Infrastructure and Evolution in Division of Labour

Transcription

1 Infrarucure and Evoluion in Diviion of Labour Mei Wen Monah Univery (Thi paper ha been publihed in RDE. (), 9-06) April 997 Abrac Thi paper udie he relaionhip beween infrarucure ependure and endogenou growh generaed by ponaneou evoluion of diviion of labour. I idenifie he neceary condion for infrarucure ependure o ake place and equilibrium ime pah. Dynamic equilibrium how ha he opimal infrarucure ependure, he ize of he marke nework, and he level of diviion of labour increae concurrenly. While infrarucure can promoe he evoluion of diviion of labour hrough reducing he un ranacion co, he oal ranacion co each conumer-producer incur rie a he opimal income hare of infrarucure ependure increae wh economic developmen. Acknowledgemen: I am very graeful o Yew-Kwang Ng, Xiaokai Yang, Ro Parih, and C. Cyru Chu for heir helpful commen, cricim and uggeion. I am reponible for any remaining error.

2 . Inroducion In he Wealh of Naion, Smh (776, chaper 3 of book I) propoed he wellknown heorem ha he diviion of labour i limed by he een of he marke which relae o ranporaion co (Smh, 776, pp.3-3). The een of he marke, according o Young (98, p.53), i no area or populaion alone, bu he purchaing power, he capacy o aborb a large annual oupu of good, which in urn depend on he producive power of labour. Conequenly, he producive power i deermined by he een of diviion of labour. Therefore, Smh dicum amoun o he coincidence wh he caual obervaion ha diviion of labour and he marke emerge and evolve imulaneouly. Evoluion of diviion of labour and enlargemen of he een of marke are wo apec of economic progre. Yang and Borland (99) develop a dynamic general equilibrium model o eplain endogenou growh by ponaneou and concurren evoluion of he een of he marke and of he level of diviion of labour. Bu heir model doe no eplore ineracion beween infrarucure ependure and evoluion of diviion of labour. The purpoe of hi paper i o inroduce infrarucure ependure ino Yang-Borland model o inveigae he implicaion of inerplay among infrarucure ependure, ranacion efficiency, and peed of evoluion of diviion of labour for economic developmen. Alhough ranacion co, defined by Arrow (969) a he co of running he economic yem, include informaion co and enforcemen co, we focu on he effec of public infrarucure ependure on he ranacion co and implicaion for producivy progre. Thi ependure may include ependure for he improvemen of he law yem oward proecion of privae propery, freedom of conracing, and dimanlemen of barrier

3 of enry; ependure on he eablihmen, he mainenance and he developmen of ranporaion and communicaion yem. While ranional economie of China, former Sovie Union, and oher ociali counrie provide rich eample abou how imporan a good legal infrarucure i for a marke economy, hiory alo provide abundan obervaion on how he ranporaion and communicaion yem could reduce ranacion co. A Boerup (98, p9) noiced: In he wake of he breakhrough of he new coal-iron echnologie came railway, iron eamhip, and, laer, moor vehicle and airplane. Each of hee innovaion curailed he co of longdiance ranpor of peron or merchandie, omeime of boh. Chandler (990, p.58) ell u how infrarucure could increae producivy hrough diplaying u a vivid eample: Before he 850, American merchan rarely ook le o good; inead, hey old on commiion. They preferred o have he manufacurer run he high rik and pay he high invenory co of diribuing he produc - ome of hem already on a coninenal cale--hrough he low and uncerain ranporaion nework. Manufacurer had few alernaive if hey were o ell beyond heir immediae area. Among he wholealer, only hoe in he large eaern cie, who bough heir good (impored from Europe) a aucion, ook le o hem. Bu once he railroad, elegraphy, and coaal eamhip appeared, reducing rik and invenory co and increaing he poenial volume of ale, merchan moved quickly o prof from he new opporunie. They did o by making le o he good and making heir income from markup raher han commiion. The poenial of boh cale and cope economie encouraged uch middlemen o purchae good direcly from grower, proceor, and manufacurer. In he 850 commody dealer who bough from farmer and a grain echange and old o proceor quickly replaced facor and oher commiioned merchan in he markeing of agriculural crop...

4 In hi eample, he how u no only he reducion of ranporaion and orage co from he new infrarucure, bu alo he reuling increae of he level of pecializaion and diviion of labour (how he merchan chooe higher level of pecializaion and how he lowered average ranacion co induce he emergence of profeional middleman) and he reuling increae in he producivy of American merchan refleced in he rie of heir average income. More imporanly, he producivy increae come from pecializaion and he diviion of labour becaue of he economie of cale and cope. Thi ory ugge ha Yang and Borland approach can be ued o endogenize infrarucure ependure and eplore he rend of infrarucure ependure according o microeconomic role. Unlike Achauer (989) and Barro and Sala-i-Marin (995), Arrow and Kurz (970) diinguihe public capal from privae capal in he udie of he opimal growh pah hrough auming ha a fracion of he public capal can provide direc producion benef and he re can provide direc conumpion benef a a public good. Thi reamen can inegrae boh increaing reurn o cale and eernaly ino he udy. However, neher he public ependure in he former udie nor he public invemen in he laer ha anyhing o do wh ineracion beween ranacion co and evoluion of diviion of labour. In hi paper, a dynamic general equilibrium model i developed o udy he implicaion of uch ependure for evoluion of diviion of labour ha generae endogenou economic developmen. Secion of hi paper pecifie he dynamic general equilibrium model. Secion 3 idenifie a neceary condion for infrarucure ependure o ake place, and dicue he role of infrarucure in peeding up he evoluion of diviion of labour and economic developmen. Secion 4 eamine 3

5 he relaionhip beween opimal income hare of he infrarucure ependure and he poenial for furher evoluion of diviion of labour. Secion 5 conclude he paper.. Endogenou Specializaion and Endogenou Infrarucure Ependure When here ei economie of pecializaion and learning by doing, e ane idenical individual can gain endogenou comparaive advanage by pecializing in differen producion acivie. A each conumer-producer prefer divere conumpion, pecializing in one producion implie he purchae of good produced by oher, while chooing o pecialize more in he curren period ha he benef of generaing higher producive capacy in fuure. So he number of ranacion an individual incur a well a he oal ranacion co rie wh an individual level of pecializaion. Therefore, he opimal level of pecializaion i up o he efficien radeoff beween benef from pecializaion and diviion of labour and he aociaed increae of ranacion co. Tranacion co can be reduced by collecive finance from individual o inve in relevan infrarucure. The fuure reducion of ranacion co (or an increae in ranacion efficiency) make higher level of pecializaion and diviion of labour more favourable o ha higher producivy and welfare can be reached in he fuure. Bu he financing of he infrarucure ependure reduce conumer-producer conumpion in preen period. So opimal infrarucure ependure i deermined by he efficien radeoff beween benef of he ranacion co reducion due o new infrarucure and he welfare lo from preen forgone conumpion. They inroduced a flow of public ervice ino aggregae producion funcion o eplore he producivy implicaion of governmen ependure. 4

6 Conider an economy wh m e ane idenical conumer-producer and m conumer good. For any good i, we denoe he elf-provided amoun of he good a ime a, he amoun old and purchaed of he good a ime a and d repecively. Each individual canno receive all he amoun of good he bough from oher due o ranporaion lo or oher ranacion co incurred. Inead, he receive only d k ( 0 k ) from hi purchae of good i, where k i he un ranacion efficiency and c k i he un ranacion co. A ime, he conumer-producer gain uily from hi divere conumpion of he m good. Hi conumpion of each good would be elf-provided or received from hi purchae, o he amoun of hi conumpion of good i i + k d and he uily he gain from conumpion of all good a i m d u ( + k ) i () For implicy, we aume ha each conumer-producer ha one un of labour a any ime in hi life and alo aume ha hi oupu of good i (which can be conumed by himelf or old in he marke o echange for oher good) i a funcion of hi oal eperience in hi producion which equal oal accumulaed working ime in producing good i. The pa eperience will be idled away if he doe no produce he good for he ime being. In oher word, if hi labour inpu in he producion of good i a ime i denoed a l, he amoun of good i old in he marke i denoed a and hi oal eperience of producing good i i The aumpion ha he number of good equal he populaion ize i ued o implify he analyi, which alo implie he diviion of labour i limed by populaion ize. Thi aumpion i originally made in Yang and Borland (99). 5

7 denoed a L 0 li τ d τ, for l > 0; L 0 if l 0, hen hi producion of good i can be decribed a a + ( L ) () where a > characerize he degree of economie of pecializaion. I i aumed ha all rade in he economy i mediaed hrough conrac igned in po and fuure marke ha operae a ime 0. Thee conrac canno be renegoiaed a ome laer dae. Auming ha he fuure marke horizon and an individual deciion horizon are infine, hen a conumerproducer maimize hi lifeime uily: U ue r 0 d (3) where r i a ubjecive dicoun rae. A hown by Yang and Borland 3, an individual doe no buy and ell a ame good, doe no elf-provide and buy a ame good, and ell one good a mo a any inan in he dynamic model. Since every conumer-producer i e ane idenical and he poenial producion echnology of each good i eacly he ame, i no economical for a conumerproducer o change hi profeion. Depe he eience of increaing reurn which may accrue o individual due o pecializaion in producion, individual agen will adop price aking behaviour 4. Furhermore, due o complee ymmery of he model, individual welfare will be 3 See Yang and Borland (99), p See Buchanan and Yoon (994), p3. In he paper New Approach o Economic Organizaion and Growh, Borland and Yang argue: Uually, an aumpion of increaing reurn o an inpu would be incompaible wh priceaking behavior ince implie ha individual would wan o purchae an infine amoun of ha inpu. However, ince he labour inpu in any producion funcion i aumed o be individual-pecific and each individual ha a fine labour endowmen, hi problem doe no arie. Furhermore, alhough he equilibrium num ber of producer of a raded good may be mall, ince here i free enry o any producion acivy and ince a he ime of deciding on producion acivie all individual are e ane idenical, no individual will poe monopoly power. 6

8 deermined by he number of raded good n (hu he number of elf-provided good, m-n), hi labour hare inpu in he producion of each and every elf-provided good, hi labour hare inpu in he producion of he good he ell and hi demand for each and every good which he himelf doe no produce. No maer which n good he rade wh oher, hi preen welfare i no affeced. However, from a ocial poin of view, he unique Pareo opimal economic rucure i he one ha once rade ar, here i a peciali in he producion of each and every good even if each individual may rade only wo good. Thi implie ha a he number of raded good increae, no one need o change hi profeion. Any oher economic rucure would involve a higher human capal lo due o he fac ha ome individual would have o change hi profeion o he newly-raded good becaue he ocial knowledge accumulaion of ome newly-raded good wa much le han he ocial knowledge of hoe raded good markeed earlier. Therefore, he unique Pareo opimal rucure i he one in which righ a he emergence of rade, here i ome conumer-producer accumulaing he knowledge abou he producion of each and every good uch ha no individual need o change hi profeion when number of raded good for each individual increae, he ociey will have he minimal human capal lo and can reach a higher level of diviion of labour wh he lowe co and he fae peed. Call he individual who ell good i a agen i and ue n o denoe he number of good he rade a ime (n, when he doe no rade wh oher agen). A hown by Yang and Borland (99), for he ymmeric model, he dynamic equilibrium i aociaed wh uch a Pareo opimum rade paern. We adop hi reul a Lemma : 7

9 Lemma. For n (for all i), he equilibrium marke rucure ha he feaure ha here i a unique eller of every good; m good are raded in he whole economy alhough he number of good purchaed by agen i i n. Unlike he aumpion abou ranacion efficiency in Yang and Borland model, infrarucure ependure i allowed here o improve ranacion efficiency. Aume when here ha never been any infrarucure ependure, he un ranacion co of purchaing good from oher i K. For racabily, we furher aume ha he un ranacion efficiency will increae wh he infrarucure ependure in he ame period 5. The financing of he infrarucure ependure i from ome porion of he oal income of all conumer-producer in he economy, which i endogenized in hi model and will change wh ime. Since he income of he agen i i p, if we denoe he proporion of income colleced for infrarucure ependure a θ (which could be viewed a a a rae), he oal reource for infrarucure ependure will be I m θ i p (4) For implicy, I aume ha I i pen on infrarucure a ame period and pecify he un ranacion efficiency a ime a k ( µ I + B) (5) 5 Achauer (989) argue eem proper o inerpre he eimaed coefficien on he flow pending variable a a meaure of heir conribuion o producivy in he privae buine economy. Similar o he aumpion made by Barro and Sala-i-Marin (995), we aume ha he flow of infrarucure invemen improve he un ranacion efficiency. An alernae approach would ue a ock of infrarucure invemen. 8

10 which increae wh I, where B / ( K) and µ i a coefficien repreening he oal efficiency in financing, inveing and conrucing he new infrarucure 6. Under above pecificaion and whou lo of generaly, he individual who conrac o become peciali of good i a ime 0 (agen i) olve he following opimal conrol problem: r maui 0 ue d (6) d.. u k ir r R ij (uily funcion a ) a a + ( L ), ij ( Lij ), j J (producion funcion) l + lij (endowmen conrain) d ( θ ) p p (budge conrain) r R r ir k ( µ θ p + B) (ranacion echnology) m i n 0, L iy 0 0, y i, j, j J (boundary condion) l dl / d, l iy 0, y i, j, j J (ae equaion) iy iy n i a naural number. (conrain) where J i he e of good which agen i elf-provide bu doe no ell (J conain m-n- elemen), he fir leer i in he ubcrip of ij i ued o denoe he agen, he econd leer denoe he good he elf-provide bu no ell; R i he e of good which he purchae from d oher (R conain n elemen), he econd leer r in he ubcrip of ir indicae he good he 6 Under hi aumpion, k K if θ 0. The un ranacion efficiency whou any infrarucure facily K i aken a he lower bound of k. Thi ranacion echnology i imilar o he one in Chu and Tai (995). 9

11 agen i buy from he peciali r; L ij i he accumulaed eperience of he agen i in producing good j a ime, l ij i he correponding labour inpu; and L i, l i are implified a L and l. Thi i a bang-bang conrol problem, in which n i a poive naural number, i he amoun of ale, θ i aken a given o each individual and opimal value i olved ou by a benevolen governmen, while l may jump o from an inerior oluion and ome l ij will jump o 0 from an inerior oluion a n end o m. The curren value Hamilon funcion i: H u + δ l + δ l + β l + β l + β 0 ( l l ) (7) i j ij i j ij ij The fir order condion for he conrol problem are given by he maimum principle. Since individual deciion of he m agen are ymmeric, wh he dynamic equilibrium condion 7, we have p py, for all i, y,..., m. (8) M i, for all i,..., m. (9) Whou lo of generaly, we e p p L p (0) m Plugging (0) ino problem (5), we can derive d i idenical for r R. ir 7 A dynamic equilibrium i characeried by a e of marke-clearing condion and a e of uily-equalizaion condion. The marke clearing condion a ime are M M d r r peciali of good r. The uily-equalizaion condion are i ir, r m i r U U... U m.,...,, where M r i he number of agen r (or call The m- independen marke clearing condion and m- uily-equalizaion condion deermine he relaive price of good and relaive number of peciali. 0

12 Wh hi informaion, Lemma and ymmeric fir order condion of each agen a well a he marke clearing condion, we can have Lemma : Lemma., l, L are idenical for i,,..., m; L ij and l ij are idenical for all people d (i.e. for all i under correponding permuaion of j); ir i idenical for all people (i.e. for all i under correponding permuaion of R) and n i idenical for all people. According o Lemma, I implify he noaion of L ij,, l ij,, d ir, n a L j, l j,, d r, n repecively. And problem (5) can be implified a maui ue r 0 d () d.. u k r r R j (uily funcion a ) a a + ( L ), j ( L j ), j J (producion funcion) l + l j (endowmen conrain) ( ) ( n ) (budge conrain) θ d r k ( µ mθ + B) (ranacion echnology) n 0, L y 0 0, y i, j, j J (boundary condion) l dl / d, l y 0, y i, j, j J (ae equaion) y y n i a naural number. To problem (), a 0 < u k d < am, () r r R j

13 lim u e r 0 (3) So he ranveraly condion i aified. A hown in mahemaic appendi, H i concave in all conrol variable a he poin ha are given by maimum principle. Alhough H i monoonically increaing in L and L j, he opimal choice ei due o he endowmen conrain. Due o uily equalizaion among individual, he benevolen governmen maimize each individual oal dicouned uily wh repec o θ ( 0 θ ). Laer, we can ee θ may equal o 0 in an inial period of ime, hen ge ino he inerior of he inerval [0, ] and change wh economic developmen. 3. Infrarucure, Evoluion of Diviion of Labour, Enlargemen of he Een of Marke, and Economic Growh A hown in appendi, he opimal a rae for infrarucure invemen choen by he benevolen governmen hrough maimizing he individual oal dicouned uily wh repec o θ 8 i ( ) θ B + µ m B µ m, when µm > B B (4) θ 0, when µm B B (5) Equaion (4) and (5) ae ha a neceary condion for a poive level of infrarucure ependure i µm > B B, i.e. oal rade volume (he ize of he marke), m, which poively depend on he equilibrium level of diviion of labour n, i no oo mall 8 In my model, he θ which maimize individual oal dicouned uily alo maimize uilarian ocial welfare funcion.

14 and he efficiency of infrarucure ependure µ i no oo low. Thi i becaue he uilizaion rae of he infrarucure increae wh he oal rade volume. Ye, o a cerain level of µ m, he maller he B (i.e., he maller he K ), he more likely he infrarucure ependure will ake place becaue he benef from he infrarucure i more ignifican compared o he ae whou infrarucure in uch an economy. B i relaed o legal, geographical, educaional, and culural environmen. On he one hand, he neceary condion how ha beween wo economie wh imilar low level of diviion of labour (hu a low per capa rade volume ), imilar legal yem, populaion deny and geographic condion which are aociaed wh a ame value of K and wh imilar poenial efficiency of infrarucure ependure (imilar µ ), he economy wh a larger populaion (larger m) i more likely o inve in infrarucure becaue he counry wh a larger populaion ha a greaer cope for he infrarucure invemen o make more conribuion o he evoluion in diviion of labour and producivy. Bu in realy, he oal efficiency in financing, inveing and conrucing a new infrarucure of hee wo counrie could hardly be he ame. So we can eablih Propoion. A neceary condion for a poive level of infrarucure ependure i ha he oal rade volume i no oo mall (Thi may be eher due o a large populaion ize wh a cerain per capa volume of rade or due o a mall populaion ize wh coniderable per capa rade volume generaed by ufficien evoluion in diviion of labour), and he efficiency of financing, inveing and conrucing he infrarucure i no low. Ceeri paribu, he larger he populaion ize and he lower 3

15 he K, he more beneficial he infrarucure, hu i more likely ha he infrarucure ependure would ake place in an earlier economic developmen age. The implicaion of populaion for he uiliaion of infrarucure ha been widely oberved. A Boerup (98, p9) ummarize:...before he indurial revoluion one denely populaed area afer anoher became he echnological leader. During he whole of hi par of human hiory, he main advanage of a dene populaion, i.e., he beer poibilie o creae infrarucure, eem o have oubalanced he diadvanage of a le favorable raio beween populaion and naural reource. Europe ucceeded Aia a echnological leader, bu only afer arrived a relaively high populaion denie. Few economi would doub ha he Uned Sae could benef more from an invemen for ome amoun of railroad nework or communicaion nework han Canada did in heir early economic developmen age becaue he per capa co of eing up uch a railroad nework in he Uned Sae would be much lower han he per capa co in Canada. However, he benef of infrarucure ependure in large geographic naion or area i uncerain parly becaue uch benef depend on he populaion ize and he efficiency of infrarucure ependure a a cerain producivy level, parly becaue predicion abou fuure benef may be micalculaed owing o populaion change or difficuly in eimaing he governmen efficiency. So he long-erm benef from a large infrarucure ependure of a naion wh large geographic area are uually queioned. Depe he dominan role of populaion deny in infrarucure ependure, he long erm benef of infrarucure in a large geographic naion like Uned Sae ha no been negleced by Boerup ince he hough he uilizaion of new mean of ranpor, i.e. rail nework, ocean harbor, road, and airpor, ogeher wh ma elemen of immigran from more echnologically advanced area i he reaon why Norh 4

16 America uccefully challenged he echnological leaderhip of Europe lle more han a cenury afer he indurial revoluion (Boerup, 98). I i worh poining ou ha propoion only ae a neceary condion for infrarucure ependure o ake place. A o wheher an economy can reach uch a neceary condion from auarkic ae, cloe eaminaion on poible evoluion in diviion of labour whou infrarucure invemen i needed. Appendi how ha if a ( a > ) and K ( 0 < K < ) are very mall, we can have H < 0 even for very large. In hi cae, everyone in he economy adop elf-ufficiency; n he ocial knowledge accumulaion i very low 9. Due o he very weak learning by doing effec and very low ranacion efficiency, even he long-erm benef of pecializaion i much oubalanced by he ranacion co. So he economy can ay in Auarky for a very long period of ime. On he conrary, if a and K are large bu m i mall, we will have H > 0 once he n agen i ha accumulaed enough eperience uch ha L > ep { ( ln m + - ln K ) / a}. Thi implie ha he economy i very eay o reach complee diviion of labour if he learning by doing effec i rong and ranacion efficiency whou infrarucure i no oo low while he poenial cope for diviion of labour i mall. However, for inermediae a (a>), if K i no 9 In hi cae, every peron ha a ame amoun of eperience in each producion of he m good; all agen have a ame amoun of eperience in each and every producion. So, he oal knowledge he ociey accumulae i a ame a he knowledge any individual ha. 5

17 oo low and m i no mall, we have n n& & > 0 and > 0, i.e. here i evoluion in n diviion of labour baed on learning by doing effec before any invemen in infrarucure. Wh he ponaneou evoluion in diviion of labour, rade volume increae. Once he rade volume make he infrarucure beneficial in long run (he neceary condion in propoion i aified), an efficien benevolen governmen may collec funding for infrarucure invemen. A o how he uilizaion of new infrarucure can help in making a counry a echnological leader, i a queion no eay o addre. I require a lea he underanding abou he inerplay beween ranacion efficiency and producion efficiency. To ee hi clearly, we need furher eamine he opimal conrol pah afer infrarucure ependure ake place. we have Appendi 3 how, wh he ranacion efficiency improvemen owing o infrarucure, & a( n θ µ ) B + m l ( n ) B + µ m L > 0, when n (6) n n& ( n ) n n ( θ ) > 0 (7) Thee wo epreion indicae ha here will be endogenou evoluion in each peron volume of ale or purchae and endogenou evoluion in diviion of labour due o he learning by doing effec and ranacion efficiency improvemen hrough infrarucure. Here, he number of 6

18 each peron raded good, which i aken a a meaure of he level of diviion of labour 0, increae wh each peron level of pecializaion l. Define he een of marke a E m( θ ) (8) can be derived ha E E & ( ) > ( ) > 0 (9) E θ B + µ m θ B So, he een of marke enlarge a diviion of labour evolve. The increae in welfare in hi endogenou economic developmen i epreed by he growh rae of uily a u u& n θ a l + a u θ L l L j j (0) The endogenou growh rae of infrarucure ependure I mθ during he evoluion of diviion of labour afer µm > B B i I I& I θ B + µ m > 0 () (4), (5) and () imply ha once he economy ha reached a cerain ize in erm of purchaing power, owing o learning by doing effec and increaed oal ranacion co each peron incurred, he long-erm benef from furher pecializaion promoed by he improvemen of un ranacion efficiency via infrarucure ependure will ouweigh he welfare lo from 0 The number of individual raded good can be ued o meaure he level of diviion of labour becaue individual level of pecializaion will be he ame due o he aumpion of ymmery alhough each individual pecialize in differen producion, and here i no producer good in he model. 7

19 forgone preen conumpion, o he governmen will ar o inve in infrarucure o improve ranacion efficiency provided ha he oal efficiency, µ, in financing, inveing and conrucing he new infrarucure i no oo low. And he infrarucure ependure will increae wh evoluion of diviion of labour and economic developmen. The concurren increae of I, n and L imply concurren increae of ranacion efficiency, level of diviion of labour and producivy. Furhermore, a equal he oupu difference beween he agen i (i.e. he peciali in producion of good i) and hoe agen who elf-provide good i, > 0 implie he increae of he comparaive advanage of he eper o a novice. Therefore, I can eablih he following propoion on he evoluion in diviion of labour wh he inerplay of he wo mechanim a Propoion. Dynamic equilibrium will be auarky if he inial ranacion efficiency K and he degree of economie of pecializaion are oo mall. If he degree of economie of pecializaion a i grea, diviion of labour will evolve gradually unil n reache m; he level of individual pecializaion, he endogenou comparaive advanage of each eper o a novice, he infrarucure ependure, he een of marke and rade dependence will all increae wh he evoluion of diviion of labour and economic growh. Ceeri paribu, he greaer he degree of economie of pecializaion (he larger a), he faer he evoluion of he diviion of labour. Ceeri paribu, he larger a counry populaion ize, he more benef he counry can gain See appendi 3. a A a >, L increae wh L,. So he producivy increae. 8

20 from infrarucure ependure and he faer he evoluion of diviion of labour. Ceeri paribu, he larger he µ (efficiency of financing, inveing and conrucing infrarucure), he more benef he counry can gain from infrarucure ependure and he faer he evoluion of diviion of labour. When m4, if K and a are no oo mall, he evoluion of diviion of labour can be hown in Figure 4.. Paern (a) how he inial ae of Auarky, in which, every agen elfprovide each and every good. Hi labour hare in producion of each and every good are he ame. No peciali in he ociey; Paern (b) how a low degree of diviion of labour, in which, every agen ar o rade wo good alhough all good are raded in he ociey. There i a peciali for each and every producion; Paern (c) how a higher level of parial diviion of labour, in which, every agen rade hree good, he level of pecializaion of each and every peciali ha increaed wh he number and volume of good he rade; and Paern (d) i complee diviion of labour, in which every agen oally pecialize in one producion and depend on he rade wh oher agen for he conumpion of all oher good. Figure 4.. The Evoluion of he Diviion of Labour (a) Auarky, n 0 (b) Parial diviion of labour, n 9

21 (c) Parial diviion of labour, n 3 (d)complee diviion of labour, n 3 4 According o our model, he increae of infrarucure ependure i baed on high level of diviion of labour and producivy; and in urn, promoe furher diviion of labour and furher producivy improvemen. The increae in infrarucure ependure, he enhancemen of endogenou comparaive advanage, he enlargemen of he een of marke, he increae of rade dependence, and he improvemen in producivy are differen inerdependen apec of he evoluion in diviion of labour and economic developmen. Thi reul provide a juificaion for uing per capa infrarucure uch a per capa mileage of railroad, per capa power conumpion, per capa number of elephone, and o on a indicaor of a naion economic developmen level. Furhermore, alo implie ha any eaminaion on only one direcion cauaion beween he change of infrarucure ependure and producivy i an incomplee udy. 4. Infrarucure Ependure in Economic Developmen 0

22 The general equilibrium pah of evoluion of he diviion of labour coordinaed by he marke, ogeher wh he opimal ime pah of infrarucure ependure, i he be proce of human capal formaion and profeional knowledge accumulaion of each profeion and he mo efficien pah of producivy growh. To ee he role of infrarucure in economic developmen, we alo need o derive he opimal growh rae of θ from he fir-order condion and heir differeniaion. The growh rae of θ can be epreed a 3 : θ θ B + µ m [ ] a( n θ ) θ B + µ m ( n ) B + µ m l L () Thu, θ > 0, when B( B ) < µ m < B( B ) + B B( B ) θ 0, when µ m B( B ) or µ m B( B ) + B B( B ) θ < 0, when µm > B( B ) + B B( B ) (3) Afer µm ha reached B ( B ) and people ar o inve in infrarucure, he opimal income hare of infrarucure ependure will increae unil he economy develop o a very high level uch ha µm B( B ) + B B( B ). Therefore, we have: Propoion 3. In a primive economy, here i no infrarucure ependure. Wh increaed pecializaion and increaed rade, infrarucure ependure occur. In he early age of economic developmen, he opimal income hare of infrarucure ependure will increae unil he oal income of he economy ha reached a very 3 See [A45] in he appendi 3.

23 high level and he poenial for furher evoluion of diviion of labour ha nearly been ehaued. The opimal income hare will hen decline. I i worh noicing ha on one hand, he governmen efficiency, µ, in financing, inveing and conrucing infrarucure, i one of he facor which deermine when infrarucure ependure may ake place and how long he period will be during which he opimal income hare of infrarucure ependure increae wh he economic developmen. Higher governmen efficiency may make he benef from ranacion efficiency improvemen become more imporan han he economie of pecializaion in a low level of diviion of labour. Bu low governmen efficiency may no only delay he inial poive infrarucure ependure, bu alo lenghen he period during which he opimal income hare of infrarucure ependure increae. Thu, he advocacy of propelling economic developmen hrough increaing a rae and public invemen whou emphaizing he imporance of improving governmen efficiency may no come ou from a complee dynamic general equilibrium udy. On he oher hand, i alo worh noing, ha he decline of he income hare of infrarucure ependure i mainly due o he fac he mo poenialie in diviion of labour ha been apped. In realy, cope for diviion of labour may develop wh evoluion of diviion of labour. Then he income hare of infrarucure ependure may no decline. In Yang and Borland (99) paper, he un ranacion co a well a per capa oal ranacion co increae wh he evoluion of he diviion of labour, bu my udy how 4 & µ mθ ( θ + ) µ m k ( µ mθ + B) ( µ mθ + B) 3 > 0 (4) 4 They are [A5] and [A54] in appendi 3.

24 and C& > 0 (5) ( µ mθ + B) where C i per capa oal ranacion co a ime. (4) and (5) mean ha he un ranacion co decreae wh economic developmen due o infrarucure ependure alhough per capa oal ranacion co increae due o increaed demand for good produced by oher peciali. Thi reul may no be inuive, bu i cloer o realy. In fac, he World Developmen Repor 995: Worker in an Inegraed World (pp.50-5) ake he falling co of ranporaion and communicaion a he driving force of he inegraion of naional and regional marke. Moreover, i he increae of un ranacion efficiency combined wh learning by doing effec ha induce and peed up he evoluion of diviion of labour and economic rucural change. 5. Concluding Remark Thi paper develop a dynamic general equilibrium model o inveigae he developmen implicaion of inerplay of wo mechanim. The fir mechanim relae o inerdependence beween he level of diviion of labour and he een of he marke. The econd mechanim relae o ineracion among he ize of he nework of diviion of labour, ranacion co, and infrarucure ependure. The dynamic of he general equilibrium generae endogenou and concurren evoluion of diviion of labour, of he een of he marke, of producivy, and of infrarucure ependure. The comparaive dynamic of he general equilibrium how ha he larger he rade volume and he more efficien he public 3

25 ecor, he earlier he infrarucure ependure will ake place. I alo how ha afer an economy reache cerain level in erm of purchaing power, he reciprocal promoion of producion efficiency and ranacion efficiency i very imporan for furher economic growh, furher evoluion in diviion of labour and furher enlargemen of he een of he marke. 4

26 Appendi Derivaion for he Fir and Second Order Condion Thi appendi i o olve problem () and he problem conidered by he benevolen governmen. Whou lo of generaly, he agen i olve he following problem: maui ue r 0 d [A] d.. u k r R r j a + ( L ), a j ( L j ), j J l + l j ( ) ( n ) θ d r k ( µ mθ + B) n 0, L y 0 0, y i, j, j J l dl d, l y 0, y i, j, j J y y n i a naural number. 0 θ < i aken a given alhough change wh ime. The opimal pah of θ i choen by he benevolen governmen hrough maimizing individual uily. To olve [A], we ue curren value Hamilon funcion: H u + δ l + δ l + β l + β l + β ( l l ) [A] 0 i j j i j j j Denoe [ ] δ il + δ jl j + β il + β jl j + β ( 0 l l ), hen j 5

27 a ( θ ) H ( L ) ( n ) n n n n a ( ) ( ( µ mθ + B)) ( L ) + [ ] [A3] j J j Since 0 < u k d < r r R So he ranveraly condion can be aified. According o maimum principle, j am, we have lim u e r 0 [A4] H n n µ mθ + a + L ( µ mθ + B) ( µ mθ + B) u 0 yield L a n ( n ) µ mθ + ( µ mθ + B) ( µ mθ + B) [A5] Rearrange [A5], we can obain L a n µ mθ ( ) ( n )[( µ mθ ) B] [A6] and L a n m n n m B B µ θ ( )(( µ θ + ) ) [A7] The fir order condion of n H n { ln( θ ) ln ln [ ( µ θ )] ln( ) } + + m + B n u 0 yield [ µ θ ] ln( θ ) + ln + ln ( m + B) ln( n ) 0 [A8] Alhough n hould be a naural number, he n which aifie [A8] can be a good approimaion of rue n a u i coninuou in n. Along he oluion of and n from [A7] and [A8], and he opimal pah of l and l j which i olved laer, he benevolen governmen olve he problem: maui ue r 0 d [A9] 6

28 .. 0 θ < I curren value Hamilon funcion i H u + γ θ + γ ( θ ) [A0] g Hg n n µ m + θ θ ( µ mθ + B) ( µ mθ + B) u + γ γ 0 yield γ γ 0 and 0 < θ ( B + µ m B) µ m <, when µm > B B [A] γ 0 and θ 0, oherwie. So afer ha reached crical value ha i given by µm > B B, θ ( B + µ m B) µ m [A] i.e. µ m + B µ mθ + B [A3] I no difficul o verify ha for he ime pah of, n, and θ ha aify he fir order condion, we have H + µ θ + ( n m u 0 a L )( ) Φ < [A4] ( ) where Φ ( µ mθ + B ) ( µ mθ + B) n H u n < 0 [A5] H H n n H n H n + ( n ) ( L ) ( n ) a + ( µ mθ ) Φ u 0 > [A6] 7

29 So H i concave in, and n for n (people ar o rade). Similarly, on he opimal pah of, n, and θ, we have θ H n ( θ ) g + ( µ m) Φ u < 0 [A7] Therefore, H g i concave in θ. H i linear in l and l j, which i a pecial cae of concavy. Maimizing H wh repec o l, l j ( j J) yield if δ β β Similarly, l j if δ j + β j > β l i + i > 0 0 l ( 0, ) if δ i + β i β 0 l j ( 0, ) if δ j + β j β 0 l 0 if δ i + β i < β 0 l j 0 if δ j + β j < β 0 [A8] l + l j [A9] j J &δ i a H al + rδ i δ a u + r i L L [A0] & δ j H a rδ j δ j, L j L u r j j J [A] l and l j 0 iff n m ; l 0 and l j ( 0, ) iff n m When < n < m, 0 < l <, 0 < l j <, we have β i 0, β j 0, j J. Thi, ogeher wh [A8], yield δ i β 0, δ j β 0, j J When < n < m [A] I can be derived by ubuing [A3] ino [A7] ha L ( n θ ) ( n ) a [A3] 8

30 Thu, L a a ( θ ) L ( n θ ) [A4] Plugging [A4] ino [A0], we obain δ & i al a a( n θ ) δ u δ ( θ ) a + r i i L ( n θ ) ( θ ) L u + r [A5] [A5] ogeher wh [A] and [A] yield a L u a( n θ ) u j [( θ ) L ] [A6] i.e. L ( n θ ) L ( θ ) j [A7] Appendi Sponaneou Evoluion in Diviion of Labor Baed on Learning by Doing Effec From appendi 4., we know ha a neceary condion for infrarucure invemen i ha µm > B B, where B / ( K ). So here mu be rade and ponaneou evoluion of diviion of labor baed on learning by doing effec before he infrarucure could be financed. Thi appendi i o how he poible evoluion in diviion of labor whou infrarucure. When θ 0, he curren value Hamilon funcion degeneraed o 9

31 a K H L ( ) ( n ) n n n a j ( ) ( L ) + [ ] [A8] H n u a L + 0 yield a ( / n) L [A9] H n [ ln ln ln( ) ] K + n u [A30] Replacing wh [A9], [A30] change o H n [ ] ln K + a ln L ln n u [A3] Q n and L < H,, < [ ln K + a ln ] u n hu, if a ( a > ) and K ( 0 < K < ) are very mall, we can have H < 0 even for very large n. Thi mean he economy can be in Auarky for a very long period of ime if a and K are oo mall. Meanwhile, Q n m, we have H n [ ln ln ln ] K + a L m u So for a mall m bu large a and K, we will have H > 0 once he agen i ha accumulaed n enough eperience uch ha L > ep { ( lnm + - ln K) / a}. Thi implie ha he economy i very eay o reach complee diviion of labor if he poenial cope for diviion of labor i mall, learning by doing effec i rong and ranacion efficiency whou infrarucure i no oo low. However, for inermediae a (a>), he opimal level of n ( n ) in he evoluion in diviion of labor i approimaely given by 30

32 ln ln( n ) + ln K [A3] Denoe n n & & and n, oal differeniaion of he ln ranformaion of [A9] yield n + a l n L [A33] Toal differeniaion of [A3] yield n n n [A34] Combine [A33] and [A34], I derive n ( n ) a l n + L > 0 n n [A35] n and a l n n + L > 0 [A36] [A35], [A36] ogeher wh [A] indicae ha here i ponaneou evoluion of diviion of labor baed on learning by doing effec whou infrarucure invemen unil reache he crical value for infrarucure invemen o ake place. Appendi 3 Concurren Increae of Tranacion Efficiency and Producion Efficiency 3

33 Once reache he crical value, here i inerplay of ranacion efficiency and producion θ efficiency. Denoe & θ θ n, n &, and &. Toal differeniaion of [A8] n yield θθ µ mθ n θ θ n 0 ( µ mθ + B) ( µ mθ + B) ( ) n [A37] Subuing [A3] ino [A37] yield n ( θ ) ( n ) n [A38] i.e. n n n ( θ ) [A39] Toally differeniaing [A3], we can obain θ θ B + µ m [A40] The oal differeniaion on ln ranformaion of [A3] yield a l L n n θ n n n θ n θ θ + [A4] Subuing [A39] and [A40] ino [A4], we have a l L ( n ) B + µ m ( n θ ) B + µ m [A4] Rearrangemen of [A4] give a( n θ ) B + µ m l n B + µ m L > 0 ( ) when n [A43] [A39] implie 3

34 n n n ( θ ) > 0 [A44] Becaue Therefore, θ θ B + µ m [ ] a( n θ ) θ B + µ m ( n ) B + µ m l L [A45] θ > 0, when B( B ) < µ m < B( B ) + B B( B ) θ 0, when µ m B( B ) or µ m B( B ) + B B( B ) θ < 0, when µm > B( B ) + B B( B ) [A46] Define he een of marke a oal effecive demand: d E m r m( θ ) [A47] r R The oal differeniaion of ln ranformaion of [A47] how E θ θ θ + θ B + µ m θ > B > 0 [A48] Afer ha reached crical value which i given by µm > B B,he opimal infrarucure ependure i I θ m [A49] So I θ + θ B + µ m > 0 [A50] Since he un ranacion efficiency coefficien i 33

35 herefore, k ( µ mθ + B) & µ mθ ( θ + ) µ m k ( µ mθ + B) ( µ mθ + B) 3 > 0 [A5] The un ranacion co a ime i c k µ mθ + B [A5] So he per capa oal ranacion co a ime i d ( θ ) C c r c ( θ ) µ mθ + B r R [A53] Differeniae [A53] and apply [A40] and [A3], we obain C& > 0 [A54] ( µ mθ + B) The growh rae of uily i u al l a a L + n + n a l L j j [A55] Subuing [A4], [A39], and [A43] ino [A55] give u u n θ al j + a l > 0 [A56] θ L L j 34

36 Reference Arrow, K. J. (969), The Organizaion of Economic Acivy: Iue Perinen o he Choice of Marke veru Non-marke Allocaion. In he Analyi and Evaluaion of Public Ependure: The PPB Syem. Vol.. U.S. Join Economic Commee, 9 Congre,! Seion. Wahingon, D.C.: U.S. Governmen Prining Office, and M. Kurz (970), Public Invemen, he Rae of Reurn, and Opimal Fical Policy, The John Hopkin Pre, Balimore and London. Achauer, D. A. (989), I Public Ependure Producive? Journal of Moneary Economic, 3, Barro, R. J. and X. Sala-i-Marin (995), Economic Growh, New York: McGraw-Hill, 995. Boerup, E. (98), Populaion and Technological change, A Sudy of Long-Term Trend, The Univery of Chicago Pre, 98. Buchanan, J. and J. Y. Yoon (ed.) (994), The Reurn o Increaing Reurn, The univery of Michigan Pre, Ann Arbor. Chandler, A. D. JR. (990), Scale and Scope, The Dynamic of Indurial Capalim, The Belknap Pre of Harvard Univery Pre, Cambridge, 990. Chu, C. C. and Y. Tai (995), Producivy, Invemen in Infrarucure, and Populaion Size: Formalizing he Theory of Eer Boerup, Conference paper preened on Increaing Reurn and Economic Analyi--in Honour of Profeor K. J. Arrow, which i held during 7-8 Sepember, 995 a Corpu Chrii College, Vicoria, Auralia. 35

37 Smh, A. (776), Wealh of Naion, Aldine Pre, J.M.Den &Son Ld, 970. World Bank (995), World Developmen Repor 995: Worker in an Inegraing World, Oford Univery Pre, Oford. Yang, X. and J. Borland (99), A Microeconomic Mechanim for Economic Growh, Journal of polical Economy, 99(3): Young, A. (98), "Increaing Reurn and Economic Progre", The Economic Journal, 38,