TECHNOLOGY ADOPTION, INDUSTRIAL STRUCTURE, AND GROWTH IN EMERGING ECONOMIES

Transcription

1 Quanttatve ethods Inqures TEHNOLOGY ADOTION, INDUSTRIAL STRUTURE, AND GROWTH IN EERGING EONOIES Al HEBBI Insttut Supéreur de Geston de Tuns, Tunsa E-mal: Sam KHEDHIRI Unversty of rnce Edward Island harlottetown, anada Abstract: Ths paper explores the lnk whch s often neglected n the lterature between the ndustral structure and the aggregate economc growth n emergng economes (EE) that are mplementng an openness trade polcy Based on the Schumpeteran technologcal paradgm concept, we show the relevance of the technology adopton hypothess rather than the nnovaton hypothess n an EE s context We develop an endogenous determnstc growth model for small open economes n whch domestc agents adopt technology ncorporated n equpment mport Through the model, we prove that equpment mport, technologcal externaltes, and the fall n relatve prces are the sources of openness growth effects In ths paper we determne endogeneously the mnmal effcency threshold of entry and ext dynamcs n the domestc ndustral structure wthn an endogenous growth framework We show that the consumpton goods dversty mproves the growth rate of consumpton and welfare by ts negatve acton on the survvng frms monopoly power We argue that for ntermedate goods, the agents heterogenety s negatvely correlated wth statonary state growth rate From an economc polcy pont of vew, t would be recommended to ntervene by mprovng the performance of the domestc frms before mplementng the trade openness polcy, and after ts mplementaton by controllng the markets to avod the monopolstc structure that s negatvely correlated wth economc growth at the aggregate level Key words: Technology Adopton; Heterogeneous Agents; onopolstc competton; Effcency Threshold; Entry-Ext Dynamcs I Introducton The lnk between trade openness and economc growth has been revewed n the lterature based upon two types of research work The frst studes the lnk between trade openness and the growth rate of per capta GD as llustrated n the endogenous growth models whch allow to establsh the transmsson channels of trade polcy dynamc effects as argued n Baldwn (998), Romer and Batz (99), and artn and Barro (995) These channels result n the spread of varous forms of technology and n types of externaltes, nternatonal captal flows, prces adjustment, and adequate macroeconomc polces But these models retan the restrctve assumpton of homogeneous agents behavors n a perfect market fnal goods context onsequently, a symmetrc equlbrum may be acheved The 33

2 Quanttatve ethods Inqures results obtaned from these models n there majorty ndcate the postve effect of trade opppenness on GD and ts growth But the extent of ths effect and ts relevance reman manly dependent on homogeneous agents assumpton and thus on symmetrc equlbrum However, the behavor of agents s ndeed not dentcal for at least two reasons Frst, the ndustral and technologcal strateges carred out separately by the agents are to gve place to product dfferentaton (hamberln, 933) 2 Second, the non-unform costs undergone by frms lead to specalzaton (Stgler, 949) In ths context, each agent postons herself as a monopoly of her own nnovaton A monopolstc structure s establshed and a symmetrc equlbrum s then evacuated from the analyss The second type of studes, ntated more recently by Bernard et al (2000), eltz (2002), and Yeaple (2002), emphasze the mcroeconomc bond between the exportng frms and ther productvty Wthn ths analyss framework, J Bradford et al (2003) explore the productvty evoluton n ndustry resultng from the frms reallocaton n response to changes n the trade costs (e, tarffs and costs of transport) Others treated the structure of the market endogenously, namely, Katja (2006) for space endogenous locaton, and azzeo (2002), for endogenous qualty choce However, they dd not treat economc growth Fnally, Holmøy (2003) s nterested n an evaluaton of the standard Dxt-Stglz model when the asymmetry s taken nto account However ths second type researchers were not nterested n economc growth at the aggregate level 3 We wll retan the assumpton of heterogenety to analyze the market structure, and to descrbe the entry and ext agents dynamcs Ths dynamcs s determned by the effcency, proftablty and compettveness of the varous agents operatng n such a heterogeneous structure (ontagna, 995) The trade openness makes t possble for the EEs to take advantage of the volume of mported equpment goods as well as the technology whch they ncorporate The structure of ther ndustry wll then be modfed and effcency condtons wll be mposed on the economc agents In fact, dversfed products and competton n terms of effcency between the agents wll characterze ther ndustral structures It would be then nterestng to adapt ths approach of heterogeneous agents to the problems of endogenous growth n an open EE whch chooses trade lberalzaton In ths paper we study the effects of dversfed equpment goods mport on ndustry structure n EE mtatng foregn technology and on ther economc growth For the ndustry entry-ext dynamcs and heterogenety effects on growth, we use a framework for an economy wtch has two sectors The ntermedate good sector has mported goods together wth foregone output to produce the large number of durable goods that are avalable for use n fnal goods producton at any tme We adopt the hypothess of all ntermedate goods beng mported Ths hypothess may be questonable when we consder all the developng countres But for the ddle East countres n specfc, the weght of domestc equpments s neglgble compared to that of mported equpment Ths assumpton s not unrealstc when technologcal nnovaton s taken n the sense of Schumpeter as presented n the prevous secton 4 Our analyss separates the case of consumpton goods dversty and mtated goods dversty so that a smple model s establshed for each Essentally, our dea s to nvestgate the followng ssues: Is there a relatonshp between the degree of agents heterogenety and ther ndvdual effcency? What are the consequences on the effcency threshold necessary for the access to ndustry, and what are the effects on the economc growth rate n a statonary state? 34

3 Quanttatve ethods Inqures Ths paper s organzed as follows: In the second secton, we show that the assumpton of technology adopton s more realstc compared to ts nnovaton n some LD s The thrd secton s devoted to the study of a statonary state equlbrum n the case of the consumer goods varety We should note that n our formulaton heterogenety of agents s not consdered n ntermedate producton sector The fourth secton ntroduces heterogenety nto the sector of mtaton of the technology ncorporated n the mported ntermedate goods Senstvty analyss by numercal smulatons wll be carred out at the end of each secton The last secton concludes the paper fndngs and suggests recommendatons of economc polcy for the EEs II Imtaton Versus Innovaton of Technology n EEs The mtaton assumpton of foregn technology s more sutable than that of technologcal nnovaton n developng countres Ths s due to two man reasons The frst s related to the technology concept and the second may be explaned by the huge nnovaton costs Frst, technology paradgm accordng to Schumpeter means a successon of stages Each one s defned by processes leadng to the nnovaton These stages start by rsng a new queston related to the lmts charged to the present technology The answer to ths queston results n a technologcal patent generatng revenue Next, ths patent s mplemented by a new tool gvng ts producer a monopoly rent Once ths new tool s standardzed by the externaltes whch t generates, competton on ts market s no longer monopolstc To avod losng ts monopolstc poston and thus ts rent, the nnovator starts another technologcal paradgm The technologcal nnovaton results n the means leadng to lower cost or at least the same level of output In realty, they are modern organsatonal forms, sophstcated tools, and dfferentated products Grossman and Helpmann (99) show that the dfferentaton of nputs (whch results n technologcal progress) prevents the decrease of ther margnal productvty It s n ths context of technologcal paradgms that Schumpeter as well as the poneer authors of the endogenous growth (Romer, 986 and 987) justfy the nnovaton manly by the revenue whch t allows Aghon and Howtt (992) ntroduce the concept of the creatve destructon through antcpatons that the nnovator formulates n connecton wth the future standardzaton of technology It s wth a vew to keep ts monopolstc power and thus ts revenue that the nnovator launches on the market hs new technology before t s standardzed In addton, one should note that ths producton of technology depends bascally on materal and socal condtons of knowledge producton Furthermore, the complance wth ntellectual copyrghts suggests that human captal accumulaton requres the dstncton between the lab equpment model and the knowledge drven model The frst supposes the combnaton between the physcal captal and prelmnary knowledge (ntal human captal endowments), whle the second supposes the combnaton between the varous types of avalable knowledge (Barro, 996, and Romer and Batz, 99) In ths way, the technology producton accordng to Schumpeter becomes a very dffcult task to acheve n EEs because of the absence of a knowledge producton sector as well as socal condtons for the mplementaton of the technologcal paradgms The foregn technology transfer n EEs should not therefore be ntended as a smple transfer of ts output 35

4 Quanttatve ethods Inqures only (technologcal product, sophstcated equpment, etc) Accordng to Schumpter, that should be equvalent to a transfer of the whole process allowng technology producton and as was the case of a very reduced number of countres n the world, that benefted from ths type of transfer (for example Japan) The second reason n favour of the technology mtaton n EEs s the huge cost whch t generates (Easterly, Kng, Levne and Rebelo, 994) and the dvergence n growth rates that t would be lkely to generate, as shown n Barro and Batz (995) wth reference to the catch-up argument Through a model of technology dffuson based on mtaton, Barro and Batz (995) show that the relatvely low cost of mtaton mples that the followers grow relatvely quckly and tend to catch up the leaders We should add that trade lberalzaton n the developng countres targets the externaltes generated by the technology ncorporated n mported equpment In what follows we keep the assumpton of technology mtaton rather than ts nnovaton for somme LD s specfc context In ths paper we deveop two models The frst consders the varety of goods and agents heterogenty only n the fnal goods sector The second takes nto account the heterogenty of agents only n mtated-ntermedate goods sector III Fnal good varetes, agents heterogenety, and economc growth We begn wth the case where heterogenety of agents n mtaton sector s not consdered Suppose that each agent produces only one fnal good The producton technology s descrbed accordng to the followng ES functon: where, s the fnal good, B s a productvty parameter, x t ( j) denotes the nput (j) j, and s the volume of homogenous labor assumed constant A s an ndcator of horzontal dfferentaton of the nputs x(j), and 0 < A Imported captal varetes are gven by x( j) dj In ths economy, ncome Y t s allocated mported at tme t, such as 0, A 0 between fnal consumpton, nvestment n the adopton of technology denoted by A da A, dt and the mport of ntermedate goods x( j) dj As mentoned above, we refer to technology 0 as the dfferentaton of product whch s defned smlarly as n Grossman and Helpmann (99) Ths can be explaned by horzontal dversty of the mported equpment goods x t ( j) A constant share of output s devoted to the fnancng of technology adopton: The producer maxmzes proft and the resultng necessary condton of equlbrum s gven by: 36

5 Quanttatve ethods Inqures where and are the prces of the fnal and the mpoted goods, respectvely From the symmetry assumpton,, the producer equlbrum condton gves the followng demand functon: (4) where tme subscrpts are omtted whenever no ambguty results It follows that, From (4) we may get the equaton of output for a fxed employment to the unt: 5 (5) s the elastcty of output to the varetes of mported goods It s nversely related to the share of mported equpment goods n ncome 6 In ths model heterogenety s due to non-unformty of costs whch are specfc to each type of product We therefore consder a monopolstc structure of the consumer goods market where competton s based on costs The representatve consumer maxmzes the followng ntertemporal utlty functon on an nfnte tme horzon, where s a composte consumer good defned by: The ntertemporal utlty functon (6) becomes then as follows: 37

6 Quanttatve ethods Inqures s the number of varetes of consumpton goods, denotes the consumpton of good, s the dscount rate, s the rsk averson parameter, and s an ntra-temporal substtuton parameter Snce labor supply s constant t wll not be ntroduced n the utlty functon because nter-temporal arbtrage between lesure and consumpton s beyond the scope of ths paper, and also because aggregate and per capta growth rates of consumpton are dentcal The general prce ndex may be expressed by: We suppose that accumulaton s fnanced by households savngs To establsh the equlbrum condtons n a statonary state we maxmze (6) subject to the followng accumulaton constrant: Equaton (8) descrbes the dynamc budgetary constrant of houshold The economc agent owns fnancal assets and labor Assets yeld a rate of return r whle labor s pad the wage rate w Then the total ncome receved by houshold s the sum of asset and labor ncome, Each houshold uses the ncome that she does not consume to accumulate more assets, Equaton (8) shows that nvestment and savng (the dfference between labor and asset revenues, and consumpton exendture, ) are equal Debt s not consdered n the model The soluton to ths optmzaton program s carred out n two stages We begn wth the determnaton of the statc optmal demand functons and how they are related, and then we compute the growth rate of control varables n a statonary state A Statonary state equlbrum In order to show just the effect of dversty consumpton goods on welfear we assume perfect competton The statonary state s defned where the control and state varables n the system (7)-(8) change at the same constant rate (the proof s n Appendx A- ) The statc demands (demand functons) are determned as follows: Equaton (9) shows that the demand for each varety depends negatvely on the number of varetes and postvely on the consumpton expendture E In addton, due to substtuton between the goods the demand for each varety depends postvely on the relatve prce of the composte good ( /) To determne the statonary state equlbrum n the second step we ntally remove the heterogenety assumpton of agents and we only keep 38

7 Quanttatve ethods Inqures the assumpton of dversty of consumer goods Heterogenety wll be ntroduced later n the paper In order to solate the effect of dversty of products on the growth rate we assume that the margnal costs are dentcal for all frms ( v v for any [,]) Later we relax ths assumpton and we ntroduce the asymmetry of equlbrum ( v v j) for the purpose of analytcal comparsons In the symmetrc equlbrum case the prces of varous consumer goods become equal and the goods enter the functon of utlty symmetrcally, and the consumpton quanttes of each varety are dentcal: j * The growth rate of homogeneous n a statonary state may be wrtten as follows: r ( ) (0) We substtute the nterest rate r = Y/ A n (0) and we obtan the growth rate expresson for a fxed labor level to unty, n a statonary state gven by: where s the growth rate of dfferentated consumer goods 7 Equaton () shows that when ( ) s less (more) than one the change of consumer goods dfferentaton / has a postve (negatve) effect on the growth rate of consumpton The sgn of ths effect depends on the preference parameters We study ths sgn wth smulaton experments n the next secton Accordng to Equaton () when the consumer goods are perfect substtutes, dversty s no longer relevant Its evoluton wll not affect the growth rate of the statonary state When these goods are perfectly complementary ( 0 ) the effect of ther dversty on the growth rate s maxmum for a gven elastcty of ntertemporal substtuton In fact, followng Grossman and Helpman (99) dversty of goods n the consumpton basket avods the fall of margnal utlty and mproves the consumer surplus In ths case when the number of varetes ncreases, the growth rate of per capta consumpton and consequently the growth rate of per capta ncome both ncrease Equaton () s mportant because t shows also that f domestc agents make an effort to dfferentate ther fnal goods and an effort to adopt mported technology ther growth rate and welfare wll mprove Ths happens due to the role of the adopted foregn technology n growth Therefore, trade openness leads to a decrease n relatve prces of mported goods and thus contrbutes postvely to growth and better resource allocaton through a growng volume of equpment goods, as argued n De Long and Summers (99) 39

8 Quanttatve ethods Inqures and Ta and Klenow (2002) In fact, not only trade lberalzaton decreases prce dstortons, t may also trgger hgher growth rate stemed from the lower relatve prces of equpment goods and the spread of technology expressed here by the dversty of mported equpements These postve dynamc effects of trade openness polcy are shown n the followng equaton, ncludng a reducton of the rate of customs duty whch s referred to as a proxy of trade openness polcy: Set, we obtan : Equaton (2-a) shows that trade openness polcy results n a decrease of and mpes a hgher growth rate (e 0 ) Ths type of result s establshed wthn the framework of a consumpton goods market where producers are homogeneous We are turn to the case of heterogeneous producers B Agents heterogenety, entry-ext dynamcs, and ndustral effcency threshold n ndustry Heterogenety allows us to analyze the ndustry structure, to descrbe the supplers behavor, and to establsh the condtons of ext and entry n ndustry Each frm has a varable specfc cost per unt produced v and a constant cost whch s dentcal to all frms for a gven ndustral actvty The constant cost s the expendture n physcal and human or fnancal captal whch s necessary to enter the ndustry The quantty and the qualty of account for the specfcty of the ndustral actvty that each agent targets The rreversble cost s then the frst necessary condton for the frm to be consdered as potental canddate to access the ndustry We show n what follows that the ndustry cost structure plays a key role for the demand of each varety of consumer goods by ts acton on the prces and the number of varetes Let defne the total cost, where s the specfc output produced by agent such as [, ] The fxed cost nvolves the need for specalzaton n a partcular product (Stgler, 949) Thus t can partally explan the heterogeneous structure of the producton n ndustry once the fnal output s produced Ths heterogeneous structure gves necessarly place to a framework of mperfect competton analyss For a cost functon gven by (3), let for any gven, then the mark-up prce of the monopoly denoted by s gven by: v (4) 40

9 Quanttatve ethods Inqures Snce the margnal cost s specfc to each frm, t follows that for a gven market structure there s an asymmetrc equlbrum that results n as many prces, quanttes and profts, as products 8 Wthn a monopolstc structure and the gven the characterstcs of costs, only the most effcent frms wll survve n the ndustry and there wll be no long term proft Agents wll to decde to enter the market accordng to the expected proft whch n turn s non predctable and follows a stochatc process generated by the varable costs These costs vary n the nterval [, ] The lmt values of ths nterval are ndcatve of the frm s technologcal heterogenety degree In other words, the degree of heterogenety of the frms ncreases wth hgher values of When 0 we go back to the case where all frms are homogeneous Faced wth gven values of cost opportunty r, a frm that has already ncurred the fxed-cost equpement n mtaton wll choose a level of output to maxmze ts revenue mns cost at every date, The proft for frm, for a gven prce s gven by: We focus the analyss on the partal equlbrum where the opportunty cost r s gven for each frm 9 As usually, equlbrum producton n equaton (5) s obtaned by takng nto account labor and captal cost For now, ths s all we need to study the effect of consumer goods dversty on growth Substtute the expresson of from equaton (4) n equaton (5), and use equaton (9) to obtan: where and It s clear that the proft of frm decreases wth the number of varetes and wth the varable costs, and t ncreases wth the general prces ndex Hence, the hgher the prce ndex, the more tempted the frm wll be to enter the market because t antcpates a hgh proft In addton, f there are more agents that specalze n the producton of only one good then the condtons of comparatve compettveness wll be more dffcult In fact these condtons are drectly related to the varable costs, and t s nterestng to fnd the value of v that matches the mnmum threshold of technologcal effcency from whch the frm decdes to enter the ndustry Ths threshold s determned by a null proft that corresponds then to a threshold of varable cost v *, such as: For = 0, we have the varable threshold of cost: K / / / v * (7) For a gven number of varetes, frms whose margnal cost s lower than v * wll have a postve proft and those frms whch have v = v * wll have a zero proft 0 Lastly, frms wth varable cost exceedng v * wll leave the ndustry because they are not effcent 4

10 Quanttatve ethods Inqures For a gven prce, there s a number of potental canddates who expect a null proft We can wrte equaton (9) n terms of growth rates to descrbe the dynamcs of frms entry to and ext from the ndustry: Both and (8) decrease wth the subttuton between goods when ncreases Also, notce that for a gven whch corresponds to the ncrease n the number of varetes, the general prce ndex drops along wth the prce of each varety To complete the descrpton of global market acton on ndvdual prce, we can rearrange terms n equaton (8) to obtan an expresson of growth rate of varety prce as follows: Intutvely, equaton (8-a) means that followng a decrease of good s prce whch s caused by a surge n the number of varetes, the proft of frm falls untl the frm exts the ndustry In addton ths ext mpacts negatvely and ths s lkely to generate an ncrease n and rather than an ncrease n the proft of the remanng frms As a consequence, there wll be new entres to the ndustry We can then descrbe the statonary state by an expected null proft of the last frm where ths entry-ext dynamc stops It should be noted however that before ther entry, all frms have the same uncertanty about ther techncal effcency But once access cost to ndustry K and margnal cost ( v ) are undergone, any uncertanty wll dsappear Lastly and followng Jovanovc (982), t s supposed that each agent who s a potental an entry canddate does not consder ther nfluence on the market structure and on the mnmum threshold of effcency Therefore the agent maxmzes expected proft a as follows: Then, Where f(v) /(2 ) s the probablty densty of a random varable v and s the standard devaton of v Ths term ndcates the dsparty of frms n terms of technologcal effcency Now t t shown that new entres wll have a negatve mpact on the prce snce the demand for each varety decreases and so does the frm s ncome Ths s lkely to rase the mnmum effcency threshold and forces non-effcent frms to leave the ndustry The statonary state s then characterzed by: a 0 (20) 0 ombnng Equatons (7-8), the soluton to ths system s gven by: E /(2 ) K /(2 ) (20-a) 42

11 Quanttatve ethods Inqures The soluton gves the number of frms * and the level of effcency v * and therefore we obtan what s known as the stable structure of ndustry Fnally, by combnng the two equatons of ths system wth equaton (7) we get the expresson of the general prce ndex: 2( ) v [ K] (2) Smulaton Experments The smulaton experments that we have conducted relate the effect of frm heterogenety to the threshold of effcency v * for varous values of degrees of ntratemporal substtuton The results are obtaned n the Fgure- : v Fgure Effcency level and frms heterogenety Fgure-- shows a negatve correlaton between the mnmal degree of effcency v * n the ndustry and the degree of frm s heterogenety Ths negatve relatonshp s due to competton costs for frms n the same ndustry In fact, competton s tougher when the dfference n effcency between frms s hgher Thus, only the more effcent frms may survve n an ndustry that s more heterogeneous oreover, n a heterogeneous ndustry the condtons of access become so dffcult because the prce of varety s lower and the margnal cost v s weaker As a consequence, ths stuaton results n a lower proft We also smulate the degree of ntra-temporal substtuton between goods The results show that effcency level s low to the extent that varetes are substtutable In fact, monopoly prce and proft decrease as the varetes are substtutable (ths can be seen from equaton (4) when s hgh) ost competton becomes harder and the condtons of margnal frm s survval become ncreasngly dffcult Ths s llustrated n the effcency curve where the dotted lnes are lower than the sold lnes for the hghest values of We can draw from ths observaton an nterestng results that shows two negatve effects on the effcency of survvng frms The effect of heterogenety and the effect of goods substtuton Agents heterogenety and substtuton between fnal goods decrease the monopolstc power of frms that are carryng out competton by costs, snce n ths case the 43

12 Quanttatve ethods Inqures margn on the prce (and thus on the revenue) may decrease Ths could result n a postve effect on consumpton and on welfare Heterogenety of agents who specalze n fnal consumer goods producton wll result n an asymmetrc equlbrum and thus wll provde a spectrum of prces, quanttes and profts It becomes now possble to establsh the mnmal threshold of technologcal effcency for the access to producton actvty The dversty of consumer goods mproves the growth rate of consumpton not only by ts negatve acton on the monopoly power of the frms and thus on the prces, but also by ts postve effect on welfare As a polcy mplcaton, t s shown that trade openness that allows more dversfed fnal goods wll have a postve mpact on consumpton an welfare IV Heterogenety of agents and economc growth We now present a second model that addresses the ssue of ndustry structure wth agents heterogenty n the mtaton sector We ntroduce agents heterogenety only n the sector of technology mtaton of mported equpment, whle agents n the sector of fnal goods are stll homogeneous What are then the effects of mtators heterogenety on economc growth? Are there technologcal condtons to access ths type of actvty? If so, how are they establshed? What are the economc polcy mplcatons of trade lberalzaton? Followng Spence (976), Dxt and Stgltz (977), and Ether (982), the technology of producton n mtaton sector s gven by: (22) s the mtated good produced, s (constant) labor used n the sector, s the ntermedate good used n the mtaton sector, and A denotes the number of mported varetes at tme t Followng Romer (990), we assume that the fnal good market s perfectly compettve, whereas the market of nternedate goods s not Agents dffer by a specfc margnal cost We keep the same cost expresson as n Romer (987), namely: 2 V x K 2 (23) denotes the coeffcent of margnal cost K s the fxed cost whch s a prerequste to access the mtaton sector To determne the economc growth rate n a statonary state, we determne the prces, the profts, and the quanttes at equlbrum n order to lay out the condtons of access to ndustry Next, we determne the growth rate of per capta ncome n order to obtan the lnks between heterogenety and growth In the mtaton sector each agent maxmzes proft as follows: The nverse demand functon of the varety perfect competton s gven by: (24) resultng from proft maxmzaton n In the mtaton sector of mperfect competton each agent maxmzes ts proft : 44

13 Quanttatve ethods Inqures where r s the opportunty cost of captal whch s ntroduced n a general equlbrum framework and whch s determned endogenously We make use of the above equatons to obtan the proft functon as: 2 xt L r ( V x K) (27) 2 It follows that From equatons (25) and (28) we can determne each varety s monopoly prce for a fxed value of labor as follows: rv (29) The monopoly prce for each varety s an ncreasng functon of the correspondng varable cost and nterest rate As shown n Appendx A-2, we can wrte frm ' s proft as follows: h r V r K (30) 2 where 22 / 2 / h L 2 Equatons (28-30) satsfy the general structure of the ndustry establshed n the frst secton Ths structure s characterzed by a spectrum of prces, quanttes, and profts Equaton (30) shows the relatonshp between the proft of frm and ts technologcal effcency V It s then a matter of comparng the frms wth repect to technologcal effcency whose threshold of entry to ndustry s to be determned thereafter The dynamcs of the mtated ntermedate goods market n whch agents are heterogeneous s smlar to the market of fnal goods developed n the the preceedng secton We follow the same approach to determne the economc growth rate n a statonary state a Each agent wshng to enter the market should have an expected proft 0 : V dv 0 a f (3) From (30) and (3), the proft equaton becomes: a h rv rk (/ 2 ) dv 0 (32) It s now possble to determne the nterest rate r* of the long term equlbrum where a entry and ext of agents n the ndustry stops when the expected proft becomes null The a soluton to (32) and the condton 0 gve the nterest rate as follows: / 2 2K / 2 / 2 / r 2 (33) where 2 / 2 h 2 / L 45

14 Quanttatve ethods Inqures It should be noted that r* s determned by the specfc market structure and the technologcal condtons of effcency to enter the ndustry It s determned, as shown n equaton (33), by the degree of heterogenety of the frms and of the fxed cost As for the mnmal threshold of effcency V*, t corresponds to a zero proft obtaned by the margnal frm Gven r*, the expected proft of the margnal frm s: r V r K (/ 2 ) dv 0 a h (34) Thus r* determnes the threshold of effcency V* Frms for whch V exceeds V* (V between V * and + ) wll leave the market snce they become noncompettve Only frms wth V n the nterval [-, V * ] wll stay The proft of survvng frms may be determned as follows: V / h rv rk / 2 dv 0 a (35) *2 / 2 / * V V K] 0 2( ) * a h r* [ (36) 2 Ths result shows that the relatonshp between threshold of effcency V * and heterogenety of the frms s ambguous The smulaton results for = 03 and a constant captal stock ndcate that the effect of agents heterogenety on effcency threshold s negatve as shown n Fgure 2: V* Fgure 2 Effcency threshold and agents heterogenety It s now clear that we obtan the same type of heterogenety effect on the effcency threshold as n the case studed n the frst secton The hgher s the varaton of effcency between the frms, the more dffcult are the survval condtons, and the more ntense becomes the competton through costs So what are the consequences on growth rate? 46

15 Quanttatve ethods Inqures From the expresson of growth rate at the statonary state shown n Appendx A and for homogeneous consumer goods (=0) we have: g r (37) Substtutng equaton (33) n equaton (37), we obtan: / 2 / 2 g 2 K (38) It can be seen that per capta ncome growth rate has changed by agents heterogenety n the mtaton sector compared to the homogenety case In fact, even compared to the case of consumer goods heterogenety the statonary state per capta growth rate s negatvely correlated wth the degree of agents heterogenety n the mtaton sector Ths negatve correlaton s shown n our smulaton results as depcted n Fgure 3 below: g Fgure 3 Statonary state growth rate and agents heterogenety Therefore, as the statonary state growth rate becomes weaker the dsparty n terms of technologcal effcency of the mtatng frms becomes hgher We can lay out two features that characterze the mtaton technology sector Frst, the mnmum threshold of rreversble captal whch s necessary to access the mtaton actvty reduces the number of canddate frms and creates competton through costs Second, ths competton occurs n a monopolstc context The resultng aggregate equlbrum s non optmal because of mperfect competton correspondng to prces hgher than n perfect competton It s the agents heterogenety and thus the mperfect structure whch s at the orgn of a nonoptmalty Wth hgher degree of heterogenety we have lower economc parformance as a whole and a resultng lower growth rate Fnally, from equatons (33) and (36) and also from fgure 2, our results show that for a gven degree of heterogenety the threshold V* would be the equvalent barrer to entry snce margnal costs are ncreasng and thus would have a negatve mpact on proft progressvely wth the accumulaton of captal as nterest rate decreases V oncluson In ths paper we shed some lght on the mportant lnk between ndustral structure and aggregate economc growth for emergng economes seekng to mplement openness n ther trade polcy 47

16 Quanttatve ethods Inqures Our results show the relevance of the technology adopton hypothess as opposed to the tradtonal hypothsess of nnovaton Followng Romer (990), we develop an endogenous growth model for small open economes where domestc agents adopt technology ncorporated n mported equpment In the model, equpment mport coupled wth technologcal externaltes and wth the fall n relatve prces explan the growth effects of openness Entry and ext dynamcs n ndustry depend on expectatons that heterogeneous agents form about future proft and also on ther technologcal compettveness The market structure characterzed by a spectrum of prces and pofts s gven endogenously In such a structure, competton takes place through costs In the long run, survvng frms would make some non-zero profts nmum effcency threshold of entry and ext dynamcs n the domestc ndustral structure are then endogeneously determned The dversty of consumpton goods mproves the growth rate of consumpton and welfare by ts negatve acton on the monopoly power of the survvng frms The results seem to be consstent wth those establshed n the basc models of endogenous growth wth dfferentated products In the case of ntermedate goods, agent s heterogenety s negatvely correlated wth statonary state growth rate In fact, monopolstc competton leads to a non-optmal growth equlbrum at the aggregate level although t wll result n a reduced number of agents For the decson maker, we argue n ths paper that openness trade polcy shows mxed results Specfcally, there are two opposte effects on economc growth A postve effect descrbed by the fall n relatve prces of the equpment whch leads to an ncrease n mports and allows more technology to be adopted A negatve effect descrbed by ext of domestc frms from ndustry as ther effcency decreases compared to foregn frms, makng the market structure more monopolstc VI References Arrow, K: "The Economc Implcatons of Learnng by Dong", Revew of Economc Studes, 29 (June), 962, p Arrow, K J, H B henery, B S nhas, and R Solow: "aptal-labour Substtuton and Economc Effcency ", Revew of Economcs and Statstcs, 43 (August), 96, p Baldwn, RE, On the Growth Effects of 992", NBER, Workng aper # 39, Baldwn, R E, "Openness and Growth: What s the Emprcal Relatonshp? NBER Workng aper # 9578, Barro, R, "Gettng It Rght: arkets and hoces n a Free Socety, The IT ress, 996, p 6 Barro, R and X S artn, "Economc Growth", cgraw-hll Inc, Eds Luclle, Barro, R and X S artn, "Imtaton and Growth", NBER Workng aper, Barro, Robert and X S artn, "Technologcal Dffuson, onvergence and Growth", NBER Workng aper # 55, Bernard, A B, J Eaton, J B Jensen, and S Kortum, ''lants and roductvty n Internatonal Trade, NBER Workng aper # 7688,

17 Quanttatve ethods Inqures 0 Bernard, A B, J B Jensen, and K Schott, ''Fallng Trade osts, Heterogeneous Frms, and Industry Dynamcs'', NBER Workng aper # 9639, 2003 hamberln, EH: ''The Theory of onopolstc ompetton'', Oxford Unversty ress, 6 th edton, rossman, G and E Helpmann, Innovaton and Growth n the Global Economy'', ambrdge, A, IT ress, 99 3 De Long, J B and L H Summers, Equpment Investment and Economc Growth'', Quarterly Journal of Economcs, 04, 99, Dxt A K, and J E Stgltz, onopolstc ompetton and Optmum roduct Dversty Amercan Economc Revew, 67, June, 977, Easterly, W, R Kng, R Levne, and S Rebelo, "olcy Technology Adopton and Growth", enter of olcy Economc Research, Dscusson aper, Ether, W J, Natonal and Internatonal Returns to Scale n the odern Theory of Internatonal Trade Amercan Economc Revew, 72, June, 982, Gorodnchenko, Y, J Svejnar, and K Terrell, Globalzaton And Innovaton In Emergng arkets NBER Workng aper # 448, Guadalupe, and J Wulf, The Flattenng Frm and roduct arket ompetton: The Effect of Trade Lberalzaton, NBER Workng paper # 449, Hartley, JE, Retrospectves The Orgns of the Representatve Agent, Journal of Economc erspectves-volume 0, Number 2-Sprng, 996, ages Holmøy, E, Aggregate Industry Behavour n a onopolstc ompetton odel wth Heterogeneous Frms, Dscusson apers No 352, (June), Statstcs Norway, Research Department, Hopenhayn, HA, ''Entry-Ext, and Frm Dynamcs n Long run Equlbrum" Econometrca, 60, 992, Hseh, T and J Klenow, "Relatve rces and Relatve rosperty", December 2002, NBER Workng aper # 9373, Jovanovc, B, "Selecton and the Evoluton of Industry'', Econometrca, 50, 982, Jovanovc, B and S Lach, Entry, Ext and Dffuson wth Learnng By Dong", The Amercan Economc Revew, 77, N 4, Lppman, SA, and R Rumelt, "Uncertan Imtablty: An Analyss of Inter-frm Dfferences n Effcences under ompetton", Bell Journal of Economcs, 3, 982, Lppman, SA, K F cardel, and R Rumelt, "Heterogenety under ompetton", Economc Inqury, 99, Lucas, J R, "On the echancs of Economc Development'', Journal of onetary Economcs, 22, 998, eltz, J, ''The Impact of Trade on Intra-Industry Reallocatons and Aggregate Industry roductvty'', NBER Workng aper # 888, azzeo, J, roduct hoce and Olgopoly arket Structure, RAND Journal of Economcs, 33, No 2, 2002, 22 49

18 Quanttatve ethods Inqures 30 ontagna,, Horzontal roduct Dfferentaton and Frm Specfc Technology: A onopolstc ompetton odel, Dscusson papers n Economcs, N 46, Unversty of Dundee, ontagna,, onopolstc ompetton wth Frm-Specfc osts", Oxford Economc apers, 47, 995, ascoa, R, "Non ooperatve Equlbrum and hamberlnan onopolstc ompetton'', Journal of Economc Theory, 60, 993, Romer,, "Increasng Returns and Long Run-Growth", Journal of oltcal Economy, 94, No 5, 986, Romer, Growth Based on Increasng Returns Due to Specalzaton", Amercan Economc Revew, 77, No2, 987, Romer, Endogenous Technologcal hange", Journal of oltcal Economy, 98, No5, 990, Romer, and A L Batz, "Economc Integraton and Economc Growth", Quarterly Journal of Economcs, 6, No2, 99, Sem, K, An Emprcal odel of Frm Entry wth Endogenous roduct-type hoces RAND Journal of Economcs, 37, No3, Spence,, roduct Selecton, Fxed osts, and onopolstc ompetton Revew of Economc Studes, 43, June, 976, Stgler, GJ, onopolstc ompetton n Retrospect'', In Fve Lectures on Economc roblems, London School of Economcs, 949, Temple, J, The New Growth Evdence", Journal of Economc Lterature, 37, 999, Yeaple, S R, A Smple odel of Frm Heterogenety, Internatonal Trade and Wages, Journal of Internatonal Economcs, 65, 2005, -20 Appendx A-: Soluton to optmzaton program (7)-(8) and determnaton of equaton (9) a) Frst soluton stage: determnaton of statc demand maxu (A-) S / E E s the total revenue allocated to consumpton The number of varetes s supposed suffcently hgh such that the varety producer neglects the effect of household total expendture by varety of goods on Let L the Lagrange functon: L E The necessary condton s: 0 L Let e, and X, then X X -e s constant 50

19 Quanttatve ethods Inqures 5 Observe that E and E multplyng and dvdng by, we obtan the followng expresson of varety statc demand, equaton (9) n the text: E Then, E b) Second resoluton stage (symmetrc equlbrum case) In ths case the prces of the varous consumer goods are equal enters the utlty functon n a symmetrc and the consumed quanttes of each varety are dentcal In other words *, and, The Hamltonan s gven by: t ra wl e H (A-3) The necessary condtons are as follows: t e H 0 r dt d, thus r The growth rate of homogeneous, n a statonary state s thus: r ) ( (A-4) The equaton (A--4) s not other than the equaton (0) of the text We replace the yeld A Y/ = r by ts value from equaton (8) n equatons (5)-(2) and we obtan the statonary state growth rate expresson, /, / ) (- B / ) ( * - / A L (A-5) Where, s the growth rate number of the of dfferentated consumer goods Equaton (A-5) s numbered () n the text A-2- Determnaton of the proft expresson n equaton (29) The proft, prce, and demand expressons are respectvely as follows: and We replace the nput demand and the prce of each varety by ther values n the proft equaton to obtan the expresson (29) n the text: K r V r L / 2 / (29)

20 Quanttatve ethods Inqures Wth h 2 22 / 2 / L 2 A-3- atlab program The smulatons results obtaned n secton 3 of ths paper are performed wth the followng atlab program: %dary alyout clear %epslon=00 ; %epslon2=003 ; %epslon3=005 ; epslon=009 ; epslon2=035 ; epslon3=049 ; sgma= ; amaj= ; kmaj=2 ; etat=(-epslon)*((/epslon)^ (-/(-epslon))) ; etat2=(-epslon2)*((/epslon2)^ (-/(-epslon2))) ; etat3=(-epslon3)*((/epslon3)^ (-/(-epslon3))) ; delta=00 :00 :099 ; % a=/(2*delta) ; a2=(-epslon)/ -2*epslon) ; a22=(-epslon2)/ -2*epslon2) ; a23=(-epslon3)/ -2*epslon3) ; a3=(+delta)^(/a2) ; a32=(+delta)^(/a22) ; a33=(+delta)^(/a23) ; a4=(+delta)^(/a2) ; a42=(+delta)^(/a22) ; a43=(+delta)^(/a23) ; a5=a3-a4 ; a52=a32-a42 ; a53=a33-a43 ; a6=(epslon-)/ epslon) ; a62=(epslon2-)/ epslon2) ; a63=(epslon3-)/ epslon3) ; vmaj=(a2*(a*a5))^a6 ; vmaj2=(a22*(a*a52))^a62 ; vmaj3=(a23*(a*a53))^a63 ; % % a=(etat*amaj/kmaj) ; a2=(etat2*amaj/kmaj) ; a3=(etat3*amaj/kmaj) ; a2=pmaj^((/-epslon))-sgma ; a22=pmaj2^((/-epslon2))-sgma ; a23=pmaj3^((/-epslon3))-sgma ; a3=(/-epslon)/(-2*epslon) ; a32=(/-epslon2)/(-2*epslon2) ; a33=(/-epslon3)/(-2*epslon3) ; a4=/2*delta) ; a5=(+delta)^(/a3) ; a52=(+delta)^(/a32) ; a53=(+delta)^(/a33) ; a6=(-delta)^(/a3) ; a62=(-delta)^(/a32) ; a63=(-delta)^(/a33) ; a7=a5-a6 ; a72=a52-a62 ; a73=a53-a63 ; mmaj=(a4*(a*a2*a3))*a7 ; mmaj2=(a4*(a2*a22*a32))*a72 ; mmaj3=(a4*(a3*a2*a33))*a73; %%% subplot(2,,2) ; 52

21 Quanttatve ethods Inqures plot(delta,vmaj'-',delta, vmaj2,'',dalta,vmaj3,'-') ; ttle(figeffcency level') xlabel ('delta') ; ylabel('v') ; legend('- :epslon=009',' ::epslon=03','-- :epslon=047') subplot(2,,2) ; plot(delta,mmaj'-',delta, mmaj2,'',dalta,mmaj3,'-') ; ttle(fig2frms number') xlabel ('delta') ; ylabel('') ; legend('- :epslon=009',' ::epslon=03','-- :epslon=047') dary off % See Baldwn (2003) and JTemple J (999) for syntheses of the emprcal lterature 2 From ths pont of vew, some authors explan that heterogenety comes from the asymmetry of nformaton and uncertanty about technologcal effcency as argued n Lppman and Rumelt (982), Lppman et al (99), and Hopenhayn (992) 3 Note n addton that the queston of ndustral structure n connecton wth trade brought about a great deal on nterest n recent emprcal lterature The reader may be referred to Guadalupe and Wulf (2008), and Gorodnchenko, et al (2008) for more detal 4 It would be possble to take nto account also a domestc producton of equpment as n Bengno and Theonssen (2008) that seems more realstc for countres n wtch a weght of domestcally produced ntermedate goods s not neglgble compared to that of mported ntermedate These authors develop an nterestng macroeconomc model whch analyzes the relatonshp between the real exchange rate and the rato of home to foregn consumpton under supply sde shocks, takng nto account both the domestcally produced and mported equpments 5 Labor demand s such for a gven real wage prces and, we have 6 In fact, s decreasng wth 7 See proof n Appendx (A-) 8 It s assumed that each frm wll not affect sgnfcantly the prce ndex 9 In the next secton we ntroduce a general equlbrum analyss to study the outcome of opportunty cost endogenety of captal as n Romer (987) and (990) 0 In ndustral organzaton, frms whose margnal cost s equal to v *, are referred to as margnal frms It should be noted that the sgn of the effect of the heterogenety of frms on the threshold of effcency s ( )/ ambguous: v [ ( )/ 2 ] 2 [ ( 2 )/( ) ( 2 )/( ) / ] All the smulaton experments are carred out n atlab 53