Quality Standards versus Taxation in a Dynamic Environmental Model of a Tourism Economy

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1 Qualy Sandard eru axaon n a Dynamc Enronmenal Model of a ourm Economy Rey-Maquera, J., J. Loano,.M. óme Deparmen of ppled Economc, Unery of he alearc Iland, Span Deparmen of Economc and Economc Hory, Unery of lcalá, Madrd, Span eyword: ourm economc, ourm polcy, ourm axaon, qualy andard, economc modellng EXEDED S he paper conruc a dynamc general equlrum model for a mall economy ha pecale n ourm o explore he long erm effec of enronmenal and ourm polce. he model aume ha our oan afacon from prae erce proded y ourm frm, good and erce proded y he pulc ecor and enronmenal qualy. Safacon from prae erce depend on he qualy of hoe erce, whch repreened y he amoun of capal per un of accommodaon. I alo aumed ha good and erce proded y he goernmen uffer from congeon. Enronmenal qualy, whch alo alued y he reden, modelled a a renewale reource ha depleed y ourm acy. ourm frm are prce aker n he nernaonal ourm marke, n he ene ha he amoun of ourm erce proded y he economy ha no drec mpac on nernaonal prce. he prce, howeer, depend poely on he qualy of he uppled ourm undle and herefore ourm frm n he denaon can charge hgher or lower prce dependng on he qualy of prae ourm erce, congeon of pulc good and enronmenal qualy. In h eng, he long erm effec of wo alernae polcy nrumen are compared, namely an oerngh ay ax and a qualy andard ha mpoed on ourm frm. oh nrumen can e ued a accommodaon qualy and enronmenal qualy polcy ool. Howeer, her welfare conequence are dfferen a hey hae dfferen effec on he ncene o accumulae capal. Specfcally, he oerngh ay ax ac a an mplc ax on capal, reducng he ncene for nemen and capal accumulaon. From a long erm perpece, he qualy andard alway uperor o he oerngh ay ax, proded ha he former doe no caue any dynamc neffcency. 96

2 . IODUIO In many cae pecalaon n ourm ha een rggered y he aundance of naural reource. he naural enronmen par of he ourm oupu, u ourm acy exer a hgh preure on naure (dell, ; Dae and ahll, whch may harm he welfare of reden and een pu n danger he ourm aly of he economy. Much of he enronmenal damage are exernal co, leadng o an excee ourm expanon from he ocal pon of ew. he ncreang mporance of ourm ha rggered an nere n pulc nerenon. For nance, ome ourm econome re for a change of he paern of pecalaon from he ma ourm o qualy ourm. In ome cae a well, here a demand for pulc nerenon o correc enronmenal exernale generaed y he ourm ecor. o reach hee arge eeral polcy nrumen hae een ued uch a ourm axe (room axe, enry axe and ex axe, qualy requremen mpoed on he uppler of ourm erce, or he proon of pulc nfrarucure relaed o he ourm acy. In h paper we exend he dynamc general equlrum model deeloped n óme e al. (7 o nclude no only ourm axe u alo qualy andard. h model deeloped for a mall economy pecaled n ourm, where he expanon of he ourm ecor he engne of growh and whch nclude he relaonhp of dependence and mpac eween he ourm acy and he enronmen. Mehodologcally he model relaed o he leraure ha exend economc growh heory o nclude enronmenal arale (ahonen and uuluanen, 993; Sokey, 998; Hech 998, among oher. In h framework, we explore he effec of ome ourm-enronmenal polce, pecfcally, an oerngh ay ax and a qualy andard for ourm frm. he remander of he paper organed a follow. Secon dcue he model. Secon 3 compare wo polcy nrumen n erm of he conequence for long erm welfare: he oerngh ay ax and a qualy andard for he ourm frm. Fnally, econ 4 ge ome concludng commen.. HE MODEL We conder he cae of a mall open economy ha fully pecaled n prodng ourm erce o foregner... ourm preference and ourm reenue or oan afacon from hree dfferen ource: a ourm erce proded y he ourm frm. We conder capal relae o he capacy of accommodaon a a qualy ndex from he ourm frm, ha, /, where he capal of he frm and capacy of accommodaon. ood and erce proded y he pulc ecor. Some good and erce proded y he pulc ecor are manly for he ue of hoe our ha lodge n a pecfc area. Howeer, he pulc ecor alo prode good and erce for he whole ourm ndury. Le u call he fr knd of good and erce and he econd. We aume ha oh ype are ujec o congeon. c Enronmenal qualy of he reor. In many ourm reor naural ae are an eenal par of he ourm produc and a uch a key deermnan of he or afacon. We conder ha enronmenal qualy repreened y a ngle arale called. en hee aumpon we defne a uly funcon ha meaure he afacon per oerngh ay of a our ha he reor: U ϑ ( ϑ where we aume ha,, (,; >; < where U he uly of a our ha recee erce from frm, are excludale good and erce ha frm recee from he pulc ecor, he aggregae accommodaon capacy of he reor and ϑ he numer of oerngh ay per un of accommodaon capacy. From ( we can oan he reenue ha accrue o a frm gen addonal aumpon. Frly, we defne P U a he prce a our wllng o pay for a 97

3 un of afacon oaned n he reor. en h, he prce pad for he ourm erce : P P U U Secondly, and gen ha he numer of oerngh ay n he ourm frm ϑ, reenue of a frm are: where ϑ -- P U ( ggregae reenue are:.. Pulc ecor ( he pulc ecor rae reenue ung a ax leed on ourm reenue,, < and an oerngh ay ax,,. Pulc udge alway n equlrum, ha : F (3 where we allow for lump-um ranfer, F, and ϑ normaled o one..3. Frm ehaor Frm maxme prof hrng capal and akng decon oer her accommodaon capacy. wo condon follow from prof maxmaon: (4 ( R (5 ( ( ggregae prof are: ( Π (6.4. Reden ehaor Reden are modeled a a ngle repreenae agen ha maxme he followng neremporal uly funcon: ω e ( d,, > where he conan neremporal elacy of uuon, he rae of me preference and a relae wegh of enronmenal qualy on reden preference and conumpon. pplyng he maxmum prncple, he followng expreon deermne he ehaor of reden: r Π F & & r ( lm (7 (8 (9 where r ne real rae of reurn and a co-ae arale aocaed wh capal..5. Enronmenal qualy We nerpre enronmenal qualy a a renewale reource. ourm acy ha damagng effec on he enronmen. We aume ha enronmenal qualy eole oer me accordng o he followng funcon: ( ( he maxmum leel of enronmenal qualy, he rae of recoery of he enronmen due o naural regeneraon and meaure he enronmenal mpac aocaed wh a un of accommodaon capacy..6. Equlrum onderng rr-, where he rae of capal deprecaon we oan: 98

4 ( ( ( ( he model ha a aonary ae where: F ( 3 ( (4 ( ( (5 ( (6 ( (7 3. OVERIH SY X D QULIY SDRDS We compare he long-erm effec of he oerngh ay ax and a qualy andard. We defne a qualy andard a a mnmum of capal per un of accommodaon capacy mpoed o he ourm frm y he pulc ecor. Fr of all, le u conder he ehaor of he economy when here a qualy andard and no oerngh ay ax. In h conex frm adju her / o he legal mnmum. he frm and aggregae reenue funcon are repecely: κ κ where κ he qualy andard. Frm ehaor deermned y he qualy andard and: ( ( R (5 he eady ae : κ ( κ ( ( ( Prof can e nerpreed a ncome ha accrue o an mplc fxed facor (land or know-how. When he oerngh ay ax ued he ax yem faor he fxed facor o he dermen of capal whle he oher way round happen when we op for he qualy andard. well known, doron from he ax yem are mnmed when he ax urden manly orne y he fxed facor. h ugge ha he qualy andard would yeld a hgher welfare leel han he oerngh ay ax. Howeer, h no alway rue nce he qualy andard can ge place o a prolem of dynamc neffcency. o how h, le u conder ha he leel of he oerngh ay ax and he qualy andard are uch ha hey yeld he ame eady ae enronmenal qualy leel. h allow u o concenrae n he dfference n eady ae conumpon. We alo aume ha pulc expendure relae o ourm 99

5 reenue e a opmal leel, ha,,. For a gen leel of enronmenal qualy, eady ae conumpon : where ( ( Ω (6 [ ( ( ] ( Ω he expreon (6 come from (, (7 and he eady ae relaonhp eween accommodaon capacy and enronmenal qualy, (4. Form (6 he leel of capal ha maxme long erm conumpon can e worked ou: R Ω ( ( where R he golden rule leel of capal. : Wh a oerngh ay ax eady ae capal ( Ω ( Ω ( ( ( ( ( ( where and and for he eady ae leel of capal when he oerngh ay ax reenue are gen ack n lump-um fahon and when hey are ued o reduce he reenue ax, repecely. hould e expeced, n he econd cae eady ae capal hgher nce he afer ax reurn o capal are larger. Moreoer, n oh cae he leel of capal elow he golden rule proded ha he reenue ax poe. herefore, long erm conumpon alo hgher n he econd cae. When he pulc ecor e a qualy andard, capal n he eady ae : κ ( ( Ω ( ( I eay o how ha n h laer cae capal reache a hgher leel n he eady ae han when he oerngh ay ax ued. Howeer, nce <(-, wh he qualy andard he economy could end up wh a leel of capal aoe golden rule leel. herefore, proded ha he qualy andard doe no ge place o oer accumulaon of capal, h nrumen yeld a hgher long erm welfare leel han he oerngh ay ax. Pu n a dfferen way, a neceary (u no uffcen condon for he oerngh ay ax o e a eer nrumen ha under he qualy andard regme he economy uffer from dynamc neffcency. 4. OLUSIOS We hae conruced a dynamc general equlrum model for an economy pecaled n ourm o explore long erm effec of ome enronmenal and ourm polce. Specfcally, we compare he long erm effec of wo alernae polcy nrumen, ha, an oerngh ay ax and a qualy andard mpoed o he ourm frm. We how ha oh nrumen hae dfferen effec on he ncene o accumulae capal. Moreoer, from a long erm perpece, he qualy andard could e a eer nrumen han he oerngh ay ax nce he former mple lower axaon on capal. Howeer, under he qualy andard, he ncene for capal accumulaon could e excee herey leadng o dynamc neffcency. OWLEDEMES We acknowledge Mchael Mcleer for h ery helpful commen. REFEREES h alway rue nce </(<(-.

6 Dae,. and S. ahll ( Enronmenal Implcaon of he ourm Indury, Reource for he Fuure Dcuon Paper -4 (. óme,.m., J. Loano and J. Rey-Maquera (forhcomng Enronmenal polcy and long-erm welfare n a ourm economy, Spanh Economc Reew Hech, F. (998 rowh effec of a reenueneural enronmenal ax reform, Journal of Economc 67, Sokey,. (998 re here lm o growh?, Inernaonal Economc Reew 39, -3. ahonen, O. and J. uuluanen (993 Economc growh, polluon and renewale reource, Journal of Enronemal Economc and Managemen 4, -8. dell.. ( ourm Economc, he Enronmen and Deelopmen Edward Elgar, helenham. PPEDIX: Saly of he eady ae In h appendx we dcu he eady ae aly condon under he aumpon ha he polcy nrumen are conan and, omnng (, (, ( ( and (5 we arre a: ( ( ( ( ( ( ( ( ( Lnearaon around he eady ae reul n a yem whoe Jacoan : ( ( ( ( ( 3 ( ( ( ( ( ( 3 3 ( ( 3 ( 33 he deermnan of : ( ( > he deermnan poe and herefore here are wo pole: hree poe egenalue or one poe and wo negae. he characerc equaon : ( ( 3 Δ Δ where ( [ ] ( ( Δ h equaon canno e oled analycally. Howeer f we e (- /(--> he egenalue are: Δ

7 ( ( ( ( ( ( 4, 3 ± he fr egenalue poe nce ---> and <. he oher wo are negae ecaue: ( ( ( ( ( ( 4 < herefore, proded ha he roo are real, he eady ae a addle-pah. Dfferen alue for he neremporal elacy of uuon mean horonal hf of he characerc equaon. herefore, h reul would hold for a large range of alue for.

(,,, ) (,,, ). In addition, there are three other consumers, -2, -1, and 0. Consumer -2 has the utility function

(,,, ) (,,, ). In addition, there are three other consumers, -2, -1, and 0. Consumer -2 has the utility function MACROECONOMIC THEORY T J KEHOE ECON 87 SPRING 5 PROBLEM SET # Conder an overlappng generaon economy le ha n queon 5 on problem e n whch conumer lve for perod The uly funcon of he conumer born n perod,