Green Cities? Urbanization, Trade and the Environment

Transcription

1 DICUION PPER ERIE IZ DP No Green Ctes? Urbanzaton, Trade and the Envronment Ranald Borck Mchael Pflüger June 2015 Forschungsnsttut zur Zukunft der rbet Insttute for the tudy of Labor

2 Green Ctes? Urbanzaton, Trade and the Envronment Ranald Borck Unversty of Potsdam, CEfo and DIW Berln Mchael Pflüger Unversty of Würzburg, DIW Berln and IZ Dscusson Paper No June 2015 IZ P.O. Box Bonn Germany Phone: Fax: E-mal: ny opnons expressed here are those of the author(s) and not those of IZ. Research publshed n ths seres may nclude vews on polcy, but the nsttute tself takes no nsttutonal polcy postons. The IZ research network s commtted to the IZ Gudng Prncples of Research Integrty. The Insttute for the tudy of Labor (IZ) n Bonn s a local and vrtual nternatonal research center and a place of communcaton between scence, poltcs and busness. IZ s an ndependent nonproft organzaton supported by Deutsche Post Foundaton. The center s assocated wth the Unversty of Bonn and offers a stmulatng research envronment through ts nternatonal network, workshops and conferences, data servce, project support, research vsts and doctoral program. IZ engages n () orgnal and nternatonally compettve research n all felds of labor economcs, () development of polcy concepts, and () dssemnaton of research results and concepts to the nterested publc. IZ Dscusson Papers often represent prelmnary work and are crculated to encourage dscusson. Ctaton of such a paper should account for ts provsonal character. revsed verson may be avalable drectly from the author.

3 IZ Dscusson Paper No June 2015 BTRCT Green Ctes? Urbanzaton, Trade and the Envronment * Ths paper establshes a smple theoretcal framework whch comprses key forces that shape the structure and nterrelaton of ctes to study the nterdependences between urban evoluton and the envronment. We focus on the potental of the unfettered market forces to economze on emssons. key fndng s that these forces alone may suffce to generate an urban Envronmental Kuznets Curve. In partcular, reducng trade costs ncreases per capta ncomes and generates a U-shaped evoluton of emssons n the process of agglomeraton and redsperson. nother key result s that agglomeraton per se s typcally not a boon for the envronment, as total emssons n the total cty system are lkely to rse. JEL Classfcaton: F18, Q50, R11, R12 Keywords: cty structure, cty systems, envronmental polluton, global warmng, Envronmental Kuznets Curve, trade costs, commutng costs, housng Correspondng author: Mchael Pflüger Faculty of Economcs Unversty of Würzburg anderrng Würzburg Germany E-mal: [email protected] * We thank Krstan Behrens, Johannes Bröcker, Taj Furusawa, teve Gbbons, Phlpp Harms, Jota Ishkawa, Tll Requate, Jens üdekum, Takatosh Tabuch, Jacques-Francos Thsse, Klaus Wälde, and semnar partcpants at Htotsubash Unversty, TU Berln, TU Dresden, Kel, Manz, Potsdam, egen, Unversty of Tokyo, the Industral Organzaton and patal Economcs conference n t. Petersburg, the NRC/UE meetng n tlanta, the ER conference n Palermo, the Veren für ocalpoltk annual meetng n Düsseldorf, ts Regonal Economcs meetng n Vaduz and Publc Economcs meetng n Freburg for helpful comments and dscusson.

4 1 Introducton Urbanzaton s rapdly on the rse. The share of the populaton that lves n urban envronments has ncreased from 37.6% to over 50% just between 1990 and today. 1 Ctes are thought to be engnes of growth and sources of structural change. They have recently been dubbed the greatest nventon of humanty (Glaeser 2011). Is ths trumph of the cty good or bad for the envronment? In the face of global warmng, the analyss of the effects of urbanzaton on the envronment s of central socopoltcal relevance and one of the most pressng research questons n (envronmental and urban) economcs. One promnent hypothess holds that urban growth should ultmately be favorable for the envronment snce lvng n hgh densty areas goes along wth smaller housng lots and apartments and shorter drvng dstances to workplaces and for shoppng (Glaeser 2011). Yet, pontng to the compactness of ctes does not settle the ssue, snce ncreases n populaton densty very lkely go along wth bgger ctes and more commutng. More fundamentally, the ssue necesstates to look at the entre cty system and ts emergence and at the trade relatonshp between ctes and the assocated emssons, not only at one cty n solaton (Gagné, Rou and Thsse 2012). The emprcal evdence s nconclusve, too. The trend towards ever hgher degrees of urbanzaton has been paralleled by an equally notorous upward trend n carbon doxde emssons and other greenhouse gases ever snce these have been recorded. However, there are also more bengn developments. For example, n New York Cty, ar polluton levels have ncreased from 1800 to 1940, but ths trend has been reversed thereafter (Kahn 2006). The latter example suggests the possblty of an urban Envronmental Kuznets Curve (EKC), an nversely U-shaped relatonshp between development and polluton (Copeland and Taylor 2003; Kahn 2006). The lterature on the envronmental effects of urbanzaton s slm. 2 The contrbuton of ths paper s to establsh a smple theoretcal framework whch comprses key forces that shape the structure and nterrelaton of ctes and whch allows us to study fundamental nterdependences between urban evoluton and the envronment. Ths research s nspred by the semnal work of Copeland and Taylor (2003) who forcefully showed how frutful t s to have a unfyng model to address the nterface between trade and the envronment. Just as they faced the queston s free trade good for the envronment?, we ask s urbanzaton good for the envronment?. 1 tartng wth 9% around the year 1300 urbanzaton has almost doubled n the wake of the Industral Revoluton, and then ncreased to today s levels. Urban growth s expected to carry on, most spectacularly so n developng country megalopolses. ee Baroch (1988), san Development Bank (2012) and World Bank (2009). 2 lucd survey of mportant ssues s provded n Kahn and Walsh (2014). 1

5 Copeland and Taylor (2003) dentfed key parameters (factor proportons, n partcular) that drve (per capta) ncomes and polluton n open economes. Our analyss brngs n the urban perspectve and traces the effects of parameters that are key for the evoluton of cty systems, such as the costs of transportng goods between ctes, commutng costs wthn ctes and the opportunty cost of land outsde cty boundares. Fg. 1: Emssons by sector, U 2010 (EP 2015) In settng up our framework we make four mportant choces. Frst, we buld on a verson of the urban model of lonso n whch the lot sze chosen by households and, hence, the populaton densty n ctes, s endogenously determned. Ths feature s crucal to address a potentally mportant source of polluton savngs. econd, we go beyond a sngle cty and look at an urban system consstng of two ctes that trade goods and whose szes evolve endogenously n response to market sze effects establshed by the new economc geography (Fujta et al., 1999). We consder a core-perphery model wth two sectors, a farm sector and a modern sector whch produces manufactures, and wth moble sklled workers who exhbt heterogeneous locaton preferences as n Tabuch and Thsse (2002) and Murata (2003). Thrd, our model comprses the key sources of urban polluton, namely envronmental externaltes assocated wth housng, commutng, producton of ndustral and agrcultural goods and the trade of goods across ctes. Fourth, our analyss delberately refrans from takng envronmental polces and endogenous emsson ntenstes nto account. We are fully aware of the mportance of government nterventon to contan envronmental polluton. However, we defer such an applcaton of our framework to future work. Ths allows us to focus on the 2

6 potental of unfettered market forces to economze on emssons. More specfcally, t allows us to explore whether market forces alone suffce to generate an urban EKC as stpulated n Glaeser (2011). 3 Even though we keep all specfcatons as smple as possble, endogenzng the nternal cty structure and the cty nterrelatons throws up complextes that necesstate the use of numercal smulatons at several parts of our analyss. Our calbraton uses parameter values such that the greenhouse gas emssons sources wtnessed n the U shown n Fg. 1 are reproduced n the ntal equlbrum ( baselne specfcaton ). Ths llustrates that our model captures the most mportant polluton sources responsble for clmate change. Our analyss yelds the followng results. We frst consder the case of two ctes that mantan trade relatons but whose sze we exogenously keep at equal (fxed) sze. We fnd that ncreasng the degree of trade freeness, aggregate populaton sze and the share of expendtures devoted to manufacturng goods and to housng as well as decreasng the costs of commutng and the (exogenously fxed) agrcultural land rent outsde of ctes rases per capta ncomes and total emssons at the same tme. Hence, no market-nduced EKC s mpled by any of these parameter changes. Thngs are dfferent for the composton of the workforce: f the (exogenous) share of sklled workers s ncreased begnnng at low levels, per capta ncomes rse and total emssons fall. We also explore whether the cty system s greener f we exogenously ncrease the sze of one of the two ctes. We fnd that all emssons n the emergng core ncrease and that, except for the emssons assocated wth mports, the opposte holds true n the emergng perphery. Total emssons of the entre cty system rse n our baselne specfcaton. Dependng on the emsson ntenstes of pollutng actvtes, however, total emssons may also fall. We then turn to the case where sklled labor s moble so that the sze of the two ctes emerges endogenously. s trade freeness s successvely ncreased, the model exhbts the locaton pattern wth dsperson, partal agglomeraton and redsperson known from Tabuch and Thsse (2002). Remarkably, we now fnd that changes n any of the followng four sngle parameters have the potental to lead to a market-nduced EKC: the level of trade freeness, the share of sklled workers n the economy, the budget share devoted to manufactures and agrcultural land rent. Consder trade freeness. s stressed n theores of new trade and economc geography and borne out n practce, trade cost reductons are mportant stmul for ncreases n per capta 3 hbayama and Fraser (2014) s smlar n sprt. They consder a closed economy and hghlght nonhomothetc utlty and thus abstract both from space and from trade. 3

7 ncomes. We show that total emssons exhbt an nversely U-shaped behavor n the agglomeraton-deglomeraton process, because emssons from manufacturng, commutng and housng ncrease under agglomeraton but decrease wth redsperson. It s also nterestng to note that, across the scenaros wthout and wth moble sklled labor, agglomeraton per se s typcally not a boon for the envronment, as total emssons n the total cty system are lkely to rse. We also address the relatonshp between polluton and welfare and we fnd that the welfare maxmzng allocaton need not concde wth the polluton mnmzng allocaton. Prevous lterature. Our paper s related to the followng strands of prevous research. Frst, there s a recent lterature whch has started to explore the nexus between urban growth and the envronment both theoretcally and emprcally. Gagné, Rou and Thsse (2012) develop a model of an urban system wth two ctes and extensons around a central busness dstrct n order to hghlght that a compact cty may not necessarly be envronmentally-frendly when locatons are endogenous and general equlbrum effects are taken nto account. Our model s related to ther model but dffers n two key respects. Frst, the lot sze s fxed n Gagné et al. (2012) whereas we allow t to be endogenously determned. We see two advantages of our specfcaton: t agrees wth emprcal evdence and t allows us to study how the compactness of ctes responds to key parameters. econd, we follow the new economc geography n consderng an ncreasng returns manufacturng ndustry whch produces a varety of dfferent goods whereas ther model has a homogeneous good. Further, we study more polluton sources whch makes our framework n prncple useful for quanttatve analyss of the relaton between urbanzaton and polluton and for detaled polcy analyss. Tscharaktschew and Hrte (2010) develop a spatal general equlbrum model of a sngle polycentrc cty and calbrate t to an average German cty n order to explore the effects of emsson taxes and congeston charges on land-use and emssons. Ther focus on a sngle cty allows them to consder numerous urban detals whch we delberately abstract from n order to zoom n on an urban system consstng of two ctes of endogenous sze. Glaeser and Kahn (2010) provde an mportant emprcal study whch obtans evdence supportng the vew that mercan urban development s envronmentally-frendly n the sense of beng energy-effcent and carbon savng. Larson et al. (2012) provde related smulaton analyss based on an Urban Energy Footprnt Model whch allows them to capture ntrcate and often unexpected feedback and rebound effects of energy polces that work through the urban land market. 4 4 ee also Borck (2014) and Larson and Yezer (2014). 4

8 econd, a small lterature has addressed the nterface between the envronment and agglomeraton from the pont of vew of the new economc geography. Calmette and Péchoux (2007) set up a sutable extenson of the core-perphery model and study the mplementaton of an emsson quota. They show that the quota reduces the envronmental externalty n the aggregate but ths comes wth the unexpected sde-effect that agglomeraton s nduced at hgher trade costs, already, whch drves up envronmental damage. Elbers and Wthagen (2004) study the non-cooperatve strategc choce of an envronmental polcy wthn a smlar model and fnd that ths stablzes the symmetrc equlbrum. Lange and Quaas (2007) use a footloose entrepreneur verson of the core-perphery model to analyze how the dstrbuton of economc actvty n space s affected by local envronmental polluton. They fnd that the extent of envronmental damages determnes whether symmetry, partal or full agglomeraton of economc actvty n space obtans. Followng standard practce n the new economc geography, these works gnore urban extensons and urban costs altogether, features that we hghlght n our analyss. nother dfference s that these works do not allow the envronmental externaltes to be global. Thrd, our paper s related to the research on the Envronmental Kuznets curve whch was ntated wth the emprcal work by Grossman and Krueger (1993, 1995) and whch s surveyed n Dasgupta et al. (2002). systematc theoretcal exploraton and synthess of the foundatons of the EKC and ts relaton to nternatonal trade was then provded by Copeland and Taylor (2003). recent strand of research has begun to explore the EKC from the pont of vew of ctes and urban systems (Kahn 2006; san Development Bank 2012). Fnally, there are two recent works whch hghlght the nterface between ctes and the envronment from altogether dfferent angles. Cruz and Taylor (2013) explore the role of renewable energy sources whch dffer n the energy ntensty for the sze and densty of urban agglomeratons. Desmet and Ross-Hansberg (2015) set up a dynamc spatal model whch allows for trade costs, nnovaton and technology dffuson over space to study the mpact of clmate change on the spatal dstrbuton of economc actvty, trade and mgraton patterns as well as productvty and welfare. The remander of the paper s organzed as follows. ecton 2 sets up the model and characterzes the short-run equlbrum, where the allocaton of labor across ctes s gven. ecton 3 establshes the determnants of polluton and per capta ncome and explores the potental of an urban EKC n ths short-run equlbrum. It also addresses the queston whether bg ctes are desrable from an envronmental pont of vew. The endogenous formaton of the 5

9 cty system n the long-run where sklled labor s moble across ctes s explored n secton 4. That secton reexamnes the determnants of polluton and per capta ncome and the ensung potental of an urban EKC under these crcumstances. The relatonshp between envronmental polluton and welfare s also explored. ecton 5 concludes. 2 The Model The urban-geography setup. The economy conssts of two ex-ante dentcal ctes (, j = 1, 2 ) wth central busness dstrcts (CBDs) and spatal extensons as n lonso (1964) and wth ntercty nterrelatons as n the core-perphery model of Krugman (1991). 5 There are two producton sectors, manufacturng ndexed by M, and agrculture ndexed by, whose outputs are traded across ctes. Tradng the agrcultural good s costless, whle trade of manufactures s subject to ceberg costs. There are L workers wth dentcal preferences and unt labor endowments. The fracton ρ of workers are sklled (denoted ) and λ denotes the share resdng n cty 1. We take λ as gven n the short-run. In the long-run the sklled are moble between ctes and exhbt taste heterogenety for the two locatons as n Tabuch and Thsse (2002) and Murata (2003). The sklled lve around the CBDs and commute to work n manufacturng. Commutng costs are of the ceberg type. Ths mples that the effectve labor supply of a sklled worker shrnks wth the dstance to the workplace. 6 The fracton 1 ρ of workers are (unsklled) farmers (denoted U ). They are equally dstrbuted among and mmoble across ctes and engaged n agrcultural producton. Farmers lve outsde the ctes boundares and don t commute. They collect the land rent n each cty. 7 The producton of the two types of goods, the transport of goods across ctes, commutng and housng consumpton are assocated wth global envronmental externaltes, greenhouse gas (GHG) emssons, whch harm households. We now characterze preferences and the equlbrum wthn and across ctes. Preferences and demand. Consumers of type h= U, n cty have utlty ( ) u = µ ln C + γ ln C + 1 µ γ ln C κe θ (1) h h h h M, H,, h CM, = c v dv σ/ ( σ 1) N+ Nj h( ) ( σ 1/ ) σ (2) 0 5 Our framework bulds on Tabuch (1998) and Krugman and Lvas Elzondo (1996). 6 Ths follows Krugman and Lvas Elzondo (1996) and mples that the mass of frms and varetes s larger when economc actvty s dspersed rather than agglomerated n space (see Murata and Thsse 2005). 7 The reason for ths assumpton s that the land rent does not nfluence sklled workers bd rents whch makes the nternal cty equlbrum analytcally solvable. 6

10 h where 0 < µγ,, µ + γ< 1, κ 0, θ > 0 are constants, C M, s consumpton of a manufacturng h h composte, C H, s consumpton of housng (lot sze), C, s consumpton of agrcultural goods, and E s global polluton, the sources of whch are descrbed n detal at the end of ths secton. N and h N denote the masses of varetes, ( ) j the elastcty of substtuton between any two varetes. The budget constrant of household h s gven by where h c v s consumpton of varety v, and σ > 1 s ( ) y = P C + P r C + C (3) h h h h h M, M, H, H,, ( σ ) N 1/ 1 + Nj 1 σ ( ) (4) 0 PM, = p v dv y s the ncome (net-of-commutng cost f applcable), P M, s the prce ndex for manufactures and p ( v ) s the consumer prce of varety v whch ncludes ceberg trade costs τ > 1 h when goods are mported from cty j. P ( ) H, r s the prce of housng at dstance r from the CBD. The agrcultural good s the numérare. sklled worker who lves r klometers from the CBD ncurs commutng costs whch reduce her unt labor endowment by ψ r, where < <. Hence, y ( 1 ψ ) 0 ψ 1/ r = r w, where w s the sklled wage. Farmers lve outsde the cty, don t commute, and collect proportonate shares of the cty s land rent B. Hence, a farmer s ncome s y U = w U + b where w s the unsklled wage and ( ρ ) U b B 1 L/2. Utlty maxmzaton mples demand functons and ndrect utlty h V gven by: C h M, µ y P h h σ 1 =, ( ) ( ) M, σ h M, µ c v = p v P y (5) C h H, γ y h =, C h, ( 1 µ γ) P ( r) H, h = y (6) h ( ) V = log y µ log P γ log P r κe θ (7) h h h M, H, Cty structure. The cty s lnear and extends from the CBD to r b, the endogenous cty border (we focus on the rght sde of the cty only). Fg.2 depcts ths border, the bd rent for land of sklled workers ( ) P r (derved below) and the exogenous agrcultural land rent, R > 0. By H, 7

11 assumpton, R has to be pad per unt of land outsde the cty border by all farmers. Hence, U farmers lve on equal lots of sze ( ) / log v γ w + b R as mpled by eq. (6). Usng the redefnton V together wth y = ( 1 ψ r) w and solvng eq. (7) gves a sklled workers bd rent, the maxmum amount a sklled worker lvng r km from the CBD would pay per unt of land: κ / γ µγ / ( ) = ( ) ( ψ ) E θ 1/ γ 1/ H, M, 1 γ P r e P v r w (8) Ths bd rent declnes wth dstance from the CBD to compensate for hgher commutng costs. Fg. 2: Intra-cty equlbrum, cty 1 The cty equlbrum s defned by two condtons whch determne the spatal equlbrum value of ndrect utlty for the sklled v and the cty border r b condtonal on R and on sklled wages w, the manufacturng prce ndex P M,, global envronmental externaltes E and the number of sklled workers n cty, equlbrum (whch we characterze n secton 4): L = λρl, all of whch are determned n the nter-cty κ / γ µγ / ( ) ( ) ( ψ ) E 1/ 1/ H, b = θ γ M, 1 γ b = P r R e P v r w R (9) L 0 H, ( ) ( ) ( 1 ψ ) θ κe / γ µγ / 1/ γ 1/ γ 1/ γ rb 1 e PM, v w rb w = dr = (10) C ψ w Eq. (9) states that at the cty border, the bd rent of the sklled workers equals the agrcultural rent R. Eq. (10) says that, gven ther housng demands, the sklled workers ft nto the area between the CBD and r b. olvng these two equatons gves 8

12 v r w = (11) θ κ E e µ γ PM, PU, b γ 1 R 1 = ψ P U, where PU, R+ ψ Lw (13) (12) s a measure of urban costs whch rses wth the agrcultural land rent and commutng costs and also wth the number of sklled workers and the sklled wage, whch drve up urban land rent. Utlty of sklled workers n cty s ncreasng n sklled wages but decreasng n polluton, the manufacturng prce ndex and urban costs, summarzed by P U,. Eq. (12) reveals the repercussons on cty structure. In lne wth the standard lonso model, we fnd that ctes expand spatally when agrcultural land rent or commutng costs fall, and when the sklled work force and the wage of the sklled rse. In the followng, we use D ( r) 1/ C ( r) the densty of sklled workers at dstance r from the CBD. to denote H, Producton and short-run nter-cty equlbrum. The agrcultural good s produced by farmers under perfect competton wth a unt labor requrement, X = L. nce ths good s U the numérare, the wage of farmers s equal to one, w = 1. The manufacturng sector uses sklled labor to produce dfferentated goods under ncreasng returns and monopolstc competton. There s a fxed requrement of α unts of sklled labor and a varable requrement of β unts of sklled labor per unt of output. Total cost for a frm producng varety v s: ( ) = α + β ( ) TC v w x v (14) It s well-establshed that mll prcng apples n the Dxt-tgltz framework. Let p ( ) the producer prce at mll. Then we can wrte frm profts as: ( ) ˆ ( ) ( ) ˆ v denote π v = p v βw x v αw (15) Market clearng commands that producton equals domestc and foregn demand nclusve of the ndrect demand assocated wth the ceberg trade costs, ( ) ( ) τ ( ) x v = d v + d v (16) j σ σ 1 where d ( v) = pˆ ( v) P µ Y and ( ) ˆ ( ) M, 1 ( ) σ σ, d v = τ p v P µ Y from eq. (5). j M j j 9

13 Cty s ncome comprses the land rent and the (net-of-commutng cost) wage ncomes of the r b sklled and unsklled, Y= wl + ( ρ ) L + B where ( )( 1 ψ ), 1 /2 eff effectve supply of sklled labor. L, eff falls short of shown that ( ) 1 + γ = 1 / / ψ ( 1+ γ) L D r r dr s the, eff 0 L because of commutng costs. It s easly L eff, R P U, P U, w (see ppendx 1). nce consumers spend the share γ of ther ncomes on housng, we have B = γy. olvng for Y, cty s ncome s: 1+ γ 1 L 1 P U, R L Y = wl, eff + ( 1 ρ) = 1 + ( 1 ρ) 1 γ 2 1 γ ψ ( 1 γ) P + U, 2 (17) Normalzatons. Followng Fujta et al. (1999: 54f.) we normalze the unts of measurement for output such that the margnal labor requrement satsfes ( ) β = σ 1/ σ and we set the fxed nput requrement at α = µ / σ. 8 Proft maxmzng producer prces n cty then are ( ) pˆ v = w (18) Imposng the condton of long-run zero profts mples that operatng profts just equal fxed costs. Usng producer prces (18) n eq. (15) entals that the equlbrum output s: ( ) The assocated labor nput s l ( v) x ( v) x v = µ (19) = α + β = µ. Labor market equlbrum requres that labor demand, Nl = Nµ, s equal to the effectve supply of sklled workers, L, number of frms s gven by: eff. Hence, the N 1+ γ 1 PU, R = 1 µψ ( 1+ γ ) w P U, The number of frms feeds nto the prce ndex n cty whch, usng eq. (18), s: (20) where 1 0 φ τ σ ( ) φ ( ) P = N w + N w M, j j s a parameter of trade freeness. Usng market clearng (16), demand (5) and prcng (18) we fnally obtan two nterdependent manufacturng wage equatons (21) 8 Ths mples that when we change the parameter µ, we also change the fxed cost parameter α, due to our normalzaton. However, we have performed all ensung comparatve statcs exercses also wthout ths normalzaton and the results are qualtatvely the same. 10

14 1 σ 1 σ 1 = σ M, + jφ M, j w YP Y P (22) whch, upon substtutng prce ndces, frm numbers and ncomes from (21), (20) and (17), mplctly pn down the wages of the sklled n the two ctes, w 1 and w 2, and then all other endogenous varables n the short-run equlbrum, where λ s gven. 3 The cty system and polluton n the short-run Ths secton characterzes the sources of polluton and studes ther determnants n a system of two tradng ctes of exogenously gven szes,.e. where λ s gven. 3.1 Polluton Global polluton E s due to local emssons E and j E j and takes the form E = E + E (23) We consder fve polluton sources. There are emssons from the producton of manufacturng and agrcultural goods. Intra-cty commutng and shppng of goods across ctes produces emssons from transport by cars, trucks etc. Fnally, housng produces emssons from energy use due to electrcty, heatng and ar condtonng. Total polluton generated n cty s: E = δ X + δ X + δ Ψ + δ T + δ H (24) We take the emsson ntenstes δ1, δ2, δ3, δ4, δ 5 > 0 as exogenously gven and unform across ctes. nce the output per manufacturng frm s constant (by eq. (19)), producton of manufacturng goods, X = Nx, s essentally determned by the number of manufacturng frms (20), whch tself depends on the effectve supply of sklled labor n the cty. Hence, polluton from manufacturng producton s a functon of local sklled wages and urban costs: 1+ γ 1 P U, R X = Nx = L, eff = 1 ψ ( 1+ γ) w P U, (25) Producton of agrcultural goods s determned by the local number of unsklled workers: ( ρ ) r b Total commutng dstance travelled n cty s ( ) X = L = 1 L/2 (26) Ψ = r D r dr, hence (see ppendx 1): 0 γ Ψ = γ γ ( PU, R) R( 1 PU, R ) ( 1+ ) 11 2 γ ψ w (27)

15 Polluton from commutng n a cty depends on commutng costs, local sklled wages, and urban costs, all of whch nfluence commutng through changes n urban structure. Followng the concept of the ecologcal footprnt (e.g. chele and Felbermayr 2012) we count the externaltes resultng from the mport of goods as part of the emssons generated by the mportng cty. The goods that are transported to cty may consst of manufacturng mports, N τd = N φ pˆ P µ Y, and/or of mports of the agrcultural good whch amount to the σ σ 1 j j j j M, excess of demand over local producton, ( µ γ) Y ( ρ) 1 1 L/2. Even though trade n the agrcultural good s costless, we assume that resdents consume locally produced goods unless demand exceeds supply, so there s no trade of agrcultural goods n a symmetrc equlbrum. Usng (18), (20), (21) and Nµ = L, eff, cty s mports are: T σ ( j ) j, effφµ σ ( ) + φ ( ) w L Y L = + max 0, ( 1 µ γ) Y ( 1 ρ) L w L w σ, eff j, eff j (28) Fnally, aggregate housng r b sklled, ( ) 0 ( ρ ) C D r dr = r H, b H n cty reflects the aggregate housng consumpton of the, plus the aggregate housng consumpton of the unsklled, U U CH, 1 L/2. ubsttutng the cty border, eq. (12), and C H, from eq. (6) and usng ( ρ) b 1 L/2= B = γy as well as (17) we obtan: H γ 1 R γ L 1 ( 1 = + ρ) + γwl, eff ψ P U, ( 1 γ) R 2 (29) Polluton from housng depends on the ncomes of the unsklled and sklled, on agrcultural land rent, as well as on commutng costs and urban costs. Hgher commutng costs ψ lead to lower housng consumpton. The (seemngly counterntutve) postve relatonshp between the measure of urban costs P U, and aggregate housng consumpton s explaned by the fact that ths measure of urban costs rses wth wages and the sklled populaton. Before proceedng, note that the fve sources of local polluton characterzed n eqs. (25) - (29) are fully determned by the dstrbuton of sklled workers and the wages of the sklled, w j, whch by (22) themselves depend on λ. w and 12

16 3.2 The determnants of polluton and per capta-ncome We now explore how the cty equlbrum and the polluton sources are affected by key parameters. We consder the short-run equlbrum where sklled labor s mmoble across ctes and where ther share n cty 1 s fxed at symmetry, λ = 1/2. The model then mples that there s balanced ntra-ndustry trade of manufactures and no trade of the agrcultural good. 9 Imposng ths symmetry assumpton on the wage equatons (22) and usng (13), (17), (20), and (21) we obtan an equaton for the symmetrc manufacturng wage w = w = w : j ( R ψw ρl ) ( 1 )( 1 ) ( ) 1+ γ R + R + ψw ρ L µ γ µψ γ ρ L + /2 1 = /2 1 2 (30) Eq. (30) s a non-lnear equaton n w whch has no closed-form soluton. 10 However, t s easly shown that t has a unque soluton. We resort to numercal analyss to explore how the exogenous parameters affect the varous polluton sources, total emssons and per capta ncomes n the two ctes and the cty system. Here and below we use the followng baselne parameters: R = 0.275, ψ = 0.025, µ = 0.475, γ = 0.22, ρ = 0.5, L = 4, σ = 4, ξ = , δ 1 = 0.84, δ 2 = 0.81, δ 3 = 1.48, δ 4 = 1.48 and δ 5 = We defne cty s real ncome per capta r y as the weghted average of the real ncomes of the r, sklled, y w / ( P µ M, P γ ru, = U, ), and the unsklled, y 1/ ( P µ M, R γ ) ( ρ) ( ρ) =. Hence, r r, ru, y = L y + 1 Ly /2 / L + 1 L /2. Per capta real ncome n the total cty r r, r, ru, ru, system s = + j j + ( ρ ) ( + j ) y Ly Ly 1 L y y /2 / L. Note that L = λρl= ρl/2 n the symmetrc equlbrum that we consder here. We summarze our fndngs n Table 1. n nspecton of ths table reveals that a number of key parameters mpact on the varous polluton sources ether n the same qualtatve way, or n a neutral way, so that the effect on total emssons (both per cty and for the total cty system) s unambguous. Notce that the drect effect of the varous parameters and the ndrect effect stemmng from the wage reacton obtaned from eq. (30) s taken nto account. 9 Pflüger (2001) provdes an early analyss of the trade-envronment nterface n the Krugman-Dxt-tgltz model. 10 The urban sector s the reason why there s no closed-form soluton. In fact, wthout ths sector, the (effectve) sklled work force s L, the number of frms s N = L / µ and we would have R = 0 and B = 0, so that the short-run equlbrum characterzed n secton 2 s dentcal to Krugman s CP-model. Under these crcumstances and the normalzaton ρ = µ, the wage equaton can be solved to yeld w = 1 (see Fujta et al. 1999, chapter 5). 11 s noted n the Introducton, parameters are chosen to replcate the allocaton of greenhouse gas emssons to polluton sources n Fg

17 For example, an ncrease n trade freeness φ leads to more trade (mports) and therefore to more emssons. n ncrease n commutng costs ψ reduces housng consumpton, ntra-cty commutng dstances, manufacturng producton (through the reducton n effectve labor supply) and mports, so that total emssons also fall. n ncrease n populaton affects all polluton sources and, hence, total polluton, n a postve way. Changes n the elastcty of substtuton, σ, have no drect effect on polluton. Table 1: Emssons and per capta ncomes n the symmetrc short-run equlbrum φ ψ R L ρ µ γ σ emssons of cty manufacturng producton agrcultural producton ntra-cty commutng housng mports total emssons per cty overall emssons per capta ncomes cty = cty j = total system Note: The table documents the effects of an ncrease of the respectve parameter on emssons and per capta ncomes (+ = postve effect; - = negatve effect; 0 = no effect; hump shape (non-monotonc); ntal stuaton s the symmetrc equlbrum of the two-cty system. ll effects are obtaned from numercal smulatons wth parameters at ther baselne level descrbed n the text. The other parameters affect the varous polluton sources dfferently. For example, an ncrease n the share of the sklled populaton ρ rases manufacturng producton and mports, but reduces polluton from agrcultural producton, ntra-cty commutng and housng. These latter forces domnate n our baselne scenaro, so that emssons fall. The same holds true for an ncrease of R. The mpact of both the parameter µ and the parameter γ s just the opposte. part from these dfferences, table 1 reveals a strkng regularty between emssons and per capta ncomes that we summarze n Result 1 (polluton and per capta ncomes n symmetrc short-run equlbrum). Consder the symmetrc short-run equlbrum ( λ = 1/2). Increases n the parameters φ, L, µ, and γ have a postve mpact on total emssons and per capta ncomes, whlst ncreases n ψ and have a negatve mpact on both. Increasng σ reduces per capta ncomes but has no mpact on emssons. Increasng ρ reduces total emsson and ncreases per capta ncomes at low levels of ρ but mpacts negatvely on both at hgh levels. R 14

18 Importantly, result 1 mples that n ths system of symmetrc tradng ctes most parameter changes that nduce ncreases n per capta ncomes have a postve mpact on total emssons, too. To put t dfferently, no market-nduced Envronmental Kuznets Curve s mpled by any of these parameter changes. No EKC s borne out by changes n the substtuton parameter ether, snce σ only affects per capta ncomes but not emssons. n excepton obtans for an ncrease n ρ whch has a non-monotonc effect on per capta ncomes but mples that total emssons fall unambguously. Increasng the share of sklled workers drves down sklled wages, manufacturng prces and urban costs. Our smulatons show that the latter two forces domnate at low levels of ρ whereas the fall n wages domnates at hgh levels. Hence for a range of low values of ρ per capta ncomes rse as emssons fall. However, we show n sectons 4.2 and 4.3, that, for a number of reasons, an urban EKC may appear n the long-run equlbrum where sklled labor s moble and the cty system evolves endogenously. 3.3 Bg versus small ctes o far we have looked at ctes of equal sze ( λ = 1/2). n mportant ssue s whether bg ctes are desrable from an envronmental pont of vew: can t be benefcal to shft part of the sklled populaton such that the cty system has a large (core) cty and a small perpheral cty? Ths secton explores how the varous emsson sources are affected by shftng λ beyond ½ such that cty 1 exogenously becomes the core. Table 2 summarzes our fndngs. Table 2: Evoluton of emssons n growng/declnng ctes cty 1 (emergng core) cty 2 total cty system emssons manufacturng producton agrcultural producton ntra-cty commutng housng mports total emssons Legend: The table documents the effects of an ncrease n λ beyond ½ such that cty exogenously becomes the core; + : postve effect; - : negatve effect; 0 : no effect. tart by lookng at cty 1. Increasng ts sklled populaton ncreases commutng dstances and, hence, the emssons from commuter transt. Manufacturng producton s rased even though the ncrease n the effectve supply of sklled labor falls short of the ncrease n λ snce part of ths ncrease s absorbed by commutng costs. Hence, emssons from manufacturng producton ncrease. Emssons from agrcultural producton are unaffected. Further, the populaton ncrease leads to an ncrease n total housng consumpton n cty 1, even though ndvdual lot 15

19 szes become smaller. Hence, there s an ncrease n emssons assocated wth housng. Total emssons from goods transported to cty 1 rse. t λ = 1/2 manufacturng trade s balanced and there s no agrcultural trade. When λ ncreases, the emergng core becomes a net exporter of manufacturng goods and starts mportng agrcultural goods to keep trade balanced. Hence, cty 1 s manufacturng mports fall. However, whle the value of net mports must equal the value of net exports, the ncrease n the quantty of agrcultural mports exceeds the decrease n the amount of manufacturng mports so that total mports rse. 12 Takng stock of all polluton sources reveals that (except for agrcultural producton), all emsson sources ncrease n cty 1. By the very nature of the exogenous shock that we analyze n ths secton, the effects on cty 2, the emergng perphery, (typcally) go n the opposte drecton to those we just descrbed for cty The effect on total emssons of both ctes taken together crucally depends on whether the emssons are concave, lnear or convex n populaton. For our baselne parameters we fnd the followng. Total emssons from commutng ncrease when the cty system swtches from symmetry to partal agglomeraton snce total commutng dstance can be shown to be convex n populaton. Emssons from housng are lower, however, snce housng consumpton s concave n the sze of the sklled workforce. mlarly, total emssons from manufacturng producton across both ctes are lower under partal agglomeraton: producton of each varety s unaffected (by eq. 19), but the number of goods falls as the effectve aggregate labor supply of sklled workers falls. Emssons from agrcultural producton are unchanged. Overall emssons from goods transport ncrease. 14 ggregatng the emssons from all sources we fnd that total emssons across the two ctes ncrease wth partal agglomeraton n our baselne scenaro. Hence, we have: Result 2. Consder an ncrease n the share of the sklled n cty 1 startng at symmetry ( λ = 1/2). For the baselne parameters we obtan the followng. () The emergng core has rsng emssons from commutng, manufacturng producton and housng. Its emssons from goods mports rse, ts emssons from agrcultural producton are unaffected. Total emssons rse. () The cty system comprsed of the two ctes experences ncreasng emssons assocated wth commutng and wth mports. Emssons from housng and manufacturng producton fall and the emssons from agrcultural producton reman constant. Total emssons ncrease n our baselne smulatons. 12 Ths holds true for small ncreases of λ = 1/2, startng from symmetry. 13 n excepton s goods transport: when λ rses above 1/2, cty 2 the emergng perphery mports more manufacturng varetes and ts total mports rse as well. 14 Our fndngs dffer from Gagné et al. (2012) who fnd that total transport s (always) lower wth agglomeraton, snce ther model has no mmoble workers to whom goods have to be shpped n the case of full agglomeraton. 16

20 The sgnfcance of these results derves from the fact that they contradct popular arguments whch mantan that lvng n bg ctes makes us greener by necessty. In fact, we fnd that the emergng core has rsng emssons and that the emssons n the total cty system ncrease as well. However, we should lke to stress that the fndng that agglomeraton (one bg cty) produces more emssons than dsperson (two small ctes) s not unambguous: manufacturng producton and housng are lower wth agglomeraton, whlst trade and commutng are hgher (table 2), so that the effect of agglomeraton on total emssons ultmately depends on the emssons ntenstes of these varous polluton sources. 4 Endogenous cty formaton and polluton We have so far addressed a system wth two ctes open to trade but wth fxed populaton sze. Ths secton allows for the endogenous formaton of ctes. 4.1 Moblty and long-run spatal equlbrum In the long-run sklled workers are moble and, by assumpton, exhbt heterogeneous locaton preferences as n Tabuch and Thsse (2002) and Murata (2003). sklled worker s utlty of lvng n cty s v + ε, where ε s a random utlty component whch s dentcally and ndependently dstrbuted across ndvduals accordng to a Gumbel dstrbuton wth mean zero and varance 2 πξ 2 /6. The parameter ξ 0 characterzes the dsperson of tastes. If ξ goes to zero, people choose ther locaton based on the ndrect utlty attached to that locaton, whereas when ξ goes to nfnty, they choose ther locaton at random. Followng the standards of dscrete choce theory, the probablty that a sklled worker chooses regon s Prob ( λ ) exp v ( λ) / ξ ( ) + v ( ) = exp v λ / ξ exp j λ / ξ (31) where v s gven by (11). The change n the sklled populaton s guded by the law of moton ( ) ( ) ( ) dλ/ dt = 1 λ Prob λ λprob λ (32) t an nteror long-run equlbrum, dλ / dt = 0. Usng (31) the equlbrum condton s where v ( λ) v ( λ) v ( λ). 1 2 λ v = 1 λ ( λ) ξlog 0 j (33) 17

21 Our model exhbts seven agglomeraton and dsperson forces whch can be characterzed wth reference to (33) and ndrect utlty (11). Consder a symmetrc equlbrum ( λ = 1/2) and assume that a small amount dλ of sklled workers s shfted from cty j to cty. Ths rases market sze and the sklled wage n due to the demand lnkage (market sze effect), but t also depresses the sklled wage n due to ncreased competton (crowdng), as n Krugman (1991). The nflow of sklled workers drves down the manufacturng prce level P, the supply M, lnkage of the core-perphery model. Urban costs assocated wth commutng ( P ) act as a U, dsperson force, just as n Tabuch (1998). By reducng effectve labor supply, ceberg commutng costs have a further dspersve effect. Ths lowers the mass of frms n agglomeratons and, hence, rases the manufacturng prce ndex n cty. Ths also lowers overall ncome, and wages n. nce the last term n (33) s decreasng n λ, taste heterogenety (expressed by the varance of the preference parameter dstrbuton) s a fnal dsperson force. nce we address a global externalty, greenhouse gas emssons and global warmng, envronmental polluton plays no role for the economy s bfurcaton pattern. 15 Due to the complexty of our model s urban sector whch nvolves an endogenous lot sze, no closed form soluton can be derved for the bfurcaton ponts. 16 We therefore contnue to use numercal smulatons to characterze the effects of the varous parameters. Fg 3: Bfurcaton dagram b r 1 Note: Fgure dsplays the bfurcaton dagram for our benchmark parameter values (see secton 3.2). Rasng trade freeness φ startng from autarky eventually nduces agglomeraton at φ b, the break pont, see fgure 3. The taste heterogenety of workers mples that ths agglomeraton process s smooth, stops before full agglomeraton n one cty s attaned, and reverses as trade 15 Ths s dfferent when envronmental externaltes are at least partly local, see e.g. Lange and Quaas (2007). 16 Ths s because there s no closed-form soluton for the sklled wage n the symmetrc cty system (secton 3). 18

22 freeness s contnuously ncreased, as n Tabuch and Thsse (2002). ymmetry s re-establshed at the redsperson pont φ r and contnues to be the only spatal equlbrum untl all trade costs are elmnated. 17 We summarze ths fndng n: Result 3 (symmetry breakng). Rasng trade freeness φ successvely from 0 to 1 yelds an nversely U-shaped curve of stable locaton equlbra. gglomeraton emerges at the break pont φ b and symmetry attans agan at the redsperson pont, φ r We use numercal smulatons to descrbe how the break and redsperson ponts are affected by parameter changes. Our fndngs are summarzed n: Result 4 (comparatve statcs of the bfurcaton ponts). Usng numercal analyss we fnd: there s less agglomeraton ( φ b ncreases and φ r decreases) when, () economes of scale decrease (σ rses), () the expendture share for manufactures µ falls, () commutng costs ψ rse, (v) taste heterogenety ξ rses, (v) populaton sze L ncreases, (v) the sklled populaton share ρ rses, or (v) agrcultural land rent R falls; (v) the effect of γ s ambguous: more agglomeraton ( φ b decreases and φ r ncreases) for low values of γ and less agglomeraton ( φ b ncreases and φ r decreases) for hgh values. Results 4() - 4(v) accord wth prevous fndngs. Reducng the elastcty of substtuton σ (an nverse ndcator of returns to scale n zero proft equlbrum), and rasng the budget share devoted to manufactures (and hence both market sze and trade cost savngs) enlarges the range of trade costs where agglomeraton s a spatal equlbrum, as n Krugman (1991). Increasng commutng costs ψ or the varance of the dstrbuton of the taste parameter ξ, works n favor of dsperson,.e. t rases the break pont and reduces the redsperson pont, as found by Tabuch (1998) and Murata and Thsse (2005) for commutng costs, and by Tabuch and Thsse (2002) and Murata (2003) for taste heterogenety. Results 4(v) - 4(v) are novel and therefore deserve some comments. Increasng L works n favor of dsperson whereas t has no effect on the bfurcaton pattern n standard core-perphery models (Fujta et al. 1999; Forsld and Ottavano 2003; Pflüger 2004). Ths dfference s due the urban extenson n our model. Even though several of the agglomeraton and dsperson 17 Ths depends crucally on the taste heterogenety of sklled workers. Wthout taste heterogenety, we get the same agglomeraton pattern as n Tabuch (1998): dsperson for low or hgh trade freeness, catastrophc agglomeraton wth full agglomeraton for ntermedate values of φ. When ξ s very large, we get dsperson for all values of φ. Thus, we assume n the followng that ξ s nether too small nor too large. 19

23 forces are affected by a change n populaton sze (and partly so n opposte drectons), the domnant effect s that an ncrease n L drves up the urban costs assocated wth a relocaton of sklled labor. 18 Ths can be seen by notng that, at a gven wage, dp, / dλ = ψρlw > 0 from (13). Ths effect corresponds to the fndng n the standard urban model that an ncrease n populaton sze causes sngle closed ctes to expand spatally and to provde lower utlty (e.g. Brueckner 1987). It mples that lvng n a small cty becomes more attractve and more so, the larger total populaton. Result 4(v) shows that ths drect dspersve force domnates even after all further general equlbrum repercussons on wages, prces, ncomes, the cty border and the amount of commutng have played out. Increasng the share of the moble (sklled) populaton, ρ, reduces the range of trade freeness where agglomeraton s stable (result 4(v)) - smlarly to an ncrease of the overall populaton. The key mechansm that drves ths result s the magnfcaton of urban costs: the response of P U, to λ s magnfed by ρ just as by L (see above). n ncrease n the agrcultural land rent R leads to a larger range of trade freeness where agglomeraton s stable (result 4(v)). Whle urban costs P U, rse wth R, there s no drect effect from R on the agglomeraton force mpled by urban costs (.e. dpu, / dλ = ψρlw s only ndrectly affected by R va the wage). However, an ncrease n the exogenous land rent forces a cty, ceters parbus, to become smaller, just as n the standard urban model. Hence, there s less commutng and the loss n the effectve labor supply that goes along wth a relocaton of sklled labor must then be smaller. Ths, n turn, mples that the agglomeratve demand lnkage (ncome shft) and supply lnkage (trade cost savngs) become stronger. Even though the competton effect s also strengthened and there are further general equlbrum effects, the magnfcaton of the agglomeraton forces domnates, as result 4(v) reveals. The lterature usually fnds that ncreasng the budget share devoted to housng γ works n favor of dsperson,.e. t rases the break pont and lowers the redsperson pont (see e.g. Tabuch (1998), Murata and Thsse (2005) and Pflüger and üdekum (2008). Our smulatons U 18 The other effects are the agglomeratve supply lnkage, ( dpm, / dλ < 0), whch s strengthened because, at gven wages, the effectve supply of labor L, eff ncreases when L rses, so that the relocaton of frms brngs dw / dy dy / dλ > 0, and stronger cost savngs. From (22) we can conclude that both the demand lnkage, ( )( ) the competton (crowdng) effect, ( M, )( M, ) 20 dw / dp dp / dλ < 0 are also strengthened as L goes up.

24 show that n our present model ths holds true only at hgh levels of γ whereas the nverse obtans for low levels. 4.2 The evoluton of emssons and per capta ncomes We are now n a poston to analyze how emssons and per capta ncomes are affected by parameter changes when the cty system s allowed to evolve endogenously. We characterze the effects assumng that cty 1 becomes the core when an agglomeratve process unfolds. Graphcal llustratons of our numercal results are provded n tables 3, 4 and 5. We hghlght the parameters that are partcularly prone to exhbt secular changes, namely trade costs, commutng costs and populaton sze. The effects of all other parameters are then dscussed more brefly. No matter whch parameter s concerned, we wll see n the followng that any parameter change that nduces agglomeraton, drves up total emssons of the cty system whereas total emssons fall durng redsperson, as shown above n ec [Table 3 about here] Trade freeness. Increasng the degree of trade freeness φ from autarky to costless trade mples that the cty system swtches from dsperson to (partal) agglomeraton and back to dsperson (see Fg.3 and Table 3). Cty szes are equal under dsperson, r 1b = r 2b, but become ncreasngly dfferent as agglomeraton unfolds, r 1b > r 2b. Real ncome per capta ncreases n cty 1 for two reasons: fallng trade costs mply that real ncome ncreases as long as economc actvty s dspersed. When agglomeraton s nduced at the break pont there s an addtonal boost to real ncome whch ncreases strongly and then falls n the redsperson process. The ongong reducton n trade costs causes cty 1 s real ncome to rse further, however. Cty 2 s real ncome per capta develops n parallel wth cty 1 when there s symmetry, but exhbts a U-shaped development as agglomeraton and redsperson take place. Per capta ncome of the total cty system ncreases throughout the reducton of trade freeness. Ths reveals that the ncome losses of the perphery are domnated by ncome gans of the core. The behavor of real ncome per capta n the two ctes can be traced back to ts components. The manufacturng prce level P M, falls n both ctes when symmetry s stable, but s nversely U-shaped (Ushaped) n cty 1 (cty 2) as agglomeraton and redsperson occur. Urban costs P U, and sklled wages w are only affected when the process of agglomeraton and redsperson unfolds: urban costs exhbt an nversely U-shaped behavor n the core cty and so do wages, after an ntal dp at the break pont, whereas the opposte apples for cty 2. 21

25 Total emssons n both ctes rse wth φ under symmetry. The emssons n the core rse strongly as agglomeraton unfolds, but the redsperson of economc actvty brngs back emssons, whereas cty 2 experences a U-shaped development of emssons. Wth our baselne parameters the total emssons of the cty system ncrease contnuously under dsperson, but exhbt an nversely U-shaped behavor n the agglomeraton-deglomeraton process. Total emssons reflect the behavor of ts components: emssons from manufacturng, commutng and housng are constant n the symmetrc allocaton but ncrease as cty 1 becomes the core and vce versa. Emssons from the transport of goods ncrease n both regons and overall. Emssons from the agrcultural sector are not affected by trade costs. Commutng costs. steady reducton of commutng costs ψ nduces agglomeraton n cty 1. Ths cty expands at the bfurcaton but t also experences contnuous per capta ncome growth before and after that. Per capta real ncome n the emergng perphery grows untl the bfurcaton occurs where t then strongly falls (see table 3). Overall, there s an expanson of real ncome per capta n the total cty system. Key components of real ncome evolve as follows. Both the emergng core and the emergng perphery experence a secular fall n urban costs. There s a transtory hke n the cty whch becomes the core. The manufacturng prce ndex n ths cty falls steadly, but strongly so at the bfurcaton. The perphery experences a strong ncrease n manufacturng prces after an ntal perod of slowly fallng prces. Total emssons of the cty system ncrease steadly as commutng costs fall but more strongly so at the bfurcaton, whch reflects the strong ncrease of emssons n the emergng core whch domnates the declne of emssons n the perpheral cty. The strong ncrease of emssons n the emergng core tself reflects strong ncreases of emssons from all sources except from agrcultural producton whch s not affected by commutng costs. Populaton sze. Increasng total populaton L leads to dsperson of sklled workers (result 4(v)). s shown n table 3, when populaton ncreases, per capta real ncomes ncrease, both for sklled and unsklled workers (whether sklled workers are agglomerated or dspersed). Whle urban costs ncrease, manufacturng prces fall strongly and sklled wages develop nversely U-shaped (U-shaped) n the core (the perphery). On net, real ncomes per capta are ncreasng. The effects on polluton are straghtforward. s populaton sze ncreases, total polluton ncreases, as the producton of goods ncreases, goods transport ncreases when ndustry s dspersed, people have longer commutes, and total housng consumpton ncreases. Wth agglomeraton, goods transport falls (the core mports less wth rsng populaton whle the perphery mports more, and total mports fall). In summary, total polluton rses wth populaton sze. However, ths does not necessarly mply that per capta polluton rses wth 22

26 populaton sze. In our smulatons, we fnd that commutng ncreases per capta, agrcultural producton stays constant, and goods transport, housng as well as manufacturng producton decrease per capta wth rsng populaton. 19 For our benchmark parameters, total emssons per capta rse wth rsng populaton sze, however. [Table 4 about here] grcultural land rent. The agrcultural land rent s an exogenous ndcator of the opportunty cost of land. In one nterpretaton t can thought to be a polcy nstrument to control the boundares of ctes. gglomeraton s nduced when R ncreases (result 4(v)). Real per capta ncomes n both ctes fall, and more so n the emergng perphery (see table 4). Ths fndng s due to the fact that hgher R exerts drect pressure on urban costs (see eq. 13). There are also forces that stablze real ncome n the emergng core (hgher wages, lower manufacturng prces n the agglomeraton process). However, these effects are domnated by the ncrease n urban costs, and even more so n the emergng perphery. Overall, the ncome per capta n the total cty system falls steadly. Total polluton of the cty system falls as ncreases. Ths effect s due to decreasng emssons n both ctes before the bfurcaton takes place and t contnues to hold as the steady fall of the perphery s emssons domnate the hke that the emergng core (ntally) experences when agglomeraton unfolds. The bengn development of emssons s n essence caused by decreasng emssons from housng consumpton and commutng assocated wth smaller and more expensve ctes, whereas emssons from manufacturng producton and from the transport of goods work n the other drecton. klled worker share. Next, consder a rse n the share of sklled workers, ρ. Ths puts pressure on urban costs and nduces redsperson of the cty system (result 4(v)). The concomtant change n per capta ncomes n the core (perphery) s nversely U-shaped (Ushaped) untl the two ctes are of equal sze and then exhbts an nversely U-shaped pattern (see table 4). The evoluton of per capta ncome n the total cty system s also nversely U- shaped. These outcomes reflect a nuanced nteracton of components. hgher share of sklled workers mples lower wages both n the core and n the perphery, but also lower manufacturng prce ndces (reflectng the fact that the number of avalable varetes rses as ρ s ncreased) n both locatons and fallng (rsng) urban costs n the core (perphery). Total emssons of the R 19 Goods transport per capta decreases wth populaton sze under symmetry, and frst ncreases, then decreases n the range of partal agglomeraton. 23

27 cty system fall when the share of sklled workers rses snce the fall of emssons n the emergng core s stronger than the rse of emssons n the perphery. When economc actvty s fully dspersed, emssons n both ctes fall as ρ s ncreased. These results are prmarly due to lower emssons from transport, lower emssons from housng consumpton n the core (whch falls as urban costs rse) and due to a strong fall n emssons from agrculture due to the mpled fall n the share of unsklled workers. Budget share of manufacturng. n ncrease n the budget share of manufacturng boosts the mportance of ths sector and nduces agglomeraton (result 4()). Real ncomes evolve nversely U-shaped (U-shaped) n the core (perphery). The per capta ncome n the total cty system develops n an nversely U-shaped way (see table 4). Our smulatons reveal that sklled wages rse n the core and the perphery and so does the manufacturng prce ndex. Moreover, urban costs rse strongly n the core and fall much less strongly n the perphery. Total emssons n the core (perphery) rse (fall) strongly at the break pont and then fall (rse) when redsperson sets n at hgh values of µ. Overall, total emssons are ncreasng due to rsng emssons from goods transport, producton of manufactures and housng consumpton and commutng n the core. [Table 5 about here] Locaton preferences. Parameter ξ expresses the dsperson of ndvdual tastes for locatons and t may also be nterpreted as an nverse measure of labor moblty. gglomeraton s nduced when ξ falls (result 4(v)). Real per capta ncome n the core (perphery) rses (falls) and the effect n the core domnates so that per capta ncome n the total cty system rses (see table 5). Emssons n the two ctes and n the overall cty system mmc the behavor of per capta ncome and, hence, also rse. Elastcty of substtuton. fall n the elastcty of substtuton σ mples that the economes of scale n manufacturng rse n zero-proft equlbrum and that agglomeraton s nduced (result 4()). Real per capta ncome n the core (perphery) rses (falls) and real per capta ncome n the total cty system rses, snce the effect n the core domnates (see table 5). Our smulaton reveals that the fall n the manufacturng prce ndex n the core s key for ths result. The core (perphery) experences ncreasng (decreasng) wages counteracted by an ncrease (fall) n urban costs. Total emssons n the emergng core ncrease n the agglomeraton process but fall n the perphery. The frst effect s stronger, so that emssons of the cty system rse. 24

28 The strong rse n emssons n the emergng core are due to hgher emssons from commutng, the transport of goods, manufacturng producton and from housng. Budget share of housng. The effect of an ncrease n the budget share of housng γ on the locaton pattern s non-monotonc (result 4(v)). We focus on the case where the level of γ s hgh enough so that further ncreases nduce dsperson. Then, real ncomes per capta rse both n the core and the perphery but more strongly n the former (see table 5). Hence, real ncome per capta across the two ctes s also steadly rsng. Emssons are ncreasng n both ctes (except for a dp at the break pont n the emergng perphery) and the total cty system. Takng stock of the effects of all parameter changes on total emssons and per capta ncome n the total cty system we have Result 5 (emssons and per capta ncomes). n ncrease n any parameter, except for the parameters φ, ρ and µ, nduces parallel movements n total emssons and per capta ncomes n the total cty system, ether postve ( L, γ ) or negatve (ψ, R,ξ,σ ). Increasng µ drves up total emssons and may ncrease or decrease per capta ncome. Increasng φ or ρ mples rsng per capta ncome but fallng emssons. 4.3 The possblty of an urban Envronmental Kuznets Curve The large lterature on the Envronmental Kuznets Curve (EKC) consders the possblty that emssons mght be nversely U-shaped n ncome. Here, we explore ths hypothess n the lght of our model. We hghlght the change of the trade freeness parameter φ. Fg. 3 shows how natonal real ncome per capta moves from 0 to 1 generatng rsng ncomes). r y and total emssons vary wth changng trade freeness (φ Fg. 3: n urban EKC wth rsng trade freeness e YR 25

29 s can be seen, a purely market nduced urban EKC arses as trade becomes freer over a certan range. The key to ths result s the fact that as trade gets freer, natonal real ncome steadly rses, but emssons are nversely U-shaped due to the agglomeraton and redsperson forces nduced by the changng trade freeness. We summarze ths fndng as: Result 6 (Urban EKC). s trade freeness ncreases, a market-nduced urban EKC emerges: total natonal emssons and natonal ncome ncrease for φ < φb and φ > φr, but emssons are nversely U-shaped n natonal real ncome for φ [ φ, φ ]. b r Result 6 s of great sgnfcance, as t shows that an EKC may emerge n the cty system wthout any polcy nterventon. Moreover, ths EKC s based on ncreases n trade freeness whch have been a very mportant drver for the connecton of countres, regons and cty systems and for the rse of ncomes n the last decades, and whch have therefore been hghlghted by the New Economc Geography (Head and Mayer 2004). Three further parameter changes have the potental to rase real ncomes per capta and lower total emssons at the same tme, but matters are more complcated (see table 4). reducton n the agrcultural land rent range of ntermedate values of R s assocated wth ncreases n real per capta ncome for a small R. The connecton between emssons and per capta ncomes nduced by changes n the parameters µ and ρ depends ntrcately on ther startng values and drectons, too. Reductons n µ startng at hgh levels and ncreases n ρ startng at low levels rase per capta ncomes and lower total emssons at the same tme. However, f µ s low enough or ρ s hgh enough, the consdered changes affect per capta ncomes and total emssons n the same drecton. Result 7. Reductons n R startng at ntermedate levels, reductons n µ startng at hgh levels and ncreases n ρ startng at low levels rase per capta ncomes and lower total emssons at the same tme. Even though these latter three parameters do not gve rse to a full EKC story, ther bengn effect both on per capta ncomes and on emssons makes them elements of explanaton for an EKC that buld on more than one parameter change. In concludng ths secton t s mportant to notce that a market-nduced EKC s far more lkely to obtan n long-run equlbrum where sklled labor s moble and the cty system evolves endogenously than when the allocaton of sklled labor s fxed (as was assumed n secton 3). 26

30 4.4 Polluton and welfare The socal ams to keep emssons as low as possble and to maxmze socal welfare may very well lead to dfferent recommendatons concernng the structure of ctes (e.g. Gagné et al. 2012). In ths secton we explore how the market mechansm compares wth the socal optmum. Our model contans three potental sources of market falure: prces whch dffer from margnal costs, pecunary externaltes assocated wth the moblty of sklled workers n mperfectly compettve goods markets, and envronmental externaltes. We pursue a second-best approach, where markup prces are taken as gven, but where the socal planer chooses the allocaton of sklled workers so as to maxmze a socal welfare functon. Followng Tabuch and Thsse (2002), we take the unweghted sum of all sklled and unsklled workers (expected) utlty levels as our measure of socal welfare: { 1 log 1 log 1 } ( 1 ) ( ) ( ) ( ) ( ) ( ) ( ) W λ = ρl λv U U 1 λ + λ v2 λ ξ λ λ+ λ λ + ρ L v1 + v 2 (34) It s obvous from the ndrect utlty (11) that the comparson of the market equlbrum wth the socal optmum must strongly depend on the dsutlty assocated wth global (greenhouse gas) emssons. We use the parameter κ to hghlght several cases. The case κ = 0 captures the stuaton where there are no negatve envronmental externaltes. The dark red curve n Fg. 4 depcts the optmal choce of λ by the socal planer as trade freeness vares from autarky to no trade costs to contrast t from the blue curve that depcts the locaton pattern assocated wth the market equlbrum (derved n secton 4.1 and already depcted n Fg 3). The other lght red curve shows how the socal planer soluton evolves as the parameter κ s ncreased to 0.5. s shown n Fg. 4, wthout externaltes, the bubble depctng the socal optmum does not concde wth the market equlbrum. Ths s a consequence of the varous market falures mmanent n economc geography models (see Pflüger and üdekum 2008). Moreover, the bubble shrnks the hgher the dsutlty assocated wth envronmental externaltes. Ths s ntutve, snce gven our parameters, symmetry mnmzes total polluton. Eventually, as κ becomes large enough the socal planer chooses full dsperson, λ = 1/2, for all levels of trade freeness. The dscrepancy between the market equlbrum and the socal optmum leaves a role for polces that control populaton flows drectly or ndrectly, e.g. through urban growth boundares. However, these polces should be carefully desgned, dependng on varous parameters whch may be dffcult to observe. 27

31 Fg. 4: Market equlbrum vs. socal optmum Concluson Ths paper establshes a smple theoretcal framework whch comprses key forces that shape the structure and nterrelaton of ctes to study nterdependences between urban evoluton and the envronment. We focus on the potental of unfettered market forces to economze on emssons. key fndng s that market forces alone may suffce to generate an urban Envronmental Kuznets Curve. One specfc fndng s that reducng trade costs ncreases per capta ncomes and generates an nversely U-shaped evoluton of emssons n the process of agglomeraton and redsperson. We also fnd that agglomeraton per se s typcally not a boon for the envronment, as total emssons n the total cty system are lkely to rse (although, as we have stressed, ths depends on the emsson ntenstes of varous polluton sources). We have made a number of lmtng choces n settng up our framework. n nterestng route to pursue n future work s to brng n envronmental polces and to allow for abatement actvtes to endogenze the emsson ntenstes. Ths may enhance the scope for a bengn nteracton between urbanzaton and the envronment. Moreover, we have followed the economc geography and assumed that the modern sector produces manufacturng goods only. plttng ths sector nto manufactures and (cleaner) servces s a second nterestng extenson. Fnally, the nternal cty transport system could also be dfferentated out n future work. We beleve that the smple model we have establshed proves useful to address these and further extensons. 28

32 References chele, R. and Felbermayr, G. (2012). Kyoto and the Carbon Footprnt of Natons. Journal of Envronmental Economcs and Management 63: lonso, W. (1964). Locaton and Land Use. Cambrdge M. Harvard Unversty Press. san Development Bank (2012). Key ndcators for sa and the Pacfc Green Urbanzaton n sa. pecal Chapter, san Development Bank, Mandaluyong Cty, Phlppnes. Baroch, P. (1988). Ctes and Economc Development: From the Dawn of Hstory to the Present. Unversty of Chcago Press, Chcago. Borck, R. (2014). Wll kyscrapers ave the Planet? Buldng Heght Lmts and Urban Greenhouse Gas Emssons. CEfo Workng Paper eres 4773, Munch. Brueckner, J. (1987). The tructure of Urban Equlbra: Unfed Treatment of the Muth-Mlls Model, n: E.. Mlls (ed.), Handbook of Regonal and Urban Economcs Vol. 2, North-Holland, Calmette, M.-F. and Péchoux, I. (2007). re Envronmental Polces Counterproductve? Economcs Letters 95(2): Copeland, B. R. and Taylor, M.. (2003). Trade and the Envronment: Theory and Evdence. Prnceton Unversty Press. Cruz, J.M. and Taylor, M.. (2013). patal pproach to Energy Economcs. NBER Workng Paper Dasgupta,., Laplante, B., Wang, H., and Wheeler, D. (2002). Confrontng the Envronmental Kuznets Curve. Journal of Economc Perspectves 16(1): Desmet, K. and Ross-Hansberg, E. (2015). On the patal Economc Impact of Global Warmng. Journal of Urban Economcs, forthcomng. Elbers, C. and Wthagen, C (2004). Envronmental Polcy, Populaton Dynamcs and gglomeraton. Contrbutons to Economc nalyss & Polcy 3(2), rtcle 3. EP (2015). Inventory of U.. Greenhouse Gas Emssons and nks: , U.. Envronmental Protecton gency, Washngton, DC. Fujta, M. (1989). Urban Economc Theory. Land Use and Cty ze. Cambrdge Unversty Press Fujta, M., Krugman, P., and Venables,. J. (1999). The patal Economy. Ctes, Regons, and Internatonal Trade. MIT Press, Cambrdge, Mass. Gagné, C., Rou,., and Thsse, J.-F. (2012). re Compact Ctes Envronmentally Frendly? Journal of Urban Economcs 72(2-3): Glaeser, E. (2011). Trumph of the Cty: How our Greatest Inventon Makes us Rcher, marter, Greener, Healther and Happer. Pengun, New York. Glaeser, E. L. and Kahn, M. E. (2010). The Greenness of Ctes: Carbon Doxde Emssons and Urban Development. Journal of Urban Economcs 67(3): Grossman, G. M. and Krueger,. B. (1993). Envronmental Impacts of a North mercan Free Trade greement, MIT Press, Cambrdge, M,

33 Grossman, G. M. and Krueger,. B. (1995). Economc Growth and the Envronment. Quarterly Journal of Economcs 110(2): Head, K. and Mayer, T. (2004). The Emprcs of gglomeraton and Trade, n: V. Henderson und J.-F. Thsse, (eds.) Handbook of Regonal and Urban Economcs Vol. 4, Kahn, M. E. (2006). Green Ctes: Urban Growth and the Envronment. Brookngs Insttuton Press, Washngton, D.C. Kahn, M. E. and Walsh R. (2014). Ctes and the Envronment, n: G. Duranton, J.V. Henderson, W.C. trange (eds.), Handbook of Regonal and Urban Economcs 5, forthcomng Krugman, P. (1991). Increasng Returns and Economc Geography. Journal of Poltcal Economy 99: Lange,. and Quaas, M. F. (2007). Economc Geography and the Effect of Envronmental Polluton on gglomeraton. BE Journal of Economc nalyss & Polcy, 7(1). Larson, W., Lu, F., and Yezer,. (2012). Energy Footprnt of the Cty: Effects of Urban Land Use and Transportaton Polces. Journal of Urban Economcs 72(23): Larson, W. and Yezer,. M. (2014). The energy mplcatons of cty sze and densty. Workng Paper , George Washngton Unversty, Insttute for Internatonal Economc Polcy. Murata, Y. (2003). Product dversty, taste heterogenety, and geographc dstrbuton of economc actvtes: market vs. non-market nteractons. Journal of Urban Economcs, 53(1): Murata, Y. and Thsse, J.-F. (2005). mple Model of Economc Geography à la Helpman-Tabuch. Journal of Urban Economcs 58: Pflüger, M. (2001). Ecologcal Dumpng Under Monopolstc Competton. candnavan Journal of Economcs 103(4): Pflüger, M. (2004). mple, nalytcally olvable Chamberlnan gglomeraton Model. Regonal cence and Urban Economcs 34: Pflüger, M. and J. üdekum (2008). Integraton, gglomeraton and Welfare, Journal of Urban Economcs 63: hbayama K. and Fraser, I. (2014). Nonhomothetc Growth models for the Envronmental Kuznets Curve. Internatonal Economc Revew 55 (3): Tabuch, T. (1998). Urban gglomeraton and Dsperson: ynthess of lonso and Krugman. Journal of Urban Econonomcs 44: Tabuch, T. and J.-F. Thsse (2002). Taste heterogenety, labor moblty and economc geography. Journal of Development Economcs 69: Tscharaktschew,. and Hrte, G. (2010). The Drawbacks and Opportuntes of Carbon Charges n Metropoltan reas. patal General Equlbrum pproach. Ecologcal Economcs 70(2): World Bank (2009). Reshapng Economc Geography. World Development Report World Bank, Washngton D.C. 30

34 ppendx Table 3: Emssons and per capta ncomes I locaton pattern φ ψ L per capta ncome emergng core emergng perphery total cty system emssons emergng core emergng perphery total cty system 31

35 Table 4: Emssons and per capta ncomes II locaton pattern R ρ µ per capta ncome emergng core emergng perphery total cty system emssons emergng core emergng perphery total cty system 32

36 Table 5: Emssons and per capta ncomes III locaton pattern ξ σ γ per capta ncome emergng core emergng perphery total cty system emssons emergng core emergng perphery total cty system 33

37 upplementary appendx - Not for publcaton 1 Dervaton of the effectve labor supply n cty In order to arrve at the effectve supply of labor, the reducton of the total labor supply due to the ceberg commutng costs n accordance wth the equlbrum locaton pattern of the sklled r b has to be taken nto account: L, eff D( r)( 1 ψ r) dr. Usng D( r) 1/ CH, ( r) 0 and the consumpton of housng by the sklled gven n eq. (6), C ( r) γ ( 1 ψr) w / P ( r) can be rewrtten as ( ) r b, eff H, γ w 0 = ths H, H, 1 L = P r dr. The bd rent of sklled workers n the cty equlbrum can be calculated from eqs. (8), (11) and (13) as ( ) ( 1 ψ ) 1/ P r = r P. Hence, H, U, r b PU, ( ) 1/ γ L, eff = 1 r ψ dr γ w. olvng the ntegral yelds 0 γ r r b b 1+ γ 1+ γ 1/ γ 1 γ 1 γ ( 1 r ) dr ( 1 r ) γ 1 ( 1 rb ) γ ψ = ψ = ψ ψ 1 γ ψ 1 γ Insertng the cty boundary from eq. (12) we fnally arrve at L, eff 1+ γ P R. + U, = 1 ψ ( 1 γ) w P U, 2 Dervaton of total commutng dstance n cty Total commutng (dstance) s gven by ( ) ( ) = γ ( 1 ψ ) / ( ) and ( ) ( 1 ψ ) 1/ C r r w P r as H, H, ( ) ( 1 r) w rp r P Ψ = = H, U, rb rb 1, 1, ( 1 ) 1 γ H U dr r ψ r γ dr γ ψ 0 γ w 0 rb rb r rd r dr dr C 0 0 H,. Wth Ψ = = γ P r = r P (see 1) ths can be rewrtten. olvng the ntegral yelds ( 1 r ) γ ( r ) rb r γ γ ψ b 1 b γ + ψ γ b γ ( 1 ψr) γ ( γ ψr) r ( 1 ψ r) γ dr = = ( 1+ γ) ψ ( 1+ γ) ψ 0. Hence, total commutng dstance s: γ Ψ = γ γ ( PU, R) R( 1 PU, R ) ( 1+ ) 2 γ ψ w 1 γ ψ b γ + ψ Ψ = 2 γ ψ ( 1 r ) γ ( r ) ( 1+ ). b P w U,. ubsttutng for r b we get: 34