronmental regulatons n te form of mandatory abatement nvestment and market-based polces suc as nput, output and emsson taxes and uncertanty about ter mplementatons may affect frms locaton decsons. As government regulatons are mposed to mprove te envronmental qualty, tere mgt be canges n productons of goods and spatal locatons of frms. Envronmental regulaton and te added costs generally assocated wt complance are consderatons often factored nto te coce of busness locaton Bartk, 988; Jeppesen et al., 00). Altoug natonal envronmental polces ave rased te mnmum level of envronmental standards, mportant dfferences n state envronmental polces reman. In te U.S. state regulatons governng azardous waste dsposal, wetlands fllng, ar and water polluton, and wldlfe protecton vary consderably Meyer, 995). It as been ypoteszed tat geograpc varaton n envronmental regulatons and enforcement can nduce a mgraton of ndustres across state or country boundares to polluton avens were complance costs assocated wt envronmental regulatons are lower. Analyss of ow spatal varablty of envronmental regulaton and enforcement can affect locaton decsons may provde some nsgt nto te polluton aven penomenon. It may also sed some lgt on effects of For example, te story of federal regulaton of polluton as empowered ndvdual states to set polces and terefore as allowed for te current varablty n te state regulatons of te lvestock and og sectors.

4 envronmental regulaton n te nternatonal arena. Proposals to armonze envronmental standards across nternatonal boundares add to te urgency of te queston because of concerns rased tat trade lberalzaton could nduce ncreased nvestment n countres wt lower envronmental standards. In fact, te possblty of ndvdual frms relocatng n response to envronmental costs as been a concern for publc polcy. Te possblty of te U.S. manufacturng plants relocatng to Mexco was an mportant ssue n te Nort Amercan Free Trade Agreement debate. Ts paper analyzes te optmal locaton of te frm n response to envronmental costs mposed by te costs of abatement nvestment and varous tax polces wen te cost of te envronmental regulaton vares across space spatally under uncertanty. Exstng spatal varablty of envronmental regulatons would create opportuntes for frms to locate places wt relatvely lax envronmental regulatons. Most frms make ter producton and locaton decsons under varous sources of uncertanty. Producton s often subject to uncertanty about weater or oter factors tat can not be controlled by frms. Frms are also faced wt uncertanty about envronmental regulatons. Uncertanty about envronmental regulatons n te form of eter abatement nvestment or taxes arses because seemngly random canges n government polces make economc decsons rsky. Addtonally, te envronmental polces do not ave to cange to make te frm s producton and locaton decsons uncertan. Merely te dscussons n Congress, admnstraton and te meda of potental polcy canges ntroduce some elements of rsk nto frm-plannng. In fact, n te case of tecnology adopton, t s sown tat uncertanty about government polces as te potental to mpact te nvestment decson of farmers Isk, 003). Tus, uncertanty about te mposton For example, te dfferences n te scope, degree, and tmng of current and proposed emssons control regulatons ave made power generaton company complance plannng problematc by addng substantal uncertanty about elmnaton of future fuel flexblty and orderly power plant retrement and replacement EPRI, 003). 3

5 of envronmental regulatons or labltes makes te costs of te regulaton uncertan, wc may affect te optmal producton and locaton decsons of frms. Te purpose of ts paper s to examne te mpacts of envronmental regulatons on a rsk-averse frm s producton and locaton decsons under uncertanty about tecnology producton) and envronmental regulaton. It develops a teoretcal model of frm decsonmakng by extendng a spatal locaton model to analyze te extent to wc te ntroducton of envronmental regulatons affects a rsk-averse frm s optmal locaton decsons under uncertanty. Te paper also ams at provdng a systematc analyss of a rsk-averse frm s response to varous market-based polces suc as output, nput and emsson taxes wen decdng ts locaton and te mplcatons of spatally varyng envronmental regulatons for locaton decsons. Muc of te lterature n envronmental economcs, publc fnance and nternatonal trade abstract from te locaton decsons of ndvdual frms under uncertanty. A number of studes explore te mplcatons of canges n te degree of rsk averson on a frm s producton and locaton decsons n a non-spatal context Sandmo, 97; Batra and Ulla, 974; Brys and Eeckoudt, 985; Isk, 00) and n a spatal context Alperovc and Katz, 983; su and Tan, 00; Katz, 984; Ma, 984; Matur, 983; Park and Matur, 988; Park and Matur, 990). owever, tere as been lttle attenton gven to te mplcatons of uncertanty and rsk averson on a frm s producton and locaton decsons n te presence of envronmental regulatons. A few teoretcal studes examned te mpacts of te envronmental regulaton uncertanty on te locaton decsons of rsk-neutral frms 3. Xepapadeas 999) analyzed rsk-neutral frms abatement nvestment and locaton responses to te envronmental polcy, wc takes te form 3 A few teoretcal and emprcal studes also examned te mpacts of te envronmental regulaton on te locaton of rsk-neutral frms under certanty Bommer, 999; Jeppesen et al., 00; Markusen, 997; Motta and Tsse, 994). owever, tese studes dd not focus on te mpact of envronmental regulaton uncertanty. 4

6 of emsson taxes or tradable emsson permts and subsdes under uncertanty. Smlarly, Verbeke and De Clercq 00) analyzed te relocaton of a rsk-neutral monopolst under varous assumptons wt respect to te dfference n envronmental polcy strngency between te ome and foregn country. None of tese studes, owever, examned te mpact of envronmental polcy uncertanty on a rsk-averse frm s locaton decson. Ts paper contrbutes to te lterature by ncorporatng te spatal settng nto a model of frm locaton and producton to obtan comparatve statcs results wt respect to te level of envronmental regulaton uncertanty. It also derves results regardng te spatal effects of envronmental regulatons on a rsk-averse frm s locaton decsons and examnes te mplcatons of te comparatve statcs results for te desgn and mplementaton of envronmental polces. Te results sow tat uncertanty about envronmental regulatons n te form of te abatement nvestment, output taxes, nput taxes, and emsson taxes leads a rskaverse frm to locate closer to te output market, wle t does not affect a rsk-neutral frm s locaton decsons. Under uncertanty, an ncrease n nput and/or emsson taxes leads to a decrease n te dstance between a rsk-averse frm s locaton and te output market, wle t does not mpact a rsk-neutral frm s locaton decson. Te results ave mplcatons for te desgn and mplementatons of envronmental polces for polluton control and publc polces for regonal development.. Te Model Te Conceptual Framework e consder a compettve frm employng two transportable nputs, x and x to produce output Y. Te nputs are avalable at te nput markets I and I. Te frm supples output to a consumpton center output market). Let d be te dstance between te ste of te output market 5

7 and te nput markets and be te dstance between te output market and te frm s locaton Fgure ). Usng te law of cosnes, te dstance between te frm s plant locaton to te nput markets can be expressed as: s = d + d cosθ and s = d + d cosθ θ, were θ s te angle of d and, and θ s te angle of d and d. Te spment of nputs and output from te nput and output markets s costly. It s assumed tat spment cost of output and nputs per unt dstance s r, =0,, for output and two nputs, respectvely. e consder envronmental regulatons n te form of mandatory tecnology adopton. t te envronmental regulaton, frms are usually requred to use less polluton generatng tecnologes, wc requre captal nvestment n new tecnologes. e also consder te mpacts of varous market-based polces suc as nput, output and emsson taxes on te frm s locaton decsons, wc can be used to regulate te ndustry troug nfluencng frm locaton decson and affectng optmal nput use and output. Te frm s assumed to face two types of uncertanty n coosng te plant locaton; tecnology producton) and envronmental polcy uncertanty. Te producton tecnology s represented by te followng stocastc producton functon, Y = F x, x,ε ), were ε s a random varable representng te effects of varatons n stocastc weater condtons, labor effcency, etc. Ts functon s assumed to be a twce contnuously dfferentable functon wt F > 0 and F < 0, =, for all values of ε. It s assumed tat te ger values of ε x xx represent te more favorable state of nature,.e., F > 0. Input prces w and w ) and output ε 6

8 prce P) are assumed to be known wt certanty 4. Polluton waste) generated, z, s represented as a functon of nput use x as: z = z x ). Te frm makes decsons concernng te plant locaton and nput combnatons under uncertanty about te cost of te envronmental regulaton. Assume tat te cost of abatement nvestment from te nvestment n a new tecnology depends on were te frm locates ts operatons and volume of te polluton generated K, θ, z x ), z )) ). Te cost of te x envronmental regulaton would vary spatally because of varatons n strngency of envronmental regulatons. For example, te costs of te envronmental regulaton could vary across states or countes as n te case of ar and water polluton, azardous waste dsposal and wldlfe regulatons n te U.S. Addtonally, n many ctes, zonng as been used to control te use of land and mprove te envronmental qualty by dentfyng areas around ctes tat requre relatvely g cost of abatement nvestment compared to te oter areas. Some ctes n Sweden ntroduced envronmental zones n order to mprove te ambent ar qualty. e take nto account te strngency of te envronmental regulaton across space by makng te cost functon dependng on and θ. Gven tat te extent of te envronmental regulaton could vary across space wt and θ, te cost of abatement nvestment could take te form of K, θ, z x ), z x )) = αc, θ, z, ), were α s an uncertan parameter wt mean α and z U wt te support [,α ] 0. Uncertanty about te costs of mposton of envronmental regulatons or labltes s represented by assumng tat α s a stocastc sft varable n te cost functon. Te non-stocastc part of te cost functon C, θ, z, ) s an ncreasng functon of z te polluton generated,.e., C > 0 and C > 0. Ts form of abatement cost functon assumes z zz 4 In ts paper, we consder a compettve frm s locaton decsons. Strategc reasons for relocaton may also be mportant for frms tat operate n a monopoly or olgopoly envronments were frms output and nput use would affect output and nput prces. 7

9 tat te cost of te envronmental regulaton could vary spatally wt and θ. Te sgn of determnes weter te strngency of te envronmental regulaton and terefore te cost of te regulaton ncreases or decreases as te frm moves closer to te output market. If C < 0, te closer te frm s located to te output market te ger te extent of te envronmental regulaton s. Te cost of te regulaton could also be unform across space but vary wt te polluton generated,.e., K, θ ) = αc z, ) and C = 0. In ts type of regulatons, gven te z same level of polluton generated, frms ave to meet te same standards regardless of ter locatons. e examne te mplcatons of alternatve forms of te abatement cost functon for te optmal locaton of te frm. Te frm s assumed to ave a von Neuman-Morgenstern utlty functon, U) defned on wealt wt U > 0 and U < 0. Te wealt s represented by sum of te ntal wealt, 0 and returns from producton, π. Te Arrow-Pratt measure of absolute rsk averson at te C expected post-rsk wealt ) s defned as R A U ) =. Note tat relatve rsk averson s U ) R R = R A 5. Te frm s objectve s to maxmze te expected utlty of te wealt to fnd te optmal nput combnatons and ts locaton. Te frm s proft s gven by: π = o = P r ) Y w + r s ) x K, θ, z x ), z x )). ) Frm Locaton Decson under Uncertanty Te frm maxmzes te expected utlty of te wealt to fnd te optmal plant locaton and nput combnatons as: 5 Tere are good teoretcal and emprcal reasons to assume tat absolute rsk averson s decreasng and relatve rsk averson s ncreasng n wealt.e., dr A d < 0 and dr R d > 0 ) as argued by Arrow 97). A number of emprcal studes ave also found te evdence supportng ts assumpton Bar-Sra, Just, and Zlberman, 997; Saa, Sumway, and Talpaz, 994; Isk and Kanna, 003). 8

10 max x, x,, θ EU + π ) 0. ) e use a tree-stage algortm to solve te frm s decson problem. Te frst stage of te optmzaton problem nvolves fndng te optmum amount of x tat maxmzes te expected utlty at a gven locaton coce, θ ). Te frst-order condtons for te frst-stage maxmzaton are: EU x = EU [ P r ) F w + r s ) C z x ] = 0 o α. =, 3) z Te second-order condtons for te maxmum are assumed to be met, tat s, EU x < 0 and EU x EU x EU x x )) > 0. Under only producton uncertanty, equaton 3) can be re-wrtten as: E [ P r ) F w + r s ) C z x ] + Cov U, F ) / EU = 0 o α =, 4) z were te covarance Cov U, F ) s postve negatve) wen F > <) 0. Tereby, x s a rskncreasng rsk-decreasng) nput wen F > <) 0 under tecnology producton) uncertanty. ε Let x,θ ) be te values of x satsfyng equaton 4) and let Y,θ ) and π,θ ) ε be te correspondng values. Te second stage of te optmzaton problem s to fnd te locaton varable θ tat maxmzes + ) EU for a gven. Note tat te frm only needs to fnd te 0 π optmal locaton varable θ because θ s known wt te two nput markets. Te frst-order condton for an nteror θ s gven by: EU θ + π ) 0 = EU r s θ x αcθ = = 0. 5) Fnally, te trd stage of te optmzaton problem s to fnd an optmum tat maxmzes π, ) +, were ) EU )), 0 θ θ denotes te value of θ satsfyng equaton 5). By 9

11 dfferentatng EU π, )), ) s obtaned as 6 : EU + wt respect to, te frst-order condton for an nteror 0 θ 0 + π ) = π ) = 0 EU, 6) were π = r0y r s x αc. = Impacts of Envronmental Regulaton on Locaton Decsons under Uncertanty e now examne te mpacts of te envronmental regulaton on te frm s locaton decsons under producton uncertanty assumng tat tere s no uncertanty about te envronmental regulaton. Proposton : Under producton uncertanty, an ncrease n te cost of te envronmental regulaton wll move a rsk-averse frm closer to te output market, f te regulaton s unform across space. owever, mposton of te unform cost of te envronmental regulaton does not affect a rsk-neutral frm s locaton decsons. Proof: Assume tat tere s no uncertanty about envronmental regulaton or uncertanty about mplementaton of te regulaton and terefore K, θ ) = αc, θ, z, ). Te frst-order z condton n 6) becomes π = r0y r s = x αc. Te mpact of a margnal ncrease n te cost of te envronmental regulaton troug an ncrease n α on te frm s coce of locaton s examned by totally dfferentatng te frst-order condton n 6) to obtan: < 6 Te second-order condton EU EU π ) 0 f > 0 π ) s assumed to be met. Gven tat s < 0 + C and π < 0.e., π = r sx αc < 0 ). If C 0 and terefore π > 0 EU satsfed wen ) = π < EU π., t olds, ten t s 0

12 = α [ π π ) + U π ] = E[ U π C) + U C ] E U α α 7) were < 0 s te second-order dervatve of te trd-stage maxmzaton problem. As sown n Appendx, EU π > 0, f absolute rsk averson s decreasng. Tus, an ncrease n te cost of te envronmental regulaton decreases te dstance between te frm s locaton and te output market, f te cost of te regulaton ncreases as te frm moves away from te output market.e., C > 0). On te oter and, f te cost of te regulaton decreases wt an ncrease n.e., C < 0 ), ten an augmented regulaton cost could ncrease or decrease te dstance between te frm s locaton and te output market. Te sgn of 7) s determned by E [ U π C) + U C ] C < 0, ten 7) s postve gven tat E U π C) U C >. e can wrte EU π C) > EUC EU U C) < C [ ] 0 + C π ER Aπ C < C. Let e = C C and π C e = Eπ π be te elastcty of C and π wt respect to, respectvely. Note tat e < 0 and. If we expect e π < 0. Te condton ten can be wrtten as: ER π e < e A π C. If ts condton s satsfed, ten α > 0. Tus, f te regulaton cost decreases wt an ncrease n, te frm s response to ncreased envronmental costs could be eter to locate closer to te output marker or to move away from te output market dependng on te degree of rsk averson and elastctes of cost and proft wt respect to. Assumng tat te cost of te envronmental regulaton.e., strngency of te envronmental regulaton) s unform across space.e., K, θ ) = α C z, ) and C = 0 ), te z mpact of te cost of te envronmental regulaton on te frm s locaton decsons s gven by: = α [ C) ] E U π. Tus, an ncrease n te cost of te envronmental regulaton wll cause

13 te frm to locate closer to te output market under uncertanty and rsk averson, f absolute rsk averson s decreasng. An ncrease n te cost of te envronmental regulaton does not ave any mpact on te locaton decson of a rsk-neutral frm tat maxmzes te expected profts, f te cost s unform across space.e., C = 0 ). On te oter and, t ncreases decreases) te dstance between te output market and te frm s locaton, f te cost of te regulaton ncreases decreases) as te locaton of te frm gets closer to moves away from) te output market.e., C < >) 0 ). Impacts of Envronmental Regulaton Uncertanty on Frm Locaton Decsons e now analyze te mpacts of an ncrease n uncertanty about te cost of te envronmental regulaton on te frm s locaton decsons under uncertanty about producton and envronmental regulatons. Proposton : An ncrease n uncertanty about envronmental regulaton te cost of abatement nvestment) leads a rsk-averse frm to locate closer to te output market, f te cost of regulaton s unform across space or te cost of te regulaton ncreases as te frm moves away from te output market. Proof: e consder te mpact of a margnal ncrease n uncertanty about te cost of te abatement nvestment on te frm s locaton decson. Te margnal ncrease n te envronmental regulaton uncertanty s defned by multplcatve mean-preservng spread of te probablty dstrbuton of α. Let α = γ α α ) + α. An ncrease n γ represents a meanpreservng spread of te orgnal dstrbuton of α Rotscld and Stgltz, 970). Totally dfferentatng te frst-order condton n 6) leads to: = γ [ π π ) + U π ] = E U π π Eπ ) + U π Eπ ) E U [ C C] γ γ / 8)

14 were = π Eπ ) and π Eπ ) C C π γ π γ = gven tat Y s fxed at ts optmum quantty. To determne te sgn of equaton 8), we follow an approac used by Damond and Stgltz 974) and Sandmo 97). As sown n Appendx, f absolute rsk averson s decreasng, ten π Eπ ) < 0 EU and EU π > 0, and f relatve rsk averson s ncreasng, ten EU ππ < 0. Tus, equaton 8) s negatve f C > 0, ndcatng tat an ncrease n uncertanty about te envronmental regulaton leads te frm to locate closer to te output market. en < 0 C C, equaton 8) s postve f E [ R e ] π π < e A. In ts case, te mpact of regulaton uncertanty depends on te degree of rsk averson and elastctes of cost and proft. On te oter and, f te cost of te regulaton s unform across space C = 0 ), te rsk-averse frm s lkely to move closer to te output market. Tere are two opposng effects of an ncrease n te uncertanty about envronmental regulaton on te frm s locaton decsons. Frst, ncreased uncertanty makes a rsk-averse frm worse off. Because te varance of te profts canges drectly wt, a rsk-averse frm tends to locate closer to te output market n order to reduce ts exposure to uncertanty. Second, a lower output decreases te rsk to te more rsk-averse frm, ceters parbus. Tus, te more rsk-averse frm may coose to produce n a more rsky ste by locatng farter away from te output market. Under a decreasng absolute rsk averson and ncreasng relatve rsk averson, te frst effect domnates te second effect Brys and Eeckoudt, 985), leadng a rsk-averse frm to locate closer to te output market under uncertanty tan under certanty. Under rsk-neutralty, te frm maxmzes te expected profts and terefore = γ Eπ γ, wc s equal to zero regardless of weter te regulaton s unform or not. Tus, uncertanty about te envronmental regulaton does not ave any mpact on a rsk-neutral 3

15 frm s locaton decson. Tese results ndcate ow rsk averson canges te mpacts of uncertanty on te frm s locaton decsons. Proposton 3: Under uncertanty about producton and envronmental regulaton, a more rsk-averse frm wll locate nearer to te output market. Proof: Assumng tat preferences of te frm can be represented by a utlty functon of te form U 0,π ;η ), we examne te locatonal effect of rsk averson as n Damond and Stgltz 974). Te ndex η relates to te absolute rsk averson functon as R η > 0. Tus, an ncrease n η corresponds to an ncrease n absolute rsk averson. Totally dfferentatng te frst-order condton n 6), we obtan: A = η [ π U η) ] E U. 9) t U η < 0, equaton 9) s negatve f absolute rsk averson s decreasng EU π > 0 ). Ts ndcates tat te more rsk-averse te frm s te lower te dstance between te output market and te optmal locaton of te frm. Under uncertanty about te mposton of envronmental regulatons or labltes, te frm moves closer to te output market n order to reduce te varablty of returns. As te degree of rsk averson rses, te varance of te proft and terefore te rsk premum ncreases 7. Te rsk-averse frm wt nonncreasng absolute rsk averson s lkely to seek to reduce te varablty of return or to cut ts exposure to uncertanty by locatng closer to te output market. Impacts of Output, Input and Emsson Taxes on Locaton Decsons e now examne te mpacts of varous market-based polces suc as output, nput, and emsson taxes on a rsk-averse frm s locaton decsons under producton and envronmental 7 Te rsk premum s te amount tat te frm s wllng to pay for recevng te maxmum expected proft, nstead of bearng producton and envronmental regulaton uncertanty. 4

16 polcy uncertanty 8. Market-based nstruments suc as taxes or subsdes are typcally proposed as a means for mplementng envronmental polces. For example, taxes on observable factors suc as nput use ave been proposed for acevng desrable reductons n runoff of fertlzers and ave been used n te U.S. and Europe Larson et al., 996). Now, assume tat te ndustry s regulated by mposng taxes on output, nput, or emssons. Te proft of te frm wt a predetermned output tax s gven by = P r ) t ) Y w + r s ) o 0 π x. Proposton 4: Under producton uncertanty, an augmented output tax could ncrease or decrease te dstance between te output market and te frm s locaton. owever, under rskneutralty t ncreases te dstance between te output market and te frm s locaton. An ncrease n te uncertanty about te output tax leads a rsk-averse frm to locate closer to te output market. Proof: t a pre-determned output tax, te frm s output Y ) n equaton ) wll be replaced by Y t 0 ). Te frst-order condton of te frm s locaton decson s smlar to 6), wt only dfference beng te defnton of te wealt and ) totally dfferentate te frst-order condton to obtan: = π = r0y t0 r s = x. e t 0 = E [ U P r ) Y ) U r Y ] π 0.a) o + 0 were < 0. Te sgn of equaton 0.a) s determned by te sgns of te terms nsde te brackets. If E[ RA π P ro ) ] < r0, ten equaton 0.a) s negatve, ndcatng tat te dstance between te output market and te frm s locaton decreases wt an ncreased output tax. Note 8 In ts secton, we only consder te mpacts of market-based polces on te frm s locaton decsons. owever, t s possble tat some combnatons of tese polces along wt te abatement nvestment could be mplemented to address certan envronmental problems. 5

17 tat under rsk-neutralty an ncrease n te output tax ncreases te dstance between te output market and te frm s locaton. e now consder te margnal mpact of an ncrease n uncertanty about te output taxes 0 t t t on te frm s locaton decsons. Let 0 0 ) 0 t = γ +, were γ represents a mean-preservng spread of te orgnal dstrbuton of t 0 Rotscld and Stgltz, 970). Totally dfferentatng te frst-order condton n 6) wt te output tax results n: = γ [ π π Eπ ) + U r Y + r Y π Eπ )/ P r Y ))] E U 0 0 o ). 0.b) If absolute rsk averson s decreasng, ten π Eπ ) < 0 EU and EU π > 0, and f relatve rsk averson s ncreasng, ten EU ππ < 0. Tus, equaton 0.b) s negatve wt a decreasng absolute rsk averson and ncreasng relatve rsk averson. Ts ndcates tat an ncrease n uncertanty about te output taxes leads te rsk-averse frm to locate closer to te output market. A rsk-averse frm moves closer to te output market n order to reduce ts exposure to uncertanty. t a rsk-neutral frm, equaton 0.b) s equal to zero, ndcatng tat uncertanty about envronmental regulatons does not affect te frm s locaton decsons. Proposton 5: Under uncertanty, an ncrease n an nput tax and/or an ncrease n uncertanty about ts mplementatons decreases te dstance between a rsk-averse frm s locaton and te output market. Increased nput tax does not ave any mpact on a rsk-neutral frm s locaton decson. Proof: Under an nput tax polcy, te frm s nput cost w ) n equaton ) wll be replaced by w + t ). t an nput tax polcy, te frst-order condton of te frm s locaton x 6

18 decson problem s smlar to 6), wt only dfference beng te defnton of te wealt and π = r0y r s = x. Totally dfferentatng te frst-order condton leads to: t x = [ π w x )] E U..a) Equaton.a) s negatve f absolute rsk averson s decreasng,.e., EU π > 0. ence, an ncrease n te nput tax results n a decrease n te dstance between te output market and te frm s locaton, makng frms to concentrate around te output market wc s more lkely to be populated. Under rsk-neutralty were te frm maxmzes te expected profts, an ncrease n te nput tax, owever, does not ave any mpact on a rsk-neutral frm s locaton decson. e also analyze te margnal mpact of an ncrease n uncertanty about te nput taxes on te frm s locaton decsons by lettng t x = γ t x t x ) + t x, as n te case of examnng te mpacts of uncertanty about output taxes Rotscld and Stgltz, 970). Totally dfferentatng 6) wt te nput tax leads to: = γ [ π π Eπ )] E U..b) Equaton.b) s negatve and t ndcates tat an ncrease n uncertanty about te nput taxes leads te frm to locate closer to te output market, f absolute rsk averson s decreasng. Proposton 6. An ncrease n an emsson tax and/or an ncrease n uncertanty about ts mplementatons lead to a decrease n te dstance between a rsk-averse frm s locaton and te output market under uncertanty. Under rsk-neutralty, an ncrease n te emsson tax does not mpact te frm s locaton decson f te polluton generated s ndependent of te frm s locaton. Uncertanty about emsson taxes does not mpact a rsk-neutral frm s locaton decson. 7

19 Proof: Gven tat z = z x ), te proft of te frm under a pre-determned emsson tax s gven by π = P ro ) Y w + r s ) x = = t e z x ). Te frst-order condton wt respect to s smlar to 6), wt only dfference beng te defnton of te wealt and π = r0y r s = x. Totally dfferentatng te frst-order condton wt te emsson tax leads to: t e = [ π z x )] E U..a) Equaton.a) s negatve f absolute rsk averson s decreasng,.e., EU π > 0. ence, an ncrease n te emsson tax results n a decrease n te dstance between te output market and te frm s locaton, makng frms to concentrate around te output market wc s more lkely to be populated. Note tat an ncrease n te emsson tax, owever, does not ave any mpact on a rsk-neutral frm s locaton decson. Now suppose tat te polluton generated s a functon of x, and θ as: z = z, θ, x ). In ts case, te polluton generated vares across space, gven te same level of nput use. For example, ts would be te case n agrculture were te runoff generated depends not only on te nput use but also on te pyscal sol caracterstcs, weater condtons, and producton tecnology avalable to te frm across space. t te assumpton of z, θ, x ) and rsk-averson, π = r0y r s x z and = E[ Uπ z x, θ, x ) + U z ]. = te If absolute rsk averson s decreasng and z > 0, ten t < 0. If z < 0, ten t > 0, provded tat [ A ] E R π z > z. On te oter and, under rsk neutralty, t < >) 0, f e e e 8

20 z > <)0. Tus, ncreased emsson tax does not mpact a rsk-neutral frm s locaton decson f te envronmental regulaton s unform across space wle t s lkely to affect te locaton coce f te polluton functon depends on. e also analyze te margnal mpact of an ncrease n uncertanty about emsson taxes on te frm s locaton decsons. Let t e = γ te te ) + te, as n te case of examnng te mpacts of uncertanty about output and nput taxes analyzed above. Totally dfferentatng 6) wt te emsson tax and z = z, θ, x ) leads to = γ [ π π Eπ ) + U π Eπ ) z ] E U..b) As sown above, under a nonncreasng absolute rsk averson and nondecreasng relatve rsk averson, equaton.b) s negatve f z 0. Ts ndcates tat an augmented uncertanty about te envronmental regulaton leads te frm to locate closer to te output market. Ts occurs because a rsk-averse frm seeks to reduce ts exposure to uncertanty. If z < 0, ten te mpact of uncertanty on te locaton decsons s ambguous. If z = z x ).e., z = 0 ), an ncrease n uncertanty about te emsson taxes leads te rsk-averse frm to locate closer to te output market. Under rsk-neutralty, te frm maxmzes te expected profts and terefore = γ Eπ γ, wc s equal to zero regardless of weter z s zero or not. 3. Conclusons and Polcy Implcatons Ts paper develops a teoretcal model of frm decson-makng to examne te mpacts of envronmental regulatons on a compettve frm s producton and locaton decsons under uncertanty about producton and envronmental regulaton. It also provdes a systematc analyss of a rsk-averse frm s coce of plant locaton and ts response to taxes suc as nput, output and 9

21 emsson wen decdng ts locaton under uncertanty. Ts paper makes contrbutons to te lterature by obtanng comparatve statcs results wt respect to te level of envronmental regulaton uncertanty and by dervng results regardng te spatal effects of envronmental regulatons on te frm locaton decsons. Te comparatve statcs results sow tat an ncrease n te cost of te envronmental regulaton under producton uncertanty moves a rsk-averse frm closer to te output market f te regulaton s unform across space. An augmented cost of te envronmental regulaton does not mpact a rsk-neutral frm s locaton decson, f te cost of te regulaton s unform across space. Increased emsson taxes or nput taxes causes te rsk-averse frm to locate closer to te output market. Uncertanty about envronmental polces cost of te abatement, output taxes, emsson taxes, and nput taxes) as te potental to affect te optmal locaton of te frm. In partcular, t leads a rsk-averse frm to move closer to te output market tat s lkely to be more populated. Tus, under uncertan polcy envronments, envronmental polces may not be effectve n encouragng frms not to locate nearer to te output markets or consumpton centers. Te results ave mplcatons for te desgn and mplementaton of spatal envronmental polces for polluton control. It as generally been seen tat busnesses prefer settng up ter producton facltes near bg ctes because ts gves tem proxmty to te consumer market. Tere as been a large ncrease n ndustral development around te major ctes. Emssons from tese ndustres are a concern to negborng resdents n many locatons. Many ctes ave used zonng to mprove te envronmental qualty. Te results obtaned n ts paper llustrate te usefulness of spatal envronmental polces tat ams at encouragng frms not to locate nearer to te output markets and te mportance of reducng uncertanty about envronmental regulatons n mplementng tese polces. 0

22 Te possblty of ndvdual frms relocatng n response to envronmental costs as been a major concern for publc polcy and regonal developments. Te results ave mplcatons for polces tat seek to armonze state envronmental regulatons. For example, major canges are beng consdered n federal water qualty rules for te lvestock and og ndustry n te U.S. Tese canges would armonze manure management standards across states. Addtonally, te results provde nsgt for evaluatng te nfluence of market-based polces suc as output taxes, nput taxes and emsson taxes on regonal development. Tax polces and rsk-reducng polces ave mpacts on regonal development and on te envronment troug affectng te frm locaton decsons. Locaton decsons also ave an nternatonal context, wt concerns about companes sftng nvestment outsde te U.S. and te European Unon. For example, te European Unon experence wt ts Ntrate Drectve demonstrates tat lmtng producers optons wt strct regulaton of ntrate levels n an area wt a lmted land base as te potental to reduce te scale and to nfluence te locaton of anmal producton. Moreover, armonzaton of envronmental standards across nternatonal boundares s a contentous topc n orld Trade Organzaton dscussons, because of possble effects on te locaton of busnesses and geograpc dsperson of te emssons. If unform envronmental regulatons were to rase costs of producton n some countres so g tat tey could no longer be compettve n export markets, producers n tose countres would lkely appeal for an exempton, and some countres mgt be wllng to enance ter export compettveness at te expense of te envronment.

23 Fgure. Te Frm s Locaton to te Input and Output Markets I - Input Market I -Input Market d Output Market d θ s s Frm Locaton

24 Appendx Consder two utlty functons, U and. Te utlty functon represents greater rsk averson tan U f tere exsts an ncreasng and strctly concave functon k suc tat =ku). Te frst-order condton for an nteror for te utlty functon requres [ k' U ) U' ] = 0 E π. A.) Let αˆ be te value of α suc tat π ˆ = r0 Y r s x αc = 0. Based on te defnton = tat R = U U, a decreasng R A mples A U U > < ) RA 0 + ˆ) π as α > <) ˆ α A.) For αˆ >α, because π > 0, te followng occurs U + π ˆ π ) π. A.3) 0 ) π > U 0 + π ) RA 0 + Te nequalty n A.3) also olds for αˆ <α because π < 0. Terefore, EU + π ) π > EU + π ) π RA + ˆ) π 0. A.4) = Equaton A.4) ndcates tat EU > 0. Smlarly, based on te defnton of relatve rsk π averson suc tat tat RA ) U U = 0 + π, an ncreasng R R mples + π ) U U < > ) R + ˆ) 0 R 0 π as α > <) ˆ α. A.5) Usng te same approac as above leads to EU ππ < 0. Terefore, f absolute rsk averson s decreasng, ten π Eπ ) < 0 ten EU ππ < 0. EU and EU π > 0, and f relatve rsk averson s ncreasng, 3

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