Skilled Labor, Economic Transition and Income Inequality

Transcription

1 Sklled Lbor, Economc Trnson nd Income Inequly We ZOU; Yong LIU (Insue for Advnced Sudy, Wuhn Unversy, Wuhn, Chn 4372 Absrc: We propose dynmc model of economc rnson n whch he supply consrn of sklled lbor nd skll premum re he focus. We rgue h he consrn of sklled lbor ffec boh he begnnng de nd he subsequen ph of modern growh. The model mches he observed mulple phs of ncome nequly, such s U-shped, nvered U-shped or N shped phs. Hence, he model requres fser echnology chnge nd more nvesmen on skll formon o ccoun for he curren ncome dfferences relve o models h focus only on sedy ses. Key Words: Sklled Lbor; Economc Trnson; Income Inequly JEL Clssfcon: D58, O, O4. Inroducon Ever snce he Kuznes (955 s poneerng work, economc growh nd ncome nequly hve occuped worldwde enon nd led o huge conroversy. Alhough Kuznes (955 proposes he fmous nvered U-shpe hypohess, n whch he ncome nequly my ncrese n he erly perod of growh, nd urn o decrese s he economy grows, mny emprcs of dfferen counres nd/or dfferen perods provde wdely dvergen resuls. Mos lerures n new growh heory emphsze he effec of speclzed humn cpl, spllover effec of R&D, echnology nnovon nd dopon on long-run growh, bu mke he ssumpon of homogenous lbor (Romer, 986; Lucs, 988; Aghon & How, 992; Prene & Presco, 999. Thus hese lerures gnore very mporn developmen fc: counres h hve experenced modern growh ( susned ncrese n per cp oupu lso experenced mulple evoluonry phs of ncome nequly overme. Oher lerures sudy skll dfferences nd skll premum, nd pon ou h skll dfferences mke huge dfference n dynmcs of economc growh nd resul n sgnfcn nequly (Acemoglu, 22. However, skll premum s usully defned s he ro of reurns o lbor wh dfferen educon nmens n ndusrl counres, nd hus cnno be used o nlyze how skll dfferences ffec he dynmcs of growh nd nequly n LDCs. In hs pper, we nroduce he endogenous supply of sklled lbor no he Hnsen-Presco (22 model of rnson, nd show h he dspry of echnology n modern ndusry nd rdonl grculure, s well s he supply consrn of sklled lbor ffec he economy s urnng pon from rdonl o modern growh, nd subsequen growh ph. The nl ndequcy nd slow growh re of sklled lbor dely he rnson nd resul n susned skll premum nd dspry Correspondng uhor: We Zou, eml ddress: zouwe@whu.edu.cn, Tel: The uhors hnk he Nonl Scence Foundon of Chn (#767372, Nonl Socl Scence Foundon (# 6 BJL 39 for reserch suppor. We lso benefed from commens nd dscussons wh Rober Brro, Pok-sng Lm, Heng-fu Zou, Png Wng, prcpns he 28 Annul Meeng of Mhemcl Economcs nd Fnnce n Shenzheng, Chn, he 29 Meeng of Susnble Developmen n Tokyo, Jpn, nd semnr prcpns Insue for Advnced Sudy (IAS, Wuhn Unversy.

2 n per cp ncome beween secors, whch n urn presen mulple possble phs (nvered U- shped curve s n exmple of he dynmc chnge n nequly. Hsorclly, nsed of followng he unque nvered U-shped ph, he dynmcs of nequly urn ou o chnge sgnfcnly wh he pce of rnson nd dffer cross counres nd perods. In he U.K. durng , he nequly spreds ou n N-shped curve, whch cn be segreged no n nvered-u-shped perod n nd U-shped one n In he U.S.A. from 93 o 994, he chnge n nequly s less drmc nd pursues rher fl U-shped ph. Whle n Jpn whose rnson srs ler, he nequly ncreses shrply from 886 o le 93s, bu decreses o much lower level fer WWⅡ, nd remns relvely low nequly ever snce. There re wo emprcl nd heorecl pproches o growh nd nequly. One pproch s o es he hypohess h nequly s n nvered U-shped funcon of he level of oupu. Mny provde posve evdence (Ahluwl, 976; Dennger & Squre, 996, whle ohers prove here s no enough evdence for he hypohess (Annd & Knbur, 993,993b. Some emprcs fnd ou h nequly s U-shped, or cubc funcon of oupu level (Felds & Jkubson, 995; Frncos & Rojs-Romgos, 28. Anoher prllel pproch s o es wheher more nequly enhnces or reduces growh re. Mny reserchers obn negve relonshp (Alesn & Rodrk, 994; Persson & Tbelln, 994; Pero, Oher reserchers conclude h he effec of nequly on growh s posve or ndeermne. L & Zou (998 rgue wh recen emprcl fndngs h nequly s no hrmful o growh. Forbes (2 llusres h posve relonshp presens only n he shor-run. Brro (2 conrss he negve effec n poor counres wh he posve effec n he rch 3. Lundberg & Squre (23 fnd ou number of fcors h poenlly nfluence boh growh nd nequly nd es for her jon sgnfcnce. Neverheless, remns n open queson why s oupu per cp ncrese, he ph of nequly urns ou o be mulple n dfferen economes nd perods. Anoher heorecl chllenge s o expln: wh s he possble nfluence of economc rnson on ncome nequly overme. Hnsen & Presco (22 consruc wo-perod OLG model, whch ncludes Mlhus secor nd Solow secor. The former s rdonl grculure secor h uses cpl, lbor nd lnd s npus, whle he ler s modern ndusry usng cpl nd lbor. The model esblshes crucl condon for he occurrence of ndusry, s long s he condon s ssfed, ndusry wh hgher echnology level wll moblze lbor ou of grculure. They suppose lbor s homogenous, nd here s no nsuonl brrer, hus he mgron of lbor o ces s smooh. The rnson from grculure o modern ndusry wll be fulflled wh he susned ncrese of proporons of ndusry n boh ol employmen nd oupu. The model provdes explnon of boh he sgnn growh n pre-7 perod n Europe, nd he sgnfcn ncrese n producvy nd per cp oupu fer ndusrl revoluon. However, wh lbor ndfference ssumpon, here s connuous lbor mgron from grculure o ndusry s long Reders re referred o Appendx A for descrpon of he dynmcs of nequly n he U.K., U.S.A. nd Jpn durng long perod for del. 2 The vrous explnons for negve effec nclude: nequly hs negve polcl effec (Alesn & Rodrk; nequly my hur nvesmen n physcl nd humn cpl (Glor & Zer, 23; Aghon & Bolon, 997; nequly renforces he unequl dsrbuon of nurl resources (Gylfson & Zoeg, The possble resons for posve relonshp nclude: nequly enhnces publc nvesmen (fnncng hrough xon or prve nvesmen (Sn-Pul & Verder, 993, socl cpl formon (Benbou, 996 nd echnologcl chnge (Glor & Tesson,

3 s echnology progress perms. In equlbrum, wge res equlze cross secors levng no skll premum or ncome dfferences. Therefore hs model, whch explns he economc rnson nd growh n cenures, does no expln he dynmcs of ncome dfferences ccompnyng rnson. Wng & Xe (23 consder hree fcors n he cvon of modern ndusry: skll requremens, economy of scle, nd subssence consumpon level. They compre he hgh growh n he NICs wh he sgnn growh n some Afrcn, Souh Asn counres. They propose h he cvon of modern ndusry requres no only echnology bu lso sklled lbor, moreover, he smulneous developmen of ndusry s requred o produce recprocl demnd nd ndusry-wde spllovers. Thus he brrer my come from he ndeque supply of sklled lbor. Bu hey do no sudy he possble mulple phs of ncome dsrbuon. Ng(24 shows h he brrers o prve nvesmen my dely he urnng pon nd ffec he subsequen growh. She ssumes lbor ndfference nd only explns he nver U-shped curve of ncome nequly. Emprcl evdences hve ccumuled for skll dfferences nd skll premum. Mny reserchers clcule skll premum wh he ro of wge of college grdues o h of hgh school grdues, Murphy & Welch (992 fnd ou h lhough here re more college grdues n ndusres, he skll premum for hem ncreses overme. Acemoglu (998 shows h he ncrese of sklled lbor n ol lbor forces mens lrger skll-complemenry echnology mrke nd more monopoly rens, whch n urn provde ncenve for frms o ncrese producvy of sklled lbor. Wh he ncrese of sklled lbor, skll premum my decrese nlly (subsuon effec, hen nduce skll-bsed echnology chnge (SBTC, economy of scle effec, whch n urn ncrese skll premum o level even hgher hn s orgnl level. Acemoglu (22 heoreclly formlzes he reson for SBTC. Mos reserchers focus on skll premum cross ndusres n developed economy, hus cnno specfy he supply of sklled lbor n economc rnson, or rce he ncome nequly bsed on skll premum. We nroduce skll dfferences of lbor no Hnsen & Presco (22 wo-secor frmework, nd nlyze he dynmc rnson. We show h he echnology cross secors, s well s he supply consrn of sklled lbor ffec he urnng pon of rnson, nd led o mulple possble phs of ncome nequly, ncludng nver U-shped, U-shped, N-shped curves. The remnder of he pper s orgnzed s follows. Secon 2 presens he OLG rnson model wh skll dfferences of lbor. Secon 3 dscusses he effec of supply consrn of sklled lbor on he urnng pon of rnson, he pce of developmen, nd skll premum. The qunve sudes re n Secon 4 o show he poenl of he model o ccoun for dfferen phs of ncome nequly, nd concluson follows n Secon The Model 2.. Technology Consder wo-secor economy wh grculure ( nd ndusry (. Boh echnologes re subjec o exogenous chnge nd boh hve consn reurns o scle. Indusry uses only sklled lbor, whle grculure cn use sklled nd unsklled lbor. The wo producon funcons re s follows: Y = A γ K N L ( φ µ φ µ Y = A γ K N (2 3

4 where K j, N re cpl nd lbor used me n echnology j ( j =,. Lnd s used j only n grculure, nd hus normlzed,.e. L =. φ (, s he cpl shre, µ (, s he lbor shre nd ( µ (, φ he lnd shre n grculure. (, s he cpl shre n ndusry. A nd A re nl level of TFP n boh secors, nd γ > nd γ > re he growh res of echnology. The cpl nensy n ndusry s ssumed o be hgher, > φ. Cpl s ssumed o deprece compleely ech perod 4. Oupus of he wo secors re dencl nd cn be used for consumpon or nvesmen. Fesbly requres: C + X + X = Y + Y (3 where C s ggrege consumpon, whle X nd X re ggrege nvesmens. We ke no ccoun he skll dfferences of lbor. Indusry echnology mches sklled lbor, whle ny lbor cn be used n grculure. Le ol lbor be N, he supply of sklled lbor be Q. We hve: N + N = N (4 N Q ; N / N (5 (4 s he ol lbor supply consrn. (5 mens h ndusry cnno employ more lbor hn he supply of sklled lbor, whle grculure cn use up ll lbor n he economy. In rdonl economy, ll lbor (ncludng he few sklled lbor re nvolved n grculure. Only when he supply of sklled lbor surpsses cern crcl level, cn modern ndusry be esblshed o employ sklled lbor wh skll premum. Thus n economc rnson, he supply of sklled lbor s n ncresng funcon of skll premum, nd ll lbor wll be sklled lbor wh he compleon of rnson. The supply of sklled lbor s defned s: N (, f ˆ ξ ξ ξ Q = N ( (, f > ˆ ξ z λ ξ ξ where ξ s he proporon of unsklled lbor n ol lbor, (- ˆ ξ s he mnmum requremen of sklled lbor o cve rnson. If ξ s hgher hn ˆ ξ, hen ll lbor re nvolved n grculure ernng equl wge re. Economc rnson ge sred f ξ ˆ ξ, nd he supply of sklled lbor wll ncrese s funcon of skll premum ever snce. Menwhle, unsklled lbor reduces ( ξ <, ξ <, nd n he lm, sklled lbor pproches o ol lbor. (6 4 In he qunve sudes perod s nerpreed o be 3 yers, so hs ssumpon s emprclly resonble. 4

5 We suppose ech ndvdul born n grculure secor s endowed wh he sme pece of lnd nd lbor me, he erns ncome by lbor work nd cpl-renng, whch s expended o consume, repy rens o cpl or lnd, nd ccumule cpl. Thus he prof mxmzon problem s: where Mx Y w N r K r L s..( (7 N, K, L K L w s he wge re of grculure, r K nd r L re rens of cpl nd lnd respecvely. Lnd s normlzed. Le k = K / N. The F.O.Cs of (7 re: r = φ A γ K N = φ A k N (8 φ µ + φ φ µ + φ K w = ( φ A γ K N = ( φ A k N (9 φ µ + φ µ + φ Becuse of he propery of CRS n producon (2, we ggrege ll ndusry frms. Gven echnology, neres re nd wge re of ndusry ( w, he prof mxmzon problem s: MxY r K w N f N Q ( K, N K or: MxY r K w Q f N > Q ( K K The F.O.Cs of ( nd ( re respecvely: r = Aγ K N ; w = ( Aγ K N (2 K r = Aγ K Q ; w = ( Aγ K Q (3 ' K In (3, becuse of he supply consrn of sklled lbor, wge re n ndusry presens hgher skll premum: w = ( A ( K / Q > ( A ( K / N = w. We wll dscuss hs ' pon n more del ler Household secor The model hs wo-perod overlppng generons (Dmond, 965. Le N be he number of young gens nd c be he consumpon level for he young gens n perod. Populon dynmcs re gven by N+ = g( c N, where g (. s n exogenous funcon h wll be specfed ler. In perod, here re N old gens, ech s endowed wh K / N uns of cpl nd L / N uns of lnd. Young gens re born wh one un of lbor me, whch hey supply elsclly. Dfferen from former models, only sklled lbor s demnded by ndusry. They 5

6 mke consumpon-svng decson on how much lnd nd cpl o purchse. They become old n he second perod where her sources of ncome re from renng lnd nd cpl o frms nd from he sle of lnd o he nex generon. For ech generon, young gens choose consumpon ( c, c 2 + nd nvesmen ( x, x, l + o mxmze lfeme uly: ( u c, c = ln c + β ln c ( subjec o he budge consrns: c = wj ( x + x + ql +, j=, (5 c = r ( x + x + ( q + r l (6 2+ K + L+ + where s β dscoun fcor nd q s he prce of lnd n perod. Re of reurn o cpl equlzes n boh secors, whle wge res dffer durng rnson s resul of skll premum Equlbrum Followng Hnsen & Presco (22 nd Ng (24, we nroduce he endogenous skll dfferences of lbor. The compeve equlbrum nd he dynmcs re esblshed 5. We nvesge he equlbrum where dynmcs of he model re chrcerzed by hree developmen sges. Sge s he rdonl growh sge where modern echnology s no used nd he economy s on he rdonl blnced growh ph (TBGP. The exogenous populon growh funcon s chosen such h ll he mprovemen n grculure s bsorbed by populon growh. Hence, here s no ncrese n per cp ncome or oupu. Sge 2 s he rnson sge where he level of TFP n ndusry s suffcenly hgh relve o grculure nd he supply of sklled lbor hs surpssed he mnmum requremen, nd becomes profble for ndusry o use modern echnology nd employ sklled lbor wh skll premum. The economy s n rnson o modern growh, nd more nd more lbor hs been culved s sklled lbor nd moblzed o ndusrl secor. In Sge 3, only modern echnology s used, ll lbor forces re sklled lbor nd he economy converges o modern blnced growh ph (MBGP. The dynmcs of he model shows h only when he supply of sklled lbor surpsses mnmum crcl level nd he ndusrl echnology s hgh enough o py for sklled lbor wh skll premum, cn he economy sr s rnson o modern economy. Menwhle, even f he rnson ges sred, f he supply of sklled lbor s lmed, modern ndusry cnno employ enough sklled lbor, whch n urn resuls n hgher skll premum. Hgh skll premum provdes ncenve for ccumulng sklls, nd he ncresed supply of sklled lbor cn bsorbed by modern ndusrl secor n he long run. Fnlly, wh more nd more sklled lbor beng lloced n ndusrl secor, he economy converges o blnced growh ph where oupu per worker s growng consn re. 5 Reders re referred o Appendx B for precse defnon nd proofs. 6

7 3. Economc Trnson nd he Dynmcs of Income Inequly We focus on he endogenous skll dfferences nd he role of skll premum n he hree sges of developmen o exmne he dynmcs of ncome nequly. In TBGP, ll lbor re lloced n grculure, whose echnology A mches unsklled lbor. Hence, wge re s he skll levels. Le v be he grculure cpl-oupu ro, he oupu per worker s: w regrdless of φ µ + φ /( φ γ yˆ = A v N (7 whch s consn gven populon growh re of lnd grow re of γ /( µ φ γ /( µ φ.along TBGP, he rens nd prce of, whle wge re w ˆ nd neres re of cpl r ˆK re consn. On TBGP, frms deermne when s profble o sr usng modern ndusrl echnology gven he prces of producon npus re her TBGP levels. If here s enough supply of sklled lbor n he economy,.e. ξ > ˆ ξ n (6, nd N Q, he condon of frms o sr usng modern echnology s: wˆ = γ A A z rˆk (8 where z s he skll premum n ndusrl secor ( w = zw. I urns ou h he hgher he level of echnology n ndusrl secor ( he economy o sr s economc rnson. A, he lower he skll premum, he more possble for If he sklled lbor sock hs surpssed he crcl mnmum level, bu N > Q, hen he condon of srng modern ndusrl secor s: wˆ = γ 2 A A z rˆk (9 where he wge re n ndusrl secor s w = z2w. (2 nd (3 mply z2 > z. Therefore, gven he TFP n ndusrl secors, he supply consrn of sklled lbor mkes more dffcul for frms o dop ndusrl echnology, whch delys economc rnson. Defne he urnng pon mply he followng condons. * o be he perod h he ndusrl echnology s frs used, (8 nd (9 7

8 A Bz ( A f N Q ; * * ( µ φ ( /( φ γ > γ N A Bz A N Q * * ( µ φ ( /( φ γ 2 ( > γ f > N (2 φ µ = ( φ ( where B ( v A /( φ, s funcon of echnologes nd preference prmeers. Snce he hreshold s consn, (2 wll be ssfed nd he ndusrl echnology wll ge used some pon s long s keeps growng. Therefore, no mer wh s he dfference n echnologes beween wo secors, he rnson o modern growh s nevble n ll economes. However, even f hey hve ccess o he sme echnologes, he urnng pons cn sll be dfferen, dependng on he growh re of modern echnologes n ech economy, nd wheher here s supply consrn of sklled lbor nd resulng levels of skll premum. Thus we hve he followng Proposon. Proposon : The urnng pon of rnson o modern economy depends on: ( he ccessbly o nd growh re of modern echnology; (2 wheher here s bundn supply of sklled lbor nd he level of skll premum. Skll premum ffecs economc rnson n wo wys. On he one hnd, wh relvely hgher supply of sklled lbor nd lower skll premum, he rnson s eser o cve. However, becuse of he relve surplus of sklled lbor, pr of sklled lbor ( Q N hs o work n grculure wh no skll premum. The fc provdes dsncenve for skll formon, whch my resul n shorge of sklled lbor some ler me durng rnson. On he oher hnd, he ndequcy n sklled lbor nd he hgher skll premum mkes more dffcul o cve rnson. Neverheless, hgher premum moves more skll formon nd n upgrdng of verge skll level, whch cn fcle rnson. Consder wo economes, he supply of sklled lbor s bundn n he frs one, nd ndeque n he second. From (2, he dfference of urnng pons of he wo economes s: ( ln( z / z = (2 ln γ * * 2 2 Gven echnology vlble n ndusrl secor, he urnng pon n he second economy s delyed by perod. ln γ When he economy s on s rnson o modern economy, he llocon of fcors requres equlzon of mrgnl producs cross secors. Le grculure, solves: φ f ( n φ ϕ = ( ( ϕ / z n A I N n φ φ µ φ µ z A * n be he equlbrum frcon of lbor n = (22 8

9 ( φ where ϕ =, I s he ol vlue of nvesmen by he young generon me (. µ Assume h n modern ndusrl secors he cpl nensy s hgher ( > φ, nd echnology grows fser ( A > A, he frcon of lbor n grculure s decresng nd converges o zero. Menwhle he frcon of sklled lbor s ncresng unl ll lbor re sklled lbor ( Q N. In (22, skll premum z serves s n cceleror o he process 6. If here s shorge n supply of sklled lbor, hen skll premum ( z 2 wll be hgher, whch wll furher renforce he bove effec. Therefore we hve Corollry. Corollry : Gven he echnology chnge n modern ndusrl secor, he shorge n supply of sklled lbor delys he urnng pon of rnson, bu cceleres he process n he long run. Wh more sklled lbor relloced o ndusrl secors, sympoclly he economy behves lke one-secor modern economy. Assume he populon growh re converges o consn re, he economy hen converges o MBGP. The cpl-oupu ro long MBGP s β ( v = ( + β γ /(, hus he oupu per worker s ( /( y = Aγ v. Along MBGP ll lbor wll be sklled lbor, wge nd consumpon per worker wll grow re of γ /( We now exmne he dynmc chnge of supply n sklled lbor nd ncome nequly. Le he Aγ A echnology dfference cross secors be E( = =, we consder how he skll premum A γ A chnges gven he supply consrn of sklled lbor. Proposon 2: 2 Gven supply consrn of sklled lbor (.e. ξ ˆ ξ, nd N > Q, nd he. condon of economc rnson s ssfed: wˆ = γ 2 A A z rˆk, hen we hve z / E( > 2, z / 2 Q <. Proof: By condon of prof mxmzon, we hve: 6 z > mkes he frs erm n (22 smller, nd he second erm lrger, whch resuls n fser convergence of * n owrds. The reders re referred o he Appendx B for del. 9

10 z 2 w ( A K Q = = φ w ( φ A K ( N Q φ φ ( A K Q φk ( N Q ( φ k φ φ φ A K N Q K Q φ k = = ( ( ( φ The hrd equon uses he condon of equlzon of mrgnl reurn of cpl cross secors. Becuse physcl cpl nvesmen s homogenous, mrke-clerng condon requres: Q k + ( N Q k = I. Tkng dervves on boh sdes wh respec o E(, we ge: (23 k k Q + ( N Q = E( E( (24 φ The equlzon of mrgnl produc of cpl cross secors mens: E( k = φk. Tkng nurl logrhm nd kng dervves wh respec o E( on boh sdes wll gve us: k k + ( = ( φ E( k E( k E( (25 (24 mples h k / E( nd k / E( mus be of oppose sgns. Combnng (25 leves us k / E(, k / E( 7, whch mens s he echnology dfference beween wo secors enlrges, here s cpl deepenng n ndusrl secor, whle cpl-lbor ro decreses n grculurl secor. Usng hs resul, we ge from (23: z / E( > 2. (23 lso mples k k ( ( φ > > (becuse of > φ. Bsed on Q k + ( N Q k = I, f φ supply of sklled lbor Q ncreses, hen mus be k / Q nd k / Q. We hen ge he followng resul from (23: z / 2 Q <. QED. Proposon 2 shows h under supply consrn of sklled lbor, skll premum wll enlrge wh he ncrese of echnology dfference beween secors, nd shrnk wh he ncrese n supply of sklled lbor. Le he ro of oupu per worker beween secors be φ y τ y =. We hen, bsed on y (9, (3 nd w = z2w, obn τ y = z2 > z2, whch s summrzed n Corollry 2. 7 Equon (25 does no hold f k / E( nd k / E(. Moreover, hese condons mples h he wdenng gp of echnology cross secors wll led o lower cpl-lbor ro n ndusrl secor, nd hgher cpl-lbor ro n grculurl secor, whch pprenly does no f he rely.

11 Corollry 2: 2 Under supply consrn of sklled lbor, he dfference n oupu per worker beween ndusrl nd grculurl secors s lrger hn skll premum durng economc rnson. 4. Qunve nlyss Bsed on our model, he dfferences of echnology beween secors nd supply consrn of sklled lbor ffec skll premum, whch n urn nfluences he urnng pon nd he subsequen pce of developmen. We hus esblsh clbron o nlyze how ncome nequly s ffeced. We wll provde n explnon why, nsed of pursung unque ph, he dynmcs of ncome nequly durng rnson dffers cross counres. In our clbron, perod n he economy s 3 yers n rel me. Agens wll lve 6 yers workng for he frs 3 yers n her lfespn. The nl condons, A, A, L nd N re se o rbrrly. Gven N, K s deermned such h he economy s nlly on TBGP, nd ll lbor work n grculure. The cpl shre n modern ndusry s =.6, whle he cpl shre n grculure s φ =.. For smplcy, ssume populon growh re s, whch wll no brng menngful chnge o he mn resuls. Le dscoun fcor β be. 4.. Consrn of sklled lbor supply nd he begnnng de of rnson As cn be found n (6, economc rnson cn ge sred only when he supply of sklled lbor surpsses cern crcl level. On he one hnd, dfferen counres sr rnson dfferen des, when he ndusrl echnology vlble nd he mnmum requremen of sklled lbor dffer; on he oher hnd, due o he dfferences n skll premum, he ncreses n sklled lbor supply dffer cross counres durng rnson nd he subsequen pce of developmen. Fgure presens how he mnmum requremen of sklled lbor nd he nl supply of sklled lbor ffec he begnnng de of rnson. Suppose echnology chnge re s n grculure, bu.2 (.6% per yer n ndusry, whch corresponds o he sklled lbor demnd curve.

12 .9 Sklled Lbor urnng pon sklled lbor demnd sklled lbor supply sklled lbor supply me Fgure. Inl sklled lbor, mnmum requremen of sklled lbor nd he begnnng de of rnson Noe: Sklled lbor demnd corresponds o ndusrl echnology chnge re of.2. The curves of skll lbor supply nd 2 come from (6, wh nl shres of skll lbor of. nd. respecvely, he correspondng prmeer prs of ( ξ, λ re (.9,.5 nd (.999,.5 respecvely. The mnmum requremen of sklled lbor for rnson s defned by ˆ ξ =.8. In Fgure, he curves of sklled lbor supply nd 2 come from (6, he correspondng prmeer prs ( ξ, λ re (.9,.5 nd (.999,.5 respecvely. Suppose he mnmum requremen of sklled lbor for rnson ses ˆ ξ =.8. The nl supply of sklled lbor s very low (. for sklled lbor supply 2, whch leds o sklled lbor shorge nd hgher skll premum when he ndusrl echnology s low. The supply of sklled lbor s smuled o ncrese fser perod 2 nd reches he mnmum requremen of sklled lbor round perod 2.4. As for sklled lbor supply, he nl shre of sklled lbor s hgher (bu no s hgh s.2, he mnmum requremen for rnson, he supply of sklled lbor moves o quck ncrese round perod 3, when he ndusrl echnology s hgher, nd reches he urnng pon of rnson round perod 3.2. Gven echnology chnge re of.2, Fgure presens suon h he economy wh lower nl sklled lbor my ke off erler hn he economy wh hgher nl sklled lbor. Why s he cse? As Proposon nd (2 show, he low nl sklled lbor n n economy my dely s economc ke-off (level effec, however, he supply of sklled lbor my sr o ncrese fser erler d becuse he skll premum s hgher (growh effec. If he growh effec domnes, he economy wh lower nl sklled lbor cn ke off erler hn n economy wh hgher nl sklled lbor. Neverheless, wo mpled prerequses work: ( here s mnmum requremen of sklled lbor for ke-off; (2 he supply of sklled lbor should be elsc wh respec o skll premum. Also n Fgure, f he mnmum requremen of sklled lbor shre s lower (sy,., hen he economy wh hgher nl sklled lbor (skll lbor supply wll ke off erler ( perod, whle he economy wh lower nl sklled lbor (skll lbor supply 2 wll w les 3 yers o ke off. Wheher sklled lbor supply s sensve o skll premum depends on mny fcors, ncludng educon sysem, culure, hsory, s well s echnology growh re. 2

13 sklled lbor economc ke-off sklled lbor demnd sklled lbor supply3 sklled lbor supply2 sklled lbor supply me Fgure 2. Technology chnge, skll premum nd economc ke-off Noe: Sklled lbor demnd corresponds o ndusrl echnology chnge re of.3. The curves of skll lbor supply, 2 nd 3 come from (6, he correspondng prmeer prs of ( ξ, λ re (.9,.9 nd (.999,.5 nd (.9,.5 respecvely. The mnmum requremen of sklled lbor for rnson s defned by ˆ ξ =.8. In Fgure 2, sklled lbor demnd represens hgher re of echnology chnge (.3 per perod or.88% per yer. Sklled lbor supply 2 corresponds o low nl level nd hgh growh re of sklled lbor. The nl sklled lbor s he sme for sklled lbor supply nd sklled lbor supply 3, bu he growh re for he ler s much hgher. Gven hs hgher echnology chnge, skll premum occurs erler even for he economy wh relvely hgher nl sklled lbor. The economy represened by sklled lbor supply 3 enlrges s supply of sklled lbor round perod 2, nd reches he urnng pon of rnson round 2.4 perod (erler hn he economy represened by sklled lbor supply 2. We hus conclude h hgher echnology chnge s necessry condon for n economy wh relve bundn sklled lbor o ke he led n economc rnson. Menwhle, we fnd h n economy represened by sklled lbor supply wll no rech s urnng pon unl round 3.2 perod, more hn 3 yers ler hn economy wh sklled lbor supply 3, nd bou 2 yers ler hn economy wh sklled lbor supply 2. We gn conclude h prerequse for n economy wh relvely bundn sklled lbor o ke off erler s h s supply of sklled lbor should be sensve o skll premum Skll premum, economc rnson nd he dynmcs of nequly We now focus on how he consrn of sklled lbor ffecs he dynmcs of nequly durng rnson. The echnology of grculure s se o. We consder hgher echnology chnge re of.4 (.3% nnully nd lower echnology chnge re of.2 (.6% nnully. In order o concenre on he pce of rnson, we djus he nl cpl sock o mke sure h n economy whou ny consrn of sklled lbor reches urnng pon he begnnng of perod. The supply of sklled lbor s hus smplfed s: Q = ξλ (6 3

14 where λ ( λ s he chnge re of unsklled lbor, nd nlly Q = ξ. We consder hree combnons of sklled lbor supply he urnng pon. The curve sklled lbor supply wh prmeers of ξ =. nd λ=.9 corresponds wh he cse of hgh nl level nd low growh re of sklled lbor. Curve sklled lbor supply 2 wh prmeers of ξ =.9 nd λ=.5 corresponds wh he cse of low nl level nd hgh growh re of sklled lbor. For he cse of low nl level nd low growh re of sklled lbor, we se ξ =.9 nd λ =.9 n sklled lbor supply 3. In comprson wh (6, we consder lner funcon of sklled lbor supply, nd n rcn funcon of sklled lbor supply. The ler mens when he moun of sklled lbor s nlly low, he ncrese n s supply s slow; he ncrese n supply of sklled lbor cceleres s he frcon of sklled lbor ncreses nd fnlly slows down gn when he frcon of sklled lbor s hgh enough. The funcons re se s follows: Q( = (26 Q( = rcn(2.5* +.5 (27 3 ( b.8.8 sklle d l bor.6.4 sklled lbor demnd.2 sklled lbor supply sklled lbor supply2 sklled lbor supply me sklle d l bor.6.4 sklled lbor demnd.2 lner sklled lbor supply rg-n sklled lbor supply me (c (d.8.8 sklle d l bor.6.4 sklled lbor demnd b.2 sklled lbor supply sklled lbor supply2 sklled lbor supply me sklle d l bor sklled lbor demnd b lner sklled lbor supply rg-n sklled lbor supply me Fgure 3. Demnd for nd supply of sklled lbor Noe: Sklled lbor demnd curves nd b correspond o low (.2 nd hgh (.4 echnology chnges. Curves of sklled lbor supply, 2, 3 correspond o he prmeer prs ( ξ, λ of (.,.9, (.9,.5, nd (.9,.9 respecvely. Lner supply of sklled lbor s defned by (26, whle rcn funcon of supply of sklled lbor defned by (27. 4

15 Fgure 3 depcs he dynmc chnge of he demnd for nd supply of sklled lbor durng economc rnson. The demnd curves nd b correspond o low nd hgh growh res of echnology respecvely. In Fgure 3(, gven low re of echnology chnge, he supply consrn of sklled lbor occurs he les n supply of sklled lbor (round perod 3.5, bu occurs erler n supply of sklled lbor 2 (round perod2.5, nd even erler n supply of sklled lbor 3 (bou perod.3, or yers fer he urnng pon. The comprson beween Fgure 3 (c nd ( shows h wh hgher re of echnology chnge n ndusrl secors, he supply consrn of sklled lbor wll no occur unl ler me gven he bove hree supply curves of sklled lbor. For exmple, he supply consrn of sklled lbor does no occur unl round 3.5 perods n supply of sklled lbor 3. Smlrly, n Fgure 3(b where echnology chnge s slow n ndusry, eher lner or rcn supply funcon of sklled lbor cn mee he demnd for sklled lbor durng he whole pce of rnson. Whle n Fgure 3(d, where echnology chnge s fser, supply consrn of sklled lbor occurs round 3.5 perods fer he urnng pon for lner supply funcon, he rcn funcon of supply of sklled lbor nersecs he demnd for sklled lbor hree mes represenng mul-phrse ph wh chnge from shorge (round perod 3.5 o surplus, nd noher shorge srng from round perod 6. ( ( b.9.9 sklled lbor me rnson :sklled lbor supply consrn2 rnson :no sklled lbor supply consrn rnson :sklled lbor supply consrn rnson :sklled lbor supply consrn3 sklled lbor me economc rnson of no sklled lbor supply consrn economc rnson of lner sklled lbor supply economc rnson of rg-ngen sklled lbor supply Fgure 4. Supply consrn of sklled lbor nd economc rnson Noe: Technology chnge n ndusrl secor s.2 per perod. The curves of sklled lbor supply, 2, 3 correspond o he prmeer prs (, ξ λ of (.,.9, (.9,.5, nd (.9,.9 respecvely. Lner supply of sklled lbor s se by (26, whle rcn supply funcon of sklled lbor s se by (27. We hen exmne he effec of supply consrn of sklled lbor on he pce of rnson. In Fgure 4, ssumng he echnology chnge re s.2 per perod, we depc he benchmrk of rnson wh no supply consrn of sklled lbor. In Fgure 4(, Trnson ph wh sklled lbor supply fs he whole benchmrk ph que well 8. Trnson ph wh sklled lbor 8 Erly developed Europen counres presen good exmple for sklled lbor supply. In counres such s U.K., Frnce, Germny, verge educon nd skll levels re relvely hgh her begnnng of economc rnson. The sble growh of sklled lbor ensures smooh developmen ever snce he Indusrl Revoluon. Jpn s noher exmple. As erly s he Mej Reform er, Jpn mde prmry educon unversl, whch ws even erler hn mny Europen counres. Afer World Wr wo, lhough oupu per cp dropped o much 5

16 supply 2 does no deve from he benchmrk ph unl he begnnng of perod 6 9. Obvously, he rnson ph correspondng o sklled lbor supply 3 hs been below he benchmrk level ever snce perod 3, nd he gp becomes lrger fer perod 4. We herefore conclude h low frcon nd slow growh re of sklled lbor cn negvely ffec he developmen pce. From fgure 4(b, we fnd ou h he rnson pce correspondng wh lner supply of sklled lbor s loced below he benchmrk ph ever snce round perod 3.5, nd he gp reches s summ round perod 6. Correspondng o rcn supply funcon of sklled lbor, he rnson ph s below benchmrk from perod 2 o 3.5, nd hen fs he benchmrk locus well, fnlly urns o be lower hn benchmrk level snce he begnnng of perod 5 becuse he supply of sklled lbor becomes growng slower. wge ro nequly ph2 nequly ph nequly ph3 wge ro nequly ph4 nequly ph5 (b per lbor produc ro me nequly ph2 nequly ph nequly ph3 (c me per lbor produc ro me nequly ph4 nequly ph5 (d me Fgure 5. The dynmcs of skll premum nd dfferences n oupu per worker As Fgure 5 presens, he dynmcs of nequly (represened here by wge ro nd ro of oupu per worker beween secors hve smlr phs, whle he gp n oupu per cp s lrger below s pre-wr level, nd here ws huge desrucon of lbor force durng he wr, he susned sble ccumulon of humn cpl provded bundn sklled lbor o suppor s economc recovery nd rnson. 9 U.S. s n exmple for sklled lbor supply 2. U.S. begn s rnson ler compred wh mny Europen forerunners. The ggrege oupu n he U.S. rnked No. n 894, whle s oupu per cp dd no surpss h of U.K. unl 93. U.K. begn s rnson round he er of he Cvl Wr, when he supply of sklled lbor ws very low. The U.S. mde prmry educon unversl whn 6 yers, whch provded sold supply pool of sklled lbor for economc ke-off. Before he World Wr wo, he U.S. mde secondry educon unversl, whch s bou 3-4 yers erler hn U.K., Frnce nd Germny. In he 2 h cenury, he lbor force he ge of n he U.S remns he hghes verge educon level, whch for sure s drvng force for s developmen.(clculed bsed on A.Mddson (2, Appendx A. Along MBGP, he nercon beween SBTC nd skll premum, n ddon o mmgron of humn cpl from brod helps vod severe shorge of sklled lbor (Acemoglu, 22; Murphy & Welch, 992. An exmple for sklled lbor supply 3 s Souh-Shr Afrcn counres. The verge Humn Developmen Index (HDI for hese counres s s low s.486, he ndex for dul lerry s 57.5, ndex for lfe expecncy brh s 46, nd ndex for combned gross enrollmen for schools s 46. Moreover, ll he ndexes, whch represen very low supply of sklled lbor, do no show ny sgnl for mprovemen snce 975. None of hese counres hve fulflled rnson o modern economy, he verge ndex of GDP for hem s s low s.58 (Humn Developmen Repor, UNDP,25. 6

17 s we fnd n Corollry 2. Fgure 5( provdes hree dynmc phs of ncome nequly correspondng o he hree combnons of prmeer n equon (6. Sklled lbor supply corresponds wh U-shped chnge n nequly, s wh we fnd n U.K. durng , n U.S.A. durng Sklled lbor supply 2 corresponds wh wo-phrse chnge n nequly (skll premum keeps sble n perods -5, rses o hgher level round he end of perod 5, nd roughly remns he new level, s wh we fnd n Jpn, where he Gn coeffcen drops sgnfcnly fer 945 becuse of he relve bundn humn cpl nd exreme shorge of physcl cpl hen. Sklled lbor supply 3 corresponds wh n upwrd slopng nd seep curve n nequly, whch shows h he low nl level nd low growh of supply of sklled lbor led o lrge nd ccelerng enlrgng nequly overme. In Fgure 5(b, he nequly ph correspondng wh lner supply of sklled lbor urns ou o be nvered U-shped. Inequly ncreses sgnfcnly round perod 3, nd reches s summ round perod 5, nd move no downwrd secon unl skll premum dsppers long MBGP. The nequly n U.K. from 688 o round 9 s ypcl exmple. As for he rcn supply funcon of sklled lbor, he sklled lbor s nlly lmed nd growng slowly, whch consrns rnson from he very begnnng perod nd mke skll premum ncresng. In he mddle of rnson, he ncresed supply of sklled lbor surpsses he demnd for, nd rnson moves closer o he benchmrk pce (see Fgure 4(b, whch shrnks skll premum. In he ler perod of rnson, supply of sklled lbor decreses gn, whch leds o ncresng nequly fer he begnnng of perod 6. I hus corresponds wh n N-shped chnge of nequly s wh we fnd n U.K. durng Conclusons Bsed on Hnsen & Presco (22, we nroduce skll dfferences n lbor, nd consruc dynmc model of economc rnson. The models of Hnsen & Presco (22 nd Ng (24 mke he ssumpon of lbor ndfferences so h ny lbor cn ge nvolved n grculurl or ndusrl producon. We ssume here s sgnfcn dfference n lbor sklls, eher unsklled or sklled lbor cn be employed n grculure, whle only sklled lbor cn mch modern echnology n ndusrl secors. Therefore, due o he dfferences n he nl sock of sklled lbor nd s growh re, he urnng pon of rnson my be delyed, nd he ph of rnson my be ffeced. The supply consrn ffecs boh he begnnng de nd he subsequen pce of modern growh, nd hus n urn ffecs he dynmcs of ncome dsrbuon. We provde noher pproch o he mechnsm of economc rnson nd long-run growh. Romer (986 esblshes n ncresng-reurn model nd explns he long-run non-decesng growh n mos Europen ndusrl counres. Oher reserchers expln he cross-counry dfferences n rnson nd growh wh exernles (Lucs, 988, brrers o nvesmen (Ng, 24, or economy of scle (Wng & Xe, 23. In our model, he producon funcons of boh grculure nd ndusry exhb consn reurn o scle. We prove h, whou ny consderon of exernles or brrers o prve nvesmen, he dfferences n lbor sklls nd n echnologes cross secors mke possble for sklled lbor o rnsform no modern ndusry. There wll hus be connuous cpl deepenng n ndusry, whch n urn resuls n connuous growh n oupu per cp. On MBGP, ll lbor re sklled lbor, nd he economy s growng consn re. 7

18 Our smulon nd qunve nlyss presen more evdences why cross-counry oupu per cp nd ncome dsrbuon re so dfferen. To gre exen, he dfferences n echnologes cross secors nd n he nl sock of sklled lbor expln he dynmcs of ncome dsrbuon overme. If he nl sock of sklled lbor s low, nd growng low re, hen here wll be huge dely n he begnnng de of economc rnson, nd ncome nequly wll be ncresng over longer perod. Gven echnology progress, he supply consrn nd he dynmc chnge of sklled lbor resul n mulple possble phs of ncome dsrbuon, such s U-shped, nvered-u-shped or N-shped ones. We lso rgue h he ncome nequly durng economc rnson s hgher hn h on blnced growh phs, whch mens subsnl frcon of exsng ncome dfferences s rnsonl. Therefore, durng economc rnson, no only fser echnology progress, bu lso more nvesmen on educon nd skll formon re recommended o reduce he supply consrn of sklled lbor, fcle economc rnson nd long-run growh, nd decrese ncome nequly. References: Acemoglu, D., (22, Dreced Techncl Chnge. The Revew of Economc Sudes 69:78-89 Acemoglu, D., (2, Techncl Chnge, Inequly, nd he Lbor Mrke, Mmeo, MIT. Acemoglu, D., (998, Why Do New Technologes Complemen Skll? Dreced Techncl Chnge nd Wge Inequly, Qurerly Journl of Economcs, 3, pp Acemoglu, D., (23, Perns of Skll Prem, Revew of Economc Sudes, (7, pp Aghon, P., (22, Schumpeern Growh Theory nd he Dynmcs of Income Inequly. Economerc 7: Aghon, P, E.Crol, nd C.Grc-Perlos, (999, Inequly nd Economc Growh: The Perspecve of he New Growh Theores, Journl of Economc Lerure 37, Aghon, P. nd P. Bolon, (997, A Trckle-down Theory of Growh nd Developmen wh Deb Overhng, Revew of Economc Sudes, 64, Aghon & How, (992, A Model of Growh Through Creve Desrucon, Economerc, 6, Alesn nd Rodrk, (994, Dsrbuve Polcs nd Economc Growh, Qurerly Journl of Economcs, 9, Ahluwl, M.S., (976, Income Dsrbuon nd Developmen: Some Sylzed Fcs, Amercn Economc Revew, Ppers nd Proceedngs, 66, pp Ahluwl,M.S., (976b, Inequly, Povery nd Developmen. Journl of Developmen Economcs 3: Aken, Brn, Ann Hrrson, Rober E. Lpsey, (996, Wges nd Foregn Ownershp: A Comprve Sudy of Mexco, Venezuel, nd he Uned Ses, Journl of Inernonl Economcs, NO.4, pp Annd,S. nd R.Knbur, (993, The Kuznes Process nd he Inequly Developmen Relonshp. Journl of Developmen Economcs 4:25-52 Annd,S. nd R.Knbur, (993b, Inequly nd Developmen: A Crque. Journl of Developmen Economcs 4:9-43. Brro, R. J. (2, Inequly nd growh n pnel of counres. Journl of Economc Growh, Vol. 5, No, pp Brro, J.R., nd Sl--Mrn, X., (22, Economc Growh, Second Edon, Cmbrdge: The MIT Press. 8

19 Benbou, R., (996, Heerogeney, Srfcon, nd Growh: Mcroeconomc Implcons of he Communy Srucure nd Socl Fnnce, Amercn Economc Revew, 86, Benbou, R., (996b, Equy nd Effcency n Humn Cpl Invesmen: The Locl Connecon, Revew of Economc Sudes, 63, Bermn, E., J. Bound nd Z. Grlches (994: Chnges n Demnd for Sklled Lbor Whn US Mnufcurng: Evdence from he Annul Survey of Mnufcures, Qurerly Journl of Economcs, 9:2, pp Dennger, K. & L. Squre, (996, Mesurng Income Inequly: A New D Bse, The World Bnk Economc Revew,, Dmond, P.A., (965, Nonl Deb n Neoclsscl Growh Model. Amercn Economc Revew 55:26-5. Felds,G. & G.Jkubson, (994, New Evdence on he Kuznes Curve. Mmeo (Cornell Unversy, Ihc. Forbes, K., (2, A Ressessmen of he Relonshp beween Inequly nd Growh, Amercn Economc Revew, 9, Frncos, J.F., & H., Rojs-Romgos, (28, Ressessng he Relonshp beween Inequly nd Developmen. CPB dscussng pper, NO. 7. Glor,O. & Mov, O., (22, From Physcl o Humn Cpl Accumulon: Inequly n he Process of Developmen. Brown Unversy Workng Pper No Glor, O. & D.Tsddon, (997, Technologcl Progress, Mobly, nd Economc Growh, Amercn Economc Revew, 76, Glor O. & J. Zer, (23, Income Dsrbuon nd Mcroeconomcs, Revew of Economc Sudes, 6, Grc-Penlos, C. & S.J. Turnovsky, (24, Growh, Inequly, nd Fscl Polcy wh Endogenous Lbor Supply: Wh re he Relevn Trdeoffs?, Mmeo, Unversy of Wshngon. Goldsmh, S., (967, Chnges n he Sze Dsrbuon of Income, n E.C. Budd, (ed., Inequly nd Povery (Hrper nd Row, New York, wh n upde n Budd s nroducon. Gylfson,T & G.Zoeg, (23, Inequly nd Growh: Do Nurl Resources Mer? n Inequly nd Growh: Theory nd Polcy Implcons: T.S. Echer & S.J.Turnovsky (eds. Cmbrdge MA: MIT Press. Hnsen,G.D., & E.C.Presco, (22, Mlhus o Solow. Amercn Economc Revew 92: Herl, T. & F. Zh, (26, Lbor Mrke Dsorons, Rurl-Urbn Inequly nd he Openng of Chn s Economy. Economc Modelng 23:76-9. Knbur, R., (2, Income Dsrbuon nd Developmen. Hndbook of Income Dsrbuon Volume : Knbur, R. & X. Zhng, (25, Ffy Yers of Regonl Inequly n Chn: A Journey Through Cenrl Plnnng, Reform nd Openness. Revew of Developmen Economcs 9:87-6. Kuznes,S., (955, Economc Growh nd Inequly. Amercn Economc Revew 45:-28. Kuznes, S., (953, Shres of Upper Income Groups n Income nd Svngs. New York: Columb Unversy Press. L, H.Y. & H.F. Zou, (998, Income Inequly s no Hrmful o Growh: Theory nd Evdence, Revew of Developmen Economcs, 2, Lnder, P.H., (2, Three Cenures of Inequly n Brn nd Amercn. In Aknson nd Bourgugnon (eds. Hndbook of Income Dsrbuon, Volume. Lnder, P.H. nd J.G. Wllmson, (982, Revsng Englnd s Socl Tbles, Explorons n Economc Hsory 9: Lnder, P.H. nd J.G. Wllmson, (983, Renerpreng Brn s Socl Tbles, Explorons n Economc Hsory 2:

20 Lucs, R., (988, On he Mechncs of Economc Developmen, Journl of Monery Economcs, 22(, Lundberg, M. & L. Squre, (23, The Smulneous Evoluon of Growh nd Inequly, Economc Journl, 3, Mddson, A., (2, The World Economy: A Mllennl Perspecve, OECD. Mnm, R., (998, Economc Developmen nd Income Dsrbuon n Jpn: An Assessmen of he Kuznes Hypohess, Cmbrdge Journl of Economcs, 22(: Mzoguch, T., (985, Economc Developmen Polcy nd Income Dsrbuon: he Experence n Es nd Souhes As, Journl of he Developng Economes, 23(4: Mzoguch, T. nd Tkym, N., (984, Equy nd Povery under Rpd Economc growh: he Jpnese Experence. Tokyo: Knokuny. Morguch, C. nd Sez, E.,(26, The Evoluon of Income Concenron n Jpn, : Evdence From Income Tx Sscs, NBER Workng ppr No Murphy, K. & F. Welch,(992, The Srucure of Wges. Qurerly Journl of Economcs, 7: Ng, L.R., (24, Brrers nd he Trnson o Modern Growh, Journl of Monery Economcs, Persson, T. & G. Tbelln, (994, Is Inequly Hrmful for Growh?, Amercn Economc Revew, 84, Pero, R., (996, Growh, Income Dsrbuon, nd Democrcy: Wh he D Sy, Journl of Economc Growh,, Romer, P.M., (986, Incresng Reurns nd Long-run Growh, Journl of Polcl Economy, 94, Sn-Pul, G. & T.Verder, (993, Educon, Democrcy, nd Growh, Journl of Developmen Economcs, 42, Royl Commsson on he Dsrbuon of Income nd Welh, 977, Repor No.5, Thrd Repor of he Sndng Reference (HMSO, London. Shrhse, S., 2, Jpnese Income Inequly by Household Types n Comprve Perspecve, LIS workng Pper No.268. Sculr, T., X. Yue, B. Gusfsson & S. L, (27, The Urbn-Rurl Income Gp nd Inequly n Chn. Revew of Income nd Welh 53: Volne, G., (22, Technologcl Acceleron, Skll Trnsferbly nd he Rse n Resdul Inequly. Qurerly Journl of Economcs 7 (, Wng, P. & D. Xe, (23, Acvon of Modern Indusry, Journl of Developmen Economcs, Wllmson, J.G., 985, Dd Brsh Cplsm Breed Inequly? Boson: Allen nd Unwn. Zho, Y., (999, Levng he Counrysde: Rurl-o-Urbn Mgron Decsons n Chn. Amercn Economc Revew 89: Appendx A: The dynmcs of nequly nd rnson n U.K., U.S.A. nd Jpn Ths ppendx provdes he dynmcs of nequly n hree economes: he U.K., U.S.A, nd Jpn o presen how he chngng phs of nequly re ffeced by economc rnson nd dffer cross economes. 2

21 Fgure A Evoluon of ncome nequly n UK: Noes: ( Inequly d of ncludes d of Englnd nd Wles. D source: Lnder & Wllmson (982, 983 nd Wllmson (985, curves of A2 nd A3 refer o he ncome shres of op 5% nd op 2% populon respecvely; whle A s Gn coeffcen. (2 Ler d nclude d of Gre Brn. SPI (Survey of Personl Income d of come from Royl Commsson (977, curves of B, B2, B3 refer o he ncome shre of op %, 5% nd 2% populon, B4 s Gn coeffcen. (3 SPI d of come from Economc Trends (978, 984, 987, curves of C, C2, C3 nd C4 refer o he ncome shre of op %, 5% nd 2% populon, nd Gn coeffcen respecvely. (4 D of come from Economc Trends (994, 995, 997, curves of D, D2 refer o ncome shre of op 2% populon nd Gn coeffcen respecvely. Fgure A2 Evoluon of ncome nequly n USA: Noes: ( D of come from Kuznes (953, curves A nd A2 represen he ncome shre of op % nd 5% populon. (2 D of come from Goldsmh (967 nd Offce of Busness Economcs, B2, B3, nd B4 represen he ncome shre of op 5% nd 2% populon, nd Gn coeffcen respecvely. D of come from The Census Bureu nd Curren Populon Suevey (CPS, C3 nd C4 represen ncome shre of op 2% populon nd Gn coeffcen. 2

22 Fgure A3 Evoluon of ncome nequly n Jpn: Noes: ( A s bsed on d of of he ncome shre of op % populon (Morguch & Sez, 26. (2 Mnm (998, Mzoguch (985, Ono & Wnbe (976 provde d of Gn coeffcen before WWⅡ, whch re represened by curves of B, B2, B3 respecvely. (3 D fer WWⅡ come from Mzoguch & Tkym (984 nd Shrhse (2, represened by C nd C2 respecvely. Appendx B: Compeve Equlbrum of he model Ths ppendx derves he compeve equlbrum n our hree-developmen-sge model under he ssumpons A-A6 o be specfed below. Gven N, K nd L, compeve equlbrum consss of prces vecor {,,, K, L} q w w r r, frm llocon { K, K, N, N, L, Y, Y } nd household llocon { c, c, x, x, l } 2+ +, such h: ( gven prces, household nd frm llocons mxmze uly nd prof respecvely; ( ll mrkes cler,.e. L = = N l, Y + Y = Nc + N c2 + N x, N + N = N, N Q, K K K + =. ( he cpl ccumulon nd populon growh follows he lws of moon: K = + N x, K = + N x nd N = + g( c N. Assume uly funcon s: (A u( c = ln c In equlbrum, c wj =, j=, ; R + β q + r =,f l > ; R = r,f x > or x >. L q K We cn solve he model for uly funcon of consn neremporl elscy of subsuon wh no much chnge n he key resuls. 22

23 B.. Trdonl Blnced Growh Ph(TBGP On TBGP, ll workers work n rdonl grculure. The funcon of populon growh g (. s chosen so h boh oupu per cp (or per worker ( y ˆ nd cpl per cp ( k ˆ re consn. Assume: g c γ (A2 ( ˆ g ( c g ( c ˆ /( µ φ =, nd c c, c ε, ε > >, [ ] + hen oupu per cp wll be consn: yˆ = A γ kˆ N. Defne cpl-oupu ro on φ µ + φ TBGP s v = kˆ / yˆ, where v = + β µ + β µ µφβ + β 2 ( ( 4 ( 2( + β γ /( µ φ. We hus hve φ µ + φ /( φ γ yˆ = A v N. On TBGP, The prce nd renl re of lnd grow of cpl re consn. γ /( µ φ, whle he wge re nd renl re B.2. Trnson B.2. The cse when he supply of sklled lbor s bundn ( N Q When frm srs o use modern echnology, s opmzon problem s: Ψ = γ ( rk, w Mx( A K N rk K wn K, N The opml decson of he frm mples: K N w = ( r K, so he prof funcon becomes: w w Ψ ( r, w = Mx Aγ N N ( rk K Becuse only sklled lbor cn mch he modern echnology used n ndusry, he workers h cn be rnsformed o ndusry re sklled lbor, who cn ern skll premum n ndusrl secor. The wge res n grculure nd ndusry re hus dfferen. Assume w = zw, where z > s he skll premum under he condon of N < Q. Therefore he prof funcon cn be wren s: z w z w Ψ ( r, w = Mx Aγ N K N ( rk Along TBGP, he frm wll use modern echnology f o modern ndusry s: Ψ( ˆ, wˆ. The condon of rnsform r K 23

24 wˆ = γ A A z rˆk B.2.2 The cse when he supply of sklled lbor s consrned ( N > Q In hs cse, he opmzon problem frm fces when srs o use modern echnology s: Ψ = γ ( rk, w Mx( A K Q rk K wq K, N The opml decson of he frm requres: K Q w = ( r K, nd he prof funcon becomes: w w Ψ ( rk, w = Mx Aγ Q Q ( rk Due o he scrcy of sklled lbor, ndusrl secor wll provde wge re of w = z2w, where z 2 s skll premum when he supply of sklled lbor s consrned. Becuse ndusry hs o py more o rc sklled lbor, he skll premum n hs cse s hgher hn h n he cse wh bundn supply of sklled lbor,.e. z2 > z. The prof funcon s hus rewren s: z w z w Ψ ( r, w = Mx Aγ Q 2 2 K Q ( rk Agn, long TBGP, he frm wll use modern echnology f Ψ( ˆ, wˆ, he condon of r K rnsform o modern ndusry s: wˆ = γ 2 A A z rˆk. Obvously, becuse of z2 > z, he supply consrn of sklled lbor mkes even more dffcul for he condon of rnsform o be ssfed, he economc rnsform s herefore expeced o dely. However, he hgher skll premum cn provde more ncenve for skll formon, he supply of sklled lbor wll ncrese unl cn ssfy he demnd for skll lbor n ndusry. Our followng dscusson on rnson wll focus on he cse of N Q. B.2.3 The ph of rnson Gven he nl condon /( K = ( N µ v φ, r ˆK nd w ˆ cn be represened s funcon of N. The urnng pon of economc rnson * ssfes: A Bz A * * ( µ φ ( /( φ γ ( > γ N 24

25 φ µ = ( φ ( where B ( v A /( φ. Gven q, N nd lnd normlzed o (L=, he ol vlue of nvesmen of younger generon n perod (- s: I = N ( wj c q, j=,. Prof mxmzon mples: Y K φy Y =, =, w ( K N w Y µ φ µ =, rl = ( Y N Tkng no ccoun w = zw, nd ssumng: (A3 > φ we hve: k ϕ ( φ = k, where k = K / N, k = K / N, nd ϕ = <. z µ Mrke clerng requres: k ( ϕ / z ( I / N =, where n = N / N. Becuse here re ( ( ϕ / z n skll dfferences n lbor, whle he reurns of cpl re equl cross secors, we hve: k φ A ϕ φ = A z N µ + φ Therefore, he equlbrum * n solves f n * ( =, where φ f ( n φ ϕ = ( ( ϕ / z n A I N n φ φ µ φ µ z A where µ φ > nd * unque [, n. We furher ssume: * mples f <, f ( >, nd f ( <. Thus here exss (A4 γ > γ (A5, n, s.. g( c n > f < µ g( c f µ 25

26 hen A I φ N µ A s n ncresng funcon of me, nd * n converges o zero. Snce he shre of lbor workng n grculure wll converge o, he shre of sklled lbor n ol lbor wll ncrese ccordngly,.e. n he lm, Q N. Menwhle, he skll premum z plys role n he bove funcon of f ( n n h mkes he frs erm smller nd he second erm lrger (hrough ncresng I, so helps o mke he rnson fser. If here s supply consrn of sklled lbor n he economy, he skll premum ( z 2 wll be hgher, whch my mke he bove mechnsm more sgnfcn. B.3 Modern Blnced Growh Ph(MBGP As he economy rnsforms o modern economy, n converges o, boh r nd q. * L Assume: (A6 lm g( c = g c he economy converges o MBGP. Oupu per cp ( y s growng consn re. The β β γ ( cpl-oupu ro of modern economy s v = /( ( +, nd oupu per cp hus equls o: ( /( of y = Aγ v. All lbor re sklled lbor, nd he wge nd consumpon grow re γ /(. 26