Migration and Diversity: Human versus Social Capital

Transcription

1 DISCUSSION AER SERIES IZA D No. 79 Migratio ad Diersity: Hma erss Social Capital Vlad Maole Marice Schiff Agst 004 Forschgsistitt zr Zkft der Arbeit Istitte for the Stdy of Labor

2 Migratio ad Diersity: Hma erss Social Capital Vlad Maole World Bak Marice Schiff World Bak ad IZA Bo Discssio aper No. 79 Agst 004 IZA.O. Box Bo Germay hoe: Fax: Ay opiios expressed here are those of the athors ad ot those of the istitte. Research dissemiated by IZA may iclde iews o policy, bt the istitte itself takes o istittioal policy positios. The Istitte for the Stdy of Labor IZA i Bo is a local ad irtal iteratioal research ceter ad a place of commicatio betwee sciece, politics ad bsiess. IZA is a idepedet oprofit compay spported by Detsche ost World Net. The ceter is associated with the Uiersity of Bo ad offers a stimlatig research eiromet throgh its research etworks, research spport, ad isitors ad doctoral programs. IZA egages i i origial ad iteratioally competitie research i all fields of labor ecoomics, ii deelopmet of policy cocepts, ad iii dissemiatio of research reslts ad cocepts to the iterested pblic. IZA Discssio apers ofte represet prelimiary work ad are circlated to ecorage discssio. Citatio of sch a paper shold accot for its proisioal character. A reised ersio may be aailable directly from the athor.

3 IZA Discssio aper No. 79 Agst 004 ABSTRACT Migratio ad Diersity: Hma erss Social Capital This paper examies the welfare implicatios associated with differet degrees of diersity or similarity betwee migrats ad aties der both migratio ad trade. We se a geeral eqilibrim model of migratio, hma capital ad social capital ad fid that there are three eqilibrim soltios: a iteral oe with half the poplatio of each cotry migratig to the other cotry, ad two corer soltios where eeryoe eds p i oe of the two cotries. The iteral soltio is stable ad is likely to be reached der differet leels of hma capital across the two cotries. The corer soltios are stable ad will be reached der most circmstaces. If there are hma capital differeces across the two poplatios, eeryoe eds p i the cotry with the highest iitial leel of hma capital. Welfare der ay of the eqilibrim soltios rises with the diersity i hma capital ad decreases with the diersity i social capital betwee migrats ad aties. Trade ad both migratio soltios redce ieqality betwee the poplatios of the two cotries by the same amot. I additio, trade ad migratio are ot eqialet if social capital is preset: the highest welfare is obtaied with migratio der the corer soltio, the secod highest welfare is obtaied with trade, ad the lowest welfare is obtaied with migratio der the iteral soltio. The first two soltios third soltio raise may raise or redce welfare relatie to the o-migratio case. JEL Classificatio: F, F6, F, J6 Keywords: migratio, trade, social capital, hma capital, welfare Correspodig athor: Marice Schiff Deelopmet Research Grop The World Bak Mailstop No. MC H. St. NW Washigto DC 0433 USA mschiff@worldbak.org The opiios expressed i this paper are etirely those of the athors. They do ot ecessarily represet the iew of the World Bak, its Exectie Directors, or the cotries they represet.

4 . Itrodctio Employers i idstrial cotries ted to prefer immigrats with differet skills from those of aties. olicy makers ofte go alog, first, becase of employer pressre, ad secod, becase a greater diersity of skills eables icreased gais from specializatio ad exchage. I other words, there is a preferece for importig those skills that are i relatiely short spply ad are differet from those with which aties are abdatly edowed. The preferece for immigrats with a differet skill compositio tha that of aties applies to those with high skill leels, sch as Idia software egieers i the US ad Germay, ad to those with itermediate skill leels, sch as Sother ad Easter Africa rses i the UK. Aother aspect of the preferece for immigrats who differ from aties is the demad for skilled workers to carry ot low-ed jobs that aties are willig to do e.g., i the hotel ad restarat idstries, agricltre, hose cleaig ad more. O the other had, policy makers hae ofte implemeted migratio policies that discrimiate i faor of people with a ethic, cltral, religios or lagage backgrod that is similar to that of aties. This icldes Astralia, which log faored immigratio from the UK ad where New Zealaders ca still immigrate freely Corde 003, ad the US where early immigratio policies faored those with Eropea backgrod ad discrimiated agaist others, as docmeted by Jacobso 998. Baer ad Kze, 004, preset seeral iitiaties to attract high skilled workers i OECD cotries. Some cotries, like Caada ad Astralia, icreased the mber of immigratio qotas. Similarly, the U.S sigificatly icreased the mber of HB-isas temporary isas that are sed by high skilled workers. I Agst 00, Germay itrodced the Gree Card program, facilitatig temporary isas for IT specialists a qota of isas for a maximm of fie years. Other cotries redced the trasactio costs associated with the isa process. The U.K. redced the reqiremets for high skilled isa. Startig i Jaary 00, Frace streamlied the process of obtaiig isas for high skilled workers.

5 Ths, o the oe had, migratio policy seems to faor diersity betwee immigrats ad aties, while o the other, it teds to faor similarity. The desire for similarity teds to be associated with social capital characteristics of migrats ad aties, while the desire for diersity teds to be associated with their hma capital characteristics. The model preseted i this paper icorporates characteristics of both social ad hma capital i the prodctio fctio i a two-cotry geeral eqilibrim framework. It assmes that social capital raises prodctiity ad falls with labor mobility ad migratio. Eidece o these relatioships is proided i Schiff 004. The aboe implies that migratio geerates exteralities associated with social capital. The paper examies the welfare implicatios of differet degrees of diersity or similarity betwee migrats ad aties der both migratio ad trade. The mai fidigs are:. There are three eqilibrim soltios: a iteral oe with half the poplatio of each cotry migratig to the other cotry, ad two corer soltios where eeryoe eds p i oe of the two cotries.. Welfare der ay of the eqilibrim soltios goes p as the diersity i social capital betwee migrats ad aties decreases ad that i hma capital icreases. Social capital has bee defied as the ability of people to work together for commo prposes i grops or orgaizatios Colema, 988 or as "... the set of elemets of the social strctre that affects relatios amog people ad are ipts or argmets of the tility ad/or prodctio fctio" Schiff, 99. These elemets iclde social orms, attitdes, ales, lagage ad cltre. Social capital i the form of close ties to the commity may geerate beefits by raisig tility directly, ad/or by raisig otpt throgh a redctio i the cost of trasactig bsiess de to higher trst ad eforceability of sactios. This paper focses o the latter. For migratio models focsig o the impact of social capital o tility, see Schiff 00.

6 3. Either of the two corer soltios maximizes world welfare. These soltios are obtaied if immigratio is restricted ad there are high hma capital differeces betwee the two cotries, or i the presece of social capital, if migratio is flly restricted by oe of the two cotries. 4. The welfare impact of migratio der the iteral eqilibrim soltio is ambigos. 5. Welfare icreases with free trade ad is higher tha der the iteral migratio soltio ad lower tha der the corer soltios. Coseqetly, trade ad migratio are ot eqialet i the presece of social capital. 6. Both trade ad migratio redce ieqality betwee the poplatios of the two cotries. The remaider of the paper is orgaized as follows. Sectio presets the model. Sectio 3 soles the model i the absece of migratio ad Sectio 4 does the same der migratio. Sectio 5 presets the free trade soltio ad Sectio 6 compares the migratio ad free trade soltios. Sectio 7 examies migratio dyamics ad Sectio 8 cocldes.

7 .The Model The model draws i part o Schiff 004 bt differs by proidig a more rigoros modelig of the social capital. This leads to soltios ad implicatios that differ etirely from Schiff 004. Assme two islads i,. Two-way migratio ca be obtaied by assmig differet edowmets of idstry-specific skills i each islad, zero cross-islad moig costs for labor ad prohibitie moig costs for goods. Assme that the iitial poplatio o each islad is. Deote by ij the proportio of aties of Islad i liig o Islad j i, j,. Before migratio takes place,, ad the proportio that migrates 0. Each atie of Islad i liig o Islad j cosmes X ij ad Y ij its of goods X ad Y, with tility gie by ij ij ij U X Y, < Note that a decrease i icreases the gais from diersificatio of cosmptio. Otpt of X ad Y depeds o hma capital ad o local pblic goods ad serices whose proisio is positiely related to the leel of social capital. Alteratiely, assme that otpt depeds o hma capital ad o aspects of social capital sch as the extet of trst ad cooperatio amog idiidals. Ths, X Y is prodced with hma capital or skill x y ad social capital S. Naties of Islad are edowed with skill x y ad prodce X Y. 3 Gie that the poplatio of each islad oly has oe skill ad prodces oly oe good, is also iersely related to the diersity i edowmets of skills or 3 For simplicity, the paper assmes oe skill per islad. The qalitatie reslts hold if each islad is edowed with both skills, as log as the skills ratios differ across the islads. 3

8 hma capital. 4 Ths the gais from cosmptio diersificatio icrease with the diersity i edowmets. The prodctio fctios for X ad Y are X F x, S ad j j Y F y, S, where S ij is the social capital aailable to idiidal I ij. Specifically, j j X xs Y ys ; j,. j j, j j Followig Lazear 000, assme that the social capital is characterized by etwork exteralities as with lagage, i.e., it icreases with the mber of people who share it. A idiidal I ij moig from Islad i to Islad j does ot beefit from iteractio with aties of Islad j to the extet that the aties of Islad j beefit becase creatig a etwork of social relatios ad bildig trst takes time, ad some relatios ad experieces e.g., those with family ad childhood frieds caot be recreated. Aother reaso might be that aties of Islad i may speak a differet lagage tha those i Islad j. The islads may also differ i other aspects, icldig ethicity ad race. Glaeser et al. 000 examied determiats of trst ad trstworthiess i a experimet with 58 Harard dergradates ad fod that differeces i atioality ad race redce the leel of trstworthiess. Hece, migrats are assmed to gai partial access to the social capital of aties i their islad of destiatio. Symmetrically, aties are assmed to gai partial access to the social capital of migrats to their ow islad. Specifically, the social capital aailable to a atie I ii who does ot migrate is S ii ii ij, i j ad for a migrat from Islad i to Islad j i j is S ij ij jj,. 5 4 Note that implicitly hma capital has two dimesios. The first is the leel of x ad y highly skilled or ot, ad the secod is the diersity betwee x ad y as represeted by o diersity if both x ad y are, say, farmers close to, ad greater diersity if x is farmer ad y is egieer close to zero. 5 We hae assmed here that social capital eters the prodctio fctio ad ot the tility fctio. Assmig the latter as i Schiff 998; 00 ad Schiff ad Witers 998 does ot chage the mai fidigs. 4

9 Gie these assmptios ad eqatio, idiidal otpt is: 3 X x ; Y y ; X x ; Y y 3. No Migratio I the absece of migratio, i j ad. Assmig prohibitie trasport costs for goods, X ad Y are ot traded this assmptio is relaxed i Sectio 5. Ths, qatities cosmed X ij, Y ij eqal qatities prodced X ij, Y ij. From the relatios 3, these are X X x; Y Y y ad Y Y Y Y 0. From eqatio, tility is U x ad U y. 4. Migratio The aties of Islad cosme o Y X ad the relatie price of YX i its of XY o Islad is ifiite see eqatio 8 i Sectio 5. Ths there is a icetie to migrate i both directios. Assme ow that the two islads sig a treaty itegratig their labor markets by allowig free moemet of people betwee them. eople from Islad take their skills x y to Islad i order to prodce X Y there ad exchage part of it for Y X. Becase people migrate i both directios, goods X ad Y are ow aailable o both islads. Migratio has three effects o welfare. First, sice both X ad Y are ow prodced ad cosmed o both islads, eeryoe beefits from diersificatio of cosmptio. 5

10 O the other had, migratio leads to a priate loss of prodctie skills, becase migratio leads to a decrease i oe s ow poplatio ad ths i social capital i the islad of origi. At the same time migratio raises oe s ow poplatio i the islad of destiatio ad raises social capital there. Assme good Y is the meraire. Naties ad migrats maximize their tility, i.e. idiidals from Islad maximize U j U j, j,. Cosider Islad. The first order coditio for aties ad migrats are:.a X Y.b X Y, where j is the relatie price of X i terms of Y o Islad j. Bdget costraits for aties ad migrats are:.c X Y x.d X Y y Market clearig coditios for goods X ad Y are 6 :.e X X x.f Y Y y The same coditios hold for Islad, amely:.a X Y.b X Y.c X Y x 6 Eqatio.f is ot idepedet of eqatios.c,.d ad.e Walras Law. 6

11 .d X Y y.e X X x.f Y Y y oplatio idetity: 3.a 3.b Iteral migratio eqilibrim is obtaied whe the migrats ad aties from the same poplatio hae the same leel of tility U U, U U for 0<, < or: 4.a 4.b X Y X Y Y X Y X Takig ito accot the Walras Law, we hae 4 eqatios.a.e,.a.e, 3.a, 3.b,4.a,4.b with 4 kows,,,, X, Y, X, Y, X, Y, X, Y,,. This system ca be redced to a two eqatios system with two kows for proof see the appedix: y 4 x 0 y x 5 0 I order to sole for ad we miimize the sm of the sqare of the lefthad sides of eqatio 4 ad 5 deoted by z with respect to ad. Figre shows the ariatio of z. 7

12 Figre. Variatio of the objectie fctio z o the ertical axis as ad o the horizotal axes ary from 0 to. We ote from eqatio 4 that the iteral migratio eqilibrim depeds o the ratio y/x rather tha o the leels of y ad x i each islad. The iqe iteral soltio is 0.5, as show i Figre. There are also two corer soltios where i eqatios a, b, a, b, where c, d, c, d, 3a ad 3b hold, where X j X j x replaces e ad e, ad Y j Y j y replaces f ad f, ad where 4a ad 4b do ot hold. The soltios are: C, 0; ad C 0,. We ca compte the prices with eqatios A.9 ad A.0, i the Appedix, ad the cosmptio ad tility leels with eqatios A. A.8. For the iteral migratio eqilibrim with 0.5 tility is: I I 6 U U x x y I I 7 U U y x y Both corer soltios geerate the same tility leels. Utility for the Islad corer soltio is: 8 U C x x y 9 U C y x y 8

13 The iteral eqilibrim ad the corer soltios geerate the same relatie price. The differece betwee the leels of cosmptio ad tility is de to differeces i social capital. For both poplatio grops, the social capital for the iteral eqilibrim is while for the corer soltios, it is C. The tilities ratio isu / U I >, i, j,. Ths the leel of tility is higher for corer soltios tha for the iteral oe. We ow compare the iitial tility leel with that of the iteral eqilibrim: ij ij 0 U I 0 U x y x The first term is greater tha ad the secod is smaller tha. Ths, the impact is ambigos a priori. For, there are o diersity gais ad the ratio is. Ths, migratio leads to a welfare loss if there are o diersity gais, except whe the two poplatios hae idetical social capital, i which case migratio has o impact o welfare. From eqatio 0, it follows that welfare gais from migratio icrease with ad fall with. 5. Trade We cosider the sitatio i which people caot migrate bt they ca trade. I this sitatio, there is oe price i both islads ad both goods are aailable i both islads. eople from Islad maximize U U. The first order coditios are: X Y 9

14 X Y The bdget costraits are: 3 X Y x 4 X Y y The market clearig coditios are: 7 5 x X X 6 y Y Y We ca elimiate X ad X from 5 sig first order coditios ad : 7 x Y Y Usig 6, we ca express the price: 8 y x From, 3 ad 8 we obtai cosmptio for Islad ad similarly for Islad. The tilities der free trade are: 9 0 U t x x y U t y x y 7 De to Walras Law we jst keep oe eqatio. 0

15 6.Comparig the Migratio ad the Trade Soltios We se the otatio of U U for the tility of the atie poplatio i Islad i eqilibrim From the relatios 0,4 ad 9 we obtai the followig ieqalities ad similarly for the secod islad: C t I U > U > U C t I U > U > U The ititio for these reslts is that tility is higher whe society beefits from prodct diersity ad social capital. oplatios beefit from the same leel of prodct diersity der the three soltios. Howeer, the leel of social capital differs der these soltios. Whe both poplatios are o the same islad, social capital S. Trade, with S, is a secod best. The iteral eqilibrim, with social capital S/, has the lowest tility. It is iterestig to compare social ieqality across the two poplatio grops der all these sitatios. I the iitial sitatio we hae: 3 U U 0 0 x y For the migratio ad trade sitatios we hae: 4 U U C C U U t t U U I I x y Ths, both migratio ad trade redce world ieqality.

16 7. Migratio Dyamics With mltiple migratio soltios, we frther differetiate betwee them by itrodcig a dyamic system. Cosider 5 & & U U U U where the chage i the proportio of the poplatio that migrates from oe islad to the other is eqal to the differece betwee the tility of a migrat ad the tility of a idiidal that stays at home. The eqality of tility, U U ad U U, correspods to a critical poit for the dyamic system, ad, from the precedig discssio, it is a eqilibrim coditio for the system 4.a ad 4.b ad correspods to 0.5 ad 0.5. The dyamic system is oliear ad does ot hae a closed form soltio bt we ca aalyze the behaior of the system arod the critical poit by liearizatio. We fid that for the same hma capital x y, for small ad for close to, the iteral migratio eqilibrim is a egatie attractor, ad for other ales of ad it is a saddle poit. Ths, for both sitatios the eqilibrim is stable. Let s cosider the ales of 0.5 ad 0.5. If U - U is positie the is icreasig, ad there is migratio of poplatio from Islad to Islad. If U - U is egatie the is decreasig, ad the migrats are retrig to their ow islad, with a similar discssio for. From Figre we ote that the iteral migratio eqilibrim is a saddle poit ad therefore stable, ad the corer soltios are stable poits.

17 Figre. Iteral migratio eqilibrim is a saddle poit, therefore stable, ad the corer soltios are stable poits The dyamic system 5 is well defied as log as the tilities are well defied. To compte the tilities, we eed fiite prices ad this implies the existece of migratio. How ca we defie the dyamic system i the iitial sitatio, before migratio takes place? We ca imagie a two step process. I the first stage, the first migrat moe to the other islad. 8 I the secod stage, migratio is goered by the dyamic system. We cosider three sitatios for the first stage; > ; ; 3 <. Whe we cosider the same amot of hma capital for both islads x y the reslts are symmetric Figre 3. The bold cres are merically compted soltios ad correspod to the three sitatios i the first stage we choose for the first stage: 3, 0 0 ;, ; , 3. I case, 0 migratio is higher from Islad to Islad tha from Islad to Islad. This reslts i 8 We do ot cosider trasportatio costs i this model bt it seems reasoable to assme that it is prohibitiely expesie to moe large poplatios from oe islad to aother at the begiig of the migratio, so for the first step we cosider small ales for ad. 3

18 S > S ad S > S. This implies a higher otpt i Islad tha i Islad for both poplatios ad therefore a faster migratio & tha &. Ths eerybody eds p o Islad i a stable eqilibrim, 0. I case, U - U U - U ad we obtai a similar migratio patter for the two poplatios, edig i a stable eqilibrim 0.5, 0.5. Case 3 is symmetric with case, with 0,. Note that i cases ad 3, there is a itermediate rage for ales of i case ad i case betwee 0.35 ad 0.75 i Figre 3 where we obtai retr migratio. Figre 3.The migratio trajectories for the same amot of hma capital x y. C I 0. 3 C Oe ca repeat the exercise with x y, i.e., with differet leels of hma capital for the two poplatios ad the same three cases as i the first stage. 9 Figre 4 depicts the case x, y 00. I case 3, whe more people migrate from Islad to Islad tha poplatio migrates to Islad, the ery high leel of hma capital for poplatio i 9 The iitial ales for ad for the three cases are the same as i the eqal amot of hma capital case. 4

19 Islad more tha compesates for the social capital loss, ad the gais i tility for the migrats from Islad are higher tha the correspodig gais for the migrats from Islad, so both poplatios ed p i Islad. I other words, if the assmptios of the model are satisfied, there is free migratio, migratio starts with reasoably small moemets of people, ad there are sigificat differeces i hma capital betwee poplatios, the the poplatio with lower hma capital migrates to the islad with the poplatio with higher hma capital. Gie that eeryoe eds p i Islad der case 3, eeryoe mst also ed p i Islad i cases ad 3, as is show i Figre 4. Figre 4. The migratio trajectories for higher leel of hma capital for poplatio of Islad x, y 00. C I C 8. Coclsio This paper presets a geeral eqilibrim model of migratio, hma capital ad social capital. We fid that there are three eqilibrim soltios: a iteral oe with half the poplatio of each cotry migratig to the other cotry, ad two corer soltios 5

20 where eeryoe eds p i oe of the two cotries. The iteral soltio is stable ad is likely to be reached der differet leels of hma capital across the two cotries. The corer soltios are stable ad will be reached der most circmstaces. Welfare der ay of the eqilibrim soltios rises with the icrease i the diersity i hma capital ad decreases with the diersity i social capital betwee migrats ad aties. Either of the two corer soltios maximizes world welfare. These soltios are obtaied if migratio is costraied bt there are high hma capital differeces i which case eeryoe eds p i the cotry with the highest iitial leel of hma capital - or, if immigratio is flly restricted by oe of the two cotries. I the presece of social capital, migratio restrictios by oe cotry maximize world welfare. I additio, trade ad migratio are ot eqialet if social capital is preset. Welfare icreases with free trade ad is higher tha der the iteral migratio soltio ad lower tha der the corer soltios. Both trade ad migratio redce ieqality betwee the poplatios of the two cotries. 6

21 Refereces Baer, T.K. ad A. Kze The Demad for High-Skilled Workers ad Immigratio olicy, Istitte for the Stdy of Labor IZA Discssio aper No Colema, J.S Social Capital i the Creatio of Hma Capital, America Joral of Sociology 94 Spplemet: S95-S0. Corde, W.M Millio Assies? The Immigratio Debate Reisited, Iagral Richard Sape Lectre, rodctiity Commissio, Melbore. Glaeser, E. L.,, D. Laibso, J.A. Scheikma, ad C.L. Sotter Measrig Trst, Qarterly Joral of Ecoomics, 5 3:8-46. Jacobso, M.F Whiteess of a Differet Color: Eropea Immigrats ad the Alchemy of Race. Harard Uiersity ress: Cambridge. Lazear, E Cltre ad Lagage i Essays i Hoor of Gary S. Becker. Joral of olitical Ecoomy 07 6: S95-6. art. Schiff, M. 99. Social Capital, Labor Mobility, ad Welfare: The Impact of Uitig States, Ratioality ad Society 4: Schiff, M Itegratio olitiqe, Mobilite de la Mai d Oere, Bie-etre et Capital Socio-Cltrel, Ree d ecoomie d deeloppemet Schiff, M. 00. Loe thy Neighbor: Trade, Migratio, ad Social Capital, Eropea Joral of olitical Ecoomy, 8 :87-07 Schiff, M Labor Mobility, Trade ad Social Capital, Reiew of Iteratioal Ecoomics September. Forthcomig. Schiff, M. ad L. A. Witers Regioal Itegratio as Diplomacy, World Bak Ecoomic Reiew :

22 Appedix Assmig that there is migratio for both islads ad so 0 ad 0 ad 0 <, <, we redce the iitial systems of 4 eqatios.a.e,.a.e, 3.a, 3.b,4.a,4.b with 4 kows,,,, X, Y, X, Y, X, Y, X, Y,, to a system of two eqatios with two kows. From first order coditio.a ad bdget costrait.c we ca write X ad Y as a fctio of price ad, : A. A. X Y x x I a similar way we ca express the other cosmptio terms: A.3 A.4 A.5 A.6 A.7 A.8 X Y X Y X Y x y y x y y 8

23 9 We ca se A. ad A.5 to elimiate the cosmptio terms X ad X from the market clearig eqatio.e ad to express the price as a fctio of ad : A.9 x y I a similar way we ca write as a fctio of ad : A.0 x y Util ow we did ot se the migratio eqilibrim eqatios 4.a ad 4.b ad poplatio idetity 3.a ad 3.b. We ca se the eqatios A. A.4 to elimiate the cosmptio terms X, Y, X, Y from the migratio eqilibrim eqatio 4.a ad after some maiplatios we ca write: A. We ca ow se the eqatios A.9 ad A.0 to elimiate the prices ad ad we obtai: A. x y x y I a similar way, we ca se the eqatios A.5 A.8 to elimiate the cosmptio terms X, Y, X, Y from the migratio eqilibrim eqatio 4.b ad after some maiplatios we ca write:

24 0 A.3 The right-had side ca be trasformed sig eqatio A. ad we ca frther se the eqatios A.9 ad A.0 to elimiate the prices ad ad we obtai: A.4 We ca se the poplatio idetity 3.a ad 3.b to elimiate ad from the eqatios A. ad A.4 ad we obtai a system of two eqatios with two kows: A.5 x y x y A.6 Lemma. If, is a soltio for the system of eqatios A.5 ad A.6 i the space, the -,- is also a soltio. roof. If, is a soltio the: A.7 x y x y A.8 If we plg -,- i A.5 ad A.6 we hae:

25 A.9 A.0 y x y x We otice that the ierse of the left-had side of A.9 is the left-had side of A.7 ad the ierse of the right-had side of A.9 is the right-had side of A.7, so A.9 is tre. Similarly for A. 0, so -, - is a soltio for A.5 ad A.6. There is a direct iterpretatio for this reslt. If, is a migratio eqilibrim, the we hae,- o Islad ad -, o Islad ad the tilities are the same for the same poplatio. If we switch to soltio -, -, we hae -, o Islad ad, - o Islad ad the tilities are the same for the same poplatios, so -, - is a migratio eqilibrim too. This sggests that if we hae the same combiatio of poplatios o both islads the the amot of social capital will be the same ad the tility will be the same, so this is a eqilibrim. We ca check that.5 ad.5 is a soltio for the system of eqatios A.5 ad A.6 so this is a migratio eqilibrim. Whe we redce the iitial system of 4 eqatios to eqatios, we assme that there is migratio i both islads. Let s relax this assmptio ad cosider the corer soltios i which oe or both islads does ot hae migratio. If there is a islad that is prodcig jst oe prodct, the there is a icetie for migratio from the other islad, so this is ot eqilibrim. If eerybody from oe islad is moig to the other islad, the there are gais both from diersity of cosmptio ad social capital, so ad 0 ad also 0 ad are migratio eqilibrims too.