Cycles of Technology, Naural Resources and Economic Growh By Susanna Lundsröm Α Deparmen of Economics Göeborg Universiy June, 22 Β Prepared for he 22 World Congress of Environmenal and Resource Economiss, Monerey, California, June 24-27, 22. bsrac Boh echnological and naural resource possibiliies seem o evolve in cycles. The Resource Opporuniy Model in his paper inroduces he echnological opporuniy hinking ino naural resource modeling. The naural resource indusries choice beween incremenal, complemenary, innovaions and drasic, breakhrough, innovaions will give rise o long-run cycles in he so called familiar resource sock, which is he amoun of naural resources deermined by he prevailing paradigm. Incremenal innovaions will increase he exhausion of he sock and drasic innovaions will creae a new paradigm and hereby a new sock of familiar resources. Drasic innovaions are endogenously affeced by he knowledge level and induced eiher by scarciy of echnological opporuniies or by scarciy of resources. Generally, an increased level of innovaion abiliy increases he knowledge sock and he level of income bu does no affec he susainabiliy of he resource sock, even hus he inensiy of he resource cycles increases. However, a oo low level migh lead he secor o echnological sagnaion, and resource exhausion in he long run, and a oo high level migh lead he secor o exracion sagnaion, and resource exhausion in he shor run. Keywords: cycles, economic growh, induced innovaions, naural resources, echnological opporuniies, paradigm shifs JEL classificaion: O11, O13, O31, Q3, Q43, N5 Α Deparmen of Economics, Göeborg Universiy, P.O. Box 64, 45 3 Sweden, el: +46 31 773 5252, fax: +46 31 773 143, e-mail: Susanna.Lundsrom@economics.gu.se Β I would like o hank Clas Eriksson, Maias Erlandsson, Olof Johansson-Senman, Åsa Löfgren, Ola Olsson, Sjak Smulders, Jean-Philippe Sijns, paricipans a SOM inernaional summer school a Seeon, and seminar paricipans a Göeborg Universiy for helpful commens. 1
1 INTRODUCTION The abundance of many naural resources shows a clear cyclic paern over ime. The ypical dynamics have been periods of pessimism, wih resriced resource opporuniies, ha finally have been replaced by new eras of opimism, even hough here are examples of sagnaion. The cyclic paern of innovaions, and hence economic growh, has also been acceped as a sylized fac. Drasic innovaions are replaced by periods of less revoluionary innovaions. Hence, boh echnological and naural resource possibiliies seem o evolve in cycles, which give rise o several ineresing quesions abou heir possible inerrelaions. re he effecs of innovaion on resources differen depending on he ype of innovaion? Can echnological change be he source of boh prosperiy and sagnaion in naural resource indusries? re limied naural resources he driving force of echnological shifs? David and Wrigh (1997) argue ha resource abundance is no exogenously given by geological condiions bu an endogenous social consrucion. Combined effecs from legal, insiuional, echnological and organizaional responses o resource scarciy creaed a highly elasic supply for merican mineral producs. In a survey of echnological change and he environmen Jaffe e.al. (2) conclude ha he modeling of how he various sages of echnological change are inerrelaed, how hey unfold over ime, and he differenial impac ha various policies may have on each phase of echnological change is of grea imporance o undersand he ineracion beween innovaions and he environmen. I is he purpose of his paper o model he innovaion decisions of he naural resource secor using he echnological opporuniy approach, which is one way o creae a long run cyclic paern of naural resource, and hereby idenify he crucial variables a differen sages. 1 Earlier models of innovaions and naural resources have usually modeled jumps in he exracable resource sock by assuming a Poisson disribuion wih a consan probabiliy of discovery (see Kraukreamer (1998) for an overview). In some models he frequency of discovery or innovaion aciviy is a exogenous bu in ohers i is a funcion of research expendiures. s he known sock decreases, he cos of 1 I is no he purpose of his paper o model he effecs of resource saving echnologies on he demand side. These are of course of grea imporance bu o keep he dynamics of supply responses racable his effec will only be discussed in he secion where he effecs of price changes are analyzed. 2
exracion increases and invesmens in research becomes profiable. Once he discoveries of new sources or new echnologies are made, coss decreases and here is a new period of exracion wihou any innovaion aciviy. However, he innovaion aciviy is no a discree bu a coninuous process, even hough he ype of innovaions migh differ from period o period. Research could be of differen characer; revoluionary or non-revoluionary, resource consuming or resource creaing, bu few sudies make his disincion. 2 Moreover, he uncerain oucome of he innovaion process does no have o be modeled as compleely random bu also endogenously influenced by he level of echnical knowledge. noher shorcoming of earlier models is he inducing mechanism. Many innovaions in he naural resource secor do seem o be induced by he scarciy of resources. However, i is no possible o overlook he fac ha many drasic innovaions occurred wihou any physical resource resricions (Jaffe, e.al., 2). In his aricle he cyclic paern of innovaions is, by he heory of echnological opporuniies, explained by abundance or scarciy of echnological opporuniies. Technological opporuniies are, wih decreasing reurns, urned ino incremenal innovaions and when hese are exhaused, innovaor urn o drasic innovaions, which inroduces new echnological opporuniies. This approach is especially suiable for he naural resource secor in which he scarciy hinking is crucial. Drasic innovaions in he naural resource secor can eiher be conneced o he inroducion of a new, unexpeced echnical soluion or he finding of a new ypr of resource. Some clear-cu examples of major break-roughs of imporance for he naural resource indusry are he energy sysem shifs beween horse power, wind power, coal, oil and nuclear. The common feaure of hese drasic innovaions is ha hey gave rise o sequences of follow-up or complemenary innovaions. These are non-revoluionary or incremenal innovaions in he sense ha hey are only combinaions of already exising ideas. By inroducing oil as an energy resource he mechanical revoluion became possible, he seam engine revoluionized he mining 2 One excepion is Smulders and Breschger (22) ha presens a model where one ype of innovaion is underaken a a cerain momen in ime, eiher a revoluionary general purpose echnology, or a diffusion process of his new echnology. However, i is raher cycles in polluion, no resource socks, ha is modeled and he inducing mechanism is increasing coss (as in he radiional models) because of environmenal axes, and no innovaion consrains. 3
indusry, ec. I is hrough hese incremenal progresses, he combinaion of he new idea o old knowledge, ha he drasic innovaion becomes fruiful. In he Resource Opporuniy Model (ROM) presened in his paper we add a new dimension o he echnological opporuniy approach. The choice of he naural resource producer is no beween exracion and innovaions as in many earlier sudies, bu beween he ypes of innovaions. The ineracion of incremenal innovaions and drasic innovaions will give rise o long-run cycles in he so called familiar resource sock, which is he sock of naural resources deermined by he prevailing paradigm. Incremenal innovaions will increase he exhausion of he sock and drasic innovaions will creae a new paradigm and hereby a new sock of familiar resources. Drasic innovaions are no only induced by resource consrains bu raher incremenal innovaion consrains, as in he echnological opporuniy model. However, hey are now creaed eiher by scarciy of echnological opporuniies or by scarciy of naural resources. The expeced success of hese drasic innovaions, in inroducing new echnological and resource opporuniies, is no consan as ofen assumed bu endogenously deermined by he increasing sock of knowledge. The inclusion of resriced resources opens up he analysis for sagnaion oucomes. The drasic innovaion jumps in resource availabiliy can be more or less successful which increase or decrease he probabiliy of economic sagnaion caused by echnological consrains. Moreover, he rae of incremenal innovaions migh differ, increasing or decreasing he probabiliy of sagnaion caused by oo inensive exracion. The cyclic behavior of he resource sock will also be conneced o economic growh. The incremenal phase of echnological developmen follows he paern of exogenous growh models wih decreasing reurns o scale, boh in echnological opporuniies and naural resources. However, he change in marginal reurns is no really a manna from heaven change in echnology, bu an increased poenial induced by he drasic innovaion. The drasic innovaion is herefore characerized by endogenous echnological change. This combinaion of boh exogenous and endogenous growh periods may give us new insighs abou naural resource scarciy. The general resuls is ha an increased level of abiliy o urn echnological opporuniies ino innovaions does no affec he susainabiliy of he resource sock, even hough he flucuaions increases, bu increases he knowledge sock and he 4
level of income. However, a oo low level migh lead he secor o echnological sagnaion, and resource exhausion in he long run, and a oo high level migh lead he secor o exracion sagnaion and resource exhausion in he shor run. Secion 2 gives he background of he ROM by inroducing he definiions of he resource socks and innovaions, and he echnological opporuniy approach is presened. Secion 3 inroduces he ROM, firs by presening he resource sock dynamics during differen ypes of innovaion periods, hen by modeling he profis ha deermine he ype of innovaion period, and finally by connecing he dynamics o economic growh. The resul is presened by some basic simulaions in Secion 4 and he sagnaion oucomes are discussed. lernaive assumpions are analyzed in Secion 5. Secion 6 concludes. 2 BCKGROUND Before presening he ROM we will presen some definiions when i comes o he resource socks and innovaions. In addiion he basic modeling of echnological opporuniies is presened. 2.1 Resource Socks Firs of all i is imporan o make clear he disincion beween familiar and poenial resources. Familiar resources are he physical quaniy of resources, discovered or undiscovered, under he prevailing paradigm, i.e. resources ha in some way are seen as valuable given he normal science a ha ime. Poenial resources are he physical quaniy of resources ha migh be seen as resources during oher paradigms. The familiar resource sock, S, includes all familiar resources and i is cycles in his sock ha is he focus of his paper. The sock includes boh discovered and undiscovered resources. The discovered familiar resource sock, is he sock ofen referred o in earlier sudies of naural resources and growh, i.e. he sock of familiar resources available for exracion. The undiscovered familiar resource sock include familiar resources, i.e. hey are known according o he prevailing paradigm, bu hey 5
have o be physically discovered before hey can be exraced. Incremenal innovaions will increase exracion and hence decrease he sock of familiar resources, while a paradigm shif will increase he quaniy of familiar resources, eiher by inroducing an unexpeced echnology ha improves he availabiliy of already familiar resources or by adding o he number of ypes of familiar resources. The effecs of innovaions will be furher explained in he nex secion. Figure X migh clarify he definiion of S. S ~ is defined as he poenial resource sock, including he physical quaniy of resources available under all ~ possible fuure paradigms. Z is hen he oal resource sock, i.e. Z = S + S, and he only acual resricion on resources by his definiion would be he hermodynamic laws. However, in his paper we will, as a simplificaion, assume ha S ~ is unlimied. 3 Noe ha S ~ also includes discovered and undiscovered resources. Figure X: Resource Socks Z S ~ S Discovered Drasic Innov Discovered Facor inpu Undiscovered Undiscovered Incremenal Innov ssume ha he oal resource sock we are ineresed in is he sock conneced o he use of energy. Then examples of discovered familiar resource sock are oil sources ha you physically know where hey are. They are sources ready o be exraced wih he echnological knowledge a ha ime, or ha you expec o be able o exrac wih non-revoluionary incremenal exracion echnology. Examples of 3 In he very-long-run he long-run waves in S would also be negligible and he availabiliy of familiar resources would be seen as more or less consan. If, however, we had included he hermodynamic resricions on Z here would probably be a downward sloping rend and no a consan. 6
undiscovered familiar resource sock are oil sources ha you physically have no discovered bu ha you expec o idenify using incremenal discovery echnology. The poenial resource socks are no expeced o be available a all. n example of a discovered poenial resource sock in he energy conex migh be uranium. The finding of nuclear power made uranium becoming a resource. Uranium was discovered before bu no seen as a resource. n undiscovered resource migh be an oil source no even conceivable under he curren paradigm. Wih a new revoluionary echnology such as oil drilling a sea, large sources became possible o discover. 2.2 Innovaions The view of innovaions as a rade-off beween small non-revoluionary and large revoluionary innovaions, is shared by many researchers (see e.g. Kuhn, 1962; Dosi, 1988; Jovanovic and Rob, 199; Mokyr, 199; Helpman and Trajenberg, 1998). Olsson (21) presens hree kinds of echnological innovaions relaed o knowledge in general; incremenal innovaions, drasic innovaions and poenial innovaions. 4,5 Incremenal innovaions are non-revoluionary changes in echnology ha are generaed by combining old knowledge. The coss and risks are low, and he innovaions are carried ou by profi-seeking enrepreneurs. Incremenal innovaions are he normal aciviy in he echnology field and only bounded by he prevailing echnological paradigm. Drasic innovaions are revoluionary new ideas ha combine new knowledge, a poenial innovaions, wih he old knowledge. The coss and risks are high, bu he financial rewards can be subsanial. Mos imporanly, he drasic innovaions open up for new echnological possibiliies by he new knowledge, creaing a new echnological paradigm. However, he reurns and he success of he innovaions are uncerain and he risk of free-riding high. The poenial innovaions are he pieces of new knowledge ha drasic innovaions can connec o he prevailing paradigm. These are considered as anomalies a firs, since hey do no fi ino he normal science in he old knowledge. They are no a resul of sysemaic enrepreneurship bu random findings, ofen during conducing normal science. 4 These are similar o oher conceps such as micro- and macroinvenions (Mokyr, 199), or secondary and fundamenal innovaions (ghion and Howi, 1998). The conceps are also relaed o he so-called echnology lock-in, where a paricular echnology migh creae a pah dependence for he follow-up innovaions (Dosi, 1988; Jaffe, e.al, 2). 5 Olsson (21) define poenial innovaions as discoveries bu because of he possible confusion wih resource socks we will use poenial innovaions. 7
In his sudy where we look a he echnological innovaions on he supply side affecing he naural resource secor. Poenial innovaions are islands ouside he naural resource knowledge. poenial innovaion migh have been used in anoher secor bu sill be irrelevan o he science of naural resources. This is acually he ypical siuaion for he naural resource indusry which is no a research inensive secor bu innovaive when i comes o implying echnological soluions from oher pars of he economy (Simpson, 1999). Noe ha a poenial innovaion can be eiher a compleely new echnology or a compleely new ype resource. s we will see he drasic innovaions are induced by he low reurns o incremenal innovaions, which in he ROM is eiher due o a low level of echnological opporuniies or a low level of physical resource availabiliy. 6 Since drasic innovaions are assumed o be induced by low reurns in he naural resource indusry we assume hey have posiive effecs on he sock of resources. Firs, if he poenial innovaion was a echnology, he new knowledge may make he already familiar resources las longer by more efficien echnology hen were available, or even conceivable, during he las paradigm. n example from he peroleum indusry is he inroducion of he compuer making new imaging echnologies possible, which made i possible o map oil sources earlier hidden (Bohi, 1999). Second, if he poenial innovaion was a resource, he new paradigm may make maerials earlier unknown or earlier judged as non-valuable, becoming familiar resources. sraighforward example is he discovery of uranium as a source of energy by he drasic innovaion of nuclear power. The drasic innovaions can in some sense be inerpreed as general purpose echnologies since hey have he poenial o influence large pars of he economy. drasic innovaion in he ROM could be seen as a general purpose echnology bu only conneced o he naural resource secor and general in he sense ha i affecs large pars of his secor. Incremenal innovaions are conneced o he already familiar resources ha are known under he curren paradigm. 7 They can be divided ino wo caegories; 6 This assumpion is of course only valid for he drasic innovaion connecing he poenial innovaions o knowledge in he naural resource secor and no o drasic innovaions in a more general sense. Noe ha he possibiliy of naural resource scarciy o induce a compleely new echnology (i.e. a poenial innovaion no conneced o knowledge in any secor) is possible bu i could, as menion, also be a echnology already used in oher secors bu induced o be used in he naural resource secor. 7 Of course even incremenal innovaions may have a drasic innovaion characer, i.e. combining old ideas may have revoluionary impacs. In realiy i migh be difficul o separae he wo innovaions. However, we define drasic innovaions as innovaions inroducing compleely new knowledge o he naural resource secor. 8
incremenal exracion echnology and incremenal discovery echnology. Incremenal exracion innovaions increase he efficiency, and hence he rae of exracion, of he discovered resources. n example is when he radiional verical oil drilling echnique was replaced by horizonal drilling, making i possible o approach a reservoir from any angle and hence drain i more horoughly (Bohi, 1999). Incremenal discovery echnology also increases he efficiency in finding undiscovered sources of he already familiar resources. n example from he coal indusry was he developmen of he longwall mining, which made i possible o more efficienly exploi deeper and hinner seams of coal (Darmsader, 1999). Noice he difference beween a drasic innovaion inroducing compleely unprediced sources while a source discovery from an incremenal innovaion is no surprising in he same sense. There is much less doub of he exisence of he source bu he nonrevoluionary echnology of idenifying he source was lacking. Hence, under he prevailing paradigm here is a cerain se of familiar resources, of which some sources are discovered and some are no, and he exhausion of hese are increased by incremenal innovaions. However, drasic innovaions can inroduce a new sock of familiar resources by a new paradigm. 2.3 Technological Opporuniies There is a large lieraure on growh cycles conneced o innovaion (see Sigliz (1993) and ghion and Howi (1998), Chaper 8, for an overview). Some sudies analyses he effec of growh cycles on he innovaion paern (see e.g. Sadler, 199), while oher sudies he impacs of changes in innovaion on growh (see e.g. David, 199; Juhn e al., 1993; Bresnahan and Trajenberg, 1995; Helpman and Trajenberg, 1998). However, for his sudy i is imporan o find a model ha formalizes he disincions beween drasic and incremenal innovaions and heir differen impacs on growh, and ha endogenizes he frequency and he success of he drasic innovaions insead of jus leing hem occur in a sochasic process. I will herefore follow he radiion of sudies like Jovanovic and Rob (199), Boldrin and Levine (21) and Olsson (21) where he driving force of he growh cycles is he rade-off beween new major innovaions and refinemens of old ones. Olsson (21) presens a model o explain he cyclic behavior of echnology and economic growh ha pus echnological opporuniies in he cener of he 9
analysis raher han changes in firms and consumers behavior. Unlike oher work in he area, echnological opporuniies are modeled explicily and deermined endogenously. Raional innovaors choose beween wo basic sraegies; o carry ou incremenal or drasic innovaions. The choice depends on which innovaion ha gives he highes expeced profi. During periods of normal aciviies raional enrepreneurs use he exising echnological opporuniy o make non-revoluionary, incremenal innovaions. The echnological opporuniies are limied by he prevailing paradigm so, as he opporuniies becomes exhaused, profis and economic growh decreases. Evenually profis from incremenal aciviies fall below he expeced profis from he revoluionary, drasic innovaions. This shifs he ineres of he enrepreneurs and he cluser of drasic innovaion aciviies inroduces a new echnological paradigm wih new echnological opporuniies. Once again incremenal innovaion becomes profiable. I is hrough he incremenal innovaions ha he drasic innovaion diffuses ino he economy. There are hree fundamenal variables of echnology;, B and he echnology sock, he se of all known echnological ideas a, corresponding echnological opporuniies and D. 8 is B is D he success of he drasic innovaion, in erms of abiliy o increase he amoun of echnological opporuniies. The knowledge sock evolves in he following way. echnological opporuniy exiss if i is possible o connec wo echnologically close ideas. By connecing wo ideas you creae a new idea ha in urn can be used for new combinaions. These unions of old ideas are he incremenal innovaions and hey sysemaically add new knowledge and hereby increase echnological opporuniies lef o explore, sock exploi unil, bu a he same ime hey decrease he B. Hence, a each poin in ime here is a B, he echnological opporuniy, which is he sock of poenial ideas lef o s is maximized under he curren paradigm. B becomes exhaused enrepreneurs realize ha he profis from incremenal innovaions are coming o an end and when hey reach he level of expeced profis from he more uncerain drasic innovaions, hey swich over o his aciviy insead. This phenomenon can be described as follows. par from 8 See Olsson (21, 22), on which his general par is based, for a more exended discussion and a se heory approach of he innovaion dynamics. 1
incremenal and drasic innovaions here is he hird componen in he echnological advancemen - poenial innovaions. These ideas ouside, regarded as irrelevan, do no direcly conribue o new knowledge since hey do no have any immediae commercial value. For his new knowledge o be used as normal science i has o be conneced o he old knowledge by a drasic innovaion, D. s menioned above, enrepreneurs urn o drasic innovaion aciviies when here is a small B lef o explore by incremenal innovaions. successful drasic innovaion ha connecs a poenial innovaion wih, reinroduces new echnological opporuniies and a new B can be explored. This is called a echnological paradigm shif and he old anomalies, he poenial innovaions, are now included in he normal science sock. Definiion 1 gives a formal definiion of a echnological paradigm shif. Definiion 1 If B > B 1 hen a echnological paradigm shif has occurred a. fer a echnological paradigm shif a new period of sysemaic incremenal innovaions begins. s menioned above here are wo sources of change in innovaions ha decrease formally described in Equaion (1). B and (ii) drasic innovaions ha increase B : (i) incremenal B. This is B B = B 1 1 δb 1 + D if incremenal innovaion period if drasic innovaion period (1) B B δ B During periods of incremenal echnological process 1 = ( 1 ) = 1 where δ is a measure of he capaciy of sociey o exploi inellecual opporuniies. δ is mainly a funcion of he number of innovaors and he human capial level bu also underlying insiuions such as he educaional sysem, corporae laws and he general aiude owards raionalism and scienific curiosiy. Hence, he sock of knowledge increases wih δ B 1 every period of incremenal innovaions. δ is modeled as a consan and since B is decreasing every period of normal science he enrepreneurs ge less and less oupu from incremenal aciviy. 11
Enrepreneurs form heir decision on he basis of nex periods expeced profis. If he profis from drasic innovaions are higher han he profis from incremenal innovaions, all enrepreneurs shif o drasic innovaion aciviies ha period. 1 = during his period bu B B 1 = D, i.e. he paradigm shif increases he echnological opporuniies wih he random variable incremenal innovaions nex period. E ( D ) = f (, ) 1 δ D, which can be used for describes he expeced echnological success of he drasic innovaion and increases in boh δ and. Hence, he periods of incremenal innovaions are highly predicable while he oucome of a paradigm shif is no. The assumpion ha only one ype of echnological innovaion akes place a he same ime is a simplificaion o reduce he complexiy of he model. Noe ha a period should no be seen as a year bu raher a decade. We will now urn o he ROM o see how he resource socks and heir dynamics are conneced o he waves of echnology, and how his in urn affecs economic growh. We are ineresed in he knowledge and echnological opporuniies relaed o he naural resource secor so, in he res of his paper we refer o hese more specific ses when we menion, B and D. s we will see δ and deerminans for long-erm resource availabiliy and economic growh. D are crucial 3 THE RESOURCE OPPORTUNITY MODEL n imporan difference beween he dynamics of echnology as presened in he general echnological opporuniy model, and he ROM presened here, is as menioned he driving force of echnological developmen. In he previous case i was he scarciy of echnological opporuniies ha creaed incremenal innovaion consrains and forced he economy ino a shif, while i is he scarciy of resources or echnological opporuniies ha creae incremenal innovaion consrains in his model. Noe ha boh hese scarciies are only indirecly driving he echnological changes by heir effecs on he enrepreneurs expeced profis from incremenal versus drasic innovaions. 12
We begin by describing he resource sock dynamics and is connecions o innovaions during he differen periods. We hen look a he changes in innovaion profis, which induce he shif o a new ype of innovaion period. Finally a simple growh funcion is presened. Since an analyical soluion of he model would be inracable we will presen he resul by simulaions in Secion 4. 3.1 Resource Sock Dynamics In he echnological opporuniy model he paradigm shif was induced by a small echnological opporuniy se, eiher by a small dynamics of B, bu in he ROM he shif will be induced B or by a small familiar resource sock, S. We know abou he B bu wha deermine changes in S? During boh incremenal and drasic innovaion periods, economic aciviy in general decreases S, independen of echnological changes ha specific period. The effecs on S from echnological developmen in he naural resource secor are very much dependen on he ype of innovaion period. The dynamics of S during incremenal and drasic innovaion periods are formally presened in Equaion (2). S S = S 1 1 µδb + λd 1 S γ 1 γ ( 1+ ϕ 1 ) ( 1+ ϕ ) 1 if incremenal innovaion period if drasic innovaion period (2) where µ is a parameer represening he effec of incremenal innovaions on he physical resource quaniy, γ is a parameer represening he exracion no conneced o echnological developmen in he naural resource secor, ϕ is a parameer represening he effec of an increased level of knowledge in he previous period on he exracion and λ is a parameer represening he effec of drasic innovaion on he physical resource quaniy. ( ϕ ) 1+ 1 λ is he facor inpu effec, which affecs he sock during boh periods. γ is a parameer deermined by consumpion per capia and he populaion size, bu also by end-use echnology, recycling knowledge, ec. Changes in his parameer will be discussed furher in Secion 5.2. ϕ 1 describes he effec of he 13
level of knowledge in he naural resource secor on he exracion rae. Since all incremenal innovaions add o his knowledge his is he sock effec on he exracion rae because of all previous innovaions. The facor inpu effec is nondecreasing over ime. During periods of incremenal exracion innovaions, he rae of echnical exploiaion of S, µδ B 1, increases wih he amoun of incremenal innovaions δ B 1. Firs, improved exracion echnology decreases he exracion coss per uni of he discovered resources and hereby increases he rae of exracion. Second, discovery echnology may improve wih incremenal echnological developmen, lowering he coss of discovery per uni, and his increases he ransformaion rae of undiscovered resources o discovered, and hence exracable, resources. 9 How much S is affeced depends on he amoun of familiar resources o be exraced or discovered a ( S 1 ), how much of he echnological opporuniies ha are lef o be exploied a ( B 1 ), he enrepreneurs abiliy o urn hese opporuniies ino innovaions (δ ), and he physical resource effec of incremenal innovaions ( µ ). This negaive effec from incremenal innovaion on S is decreasing during he period for wo reasons. Firs, he rae of echnological improvemens decreases since he amoun of echnological opporuniies is decreasing (less idea combinaion possible). Second, he resource sock decreases and he remaining echnological opporuniies can only be applied o a smaller amoun of resources. During periods of paradigm shifs, he effecs on S are differen. s in he model of echnological opporuniies, a drasic innovaion leads o an increase in he echnological opporuniy se of a size D. There are however more effecs from he shif when we look a he ROM. S migh increase for wo reasons; (i) discoveries of more efficien echnology make he already familiar resources las longer, and (ii) earlier poenial resources become familiar resources. λ is a parameer represening he effec on he physical resource quaniy from he drasic innovaion. λ since he drasic innovaion is induced o relax resource scarciy. 9 Wha ype of echnological change ha will occur during he incremenal innovaion period, exracion echnology which decreases S or discovery echnology which keeps S consan, depend on he expeced profis from he wo echnological improvemens. This would creae shor-run waves in he sock of discovered familiar resources bu hese are no modeled in his paper. 14
Summarizing, during he process of incremenal innovaion he familiar resource sock coninuously shrinks. In he long run he familiar resource sock or he echnological opporuniies become exhaused. a cerain poin (deermined by he relaive profis from incremenal and drasic innovaion shown in he nex secion) he criical level of resources is reached. Drasic innovaions, which are now more profiable, increase no only he physical amoun of familiar resources bu also he echnological poenial of he familiar resources. Wih a successful drasic innovaion, hese effecs will ake he naural resource indusry away from he criical level and creae new space for incremenal innovaions. The main reasons o analyze he ineracions beween echnology and naural resources in he presened periodic way are he following; he echnological areas are induced by differen kinds of scarciy, heir success is dependen on differen insiuional arrangemens and hey resul in differen resource availabiliy effecs. Incremenal echnology is induced by sraighforward profi scarciy, i.e. he coninuous hrive for lower coss in a compeiive marke. Profi maximizaion is he indirec reason for drasic innovaions as well bu he direc inducing mechanism is a low 1 S or a low B 1. The success of incremenal exracion or discovery echnology depends mainly on non-revoluionary, enrepreneurial incenives. Drasic echnology, however, is a public good wih free-riding problems and high risks involved. When i comes o he resource availabiliy effecs incremenal echnology decreases S while drasic innovaions increases S. 3.2 Deerminans of he Innovaion Period We will now look closer on he profiabiliy during he wo innovaion periods. The dynamics of hese are imporan since he expeced profis deermine he innovaion direcion during he nex period. Innovaors are assumed o be risk neural and heir planning horizon is only one period ahead. The oal profi ( Π ) of he naural resource indusry is profis from innovaions ( Π ) and profis from he facor inpu ( Π ): Π F = Π I + Π II Π or drasic innovaions F, where ID I I Π is eiher profis from incremenal innovaions F Π. Π = p ( ϕ ) γ where p is he price index of he 1 1 15
resource ha we for now assume is consan (see Secion 5.2 for an exended price effec analysis). Since he profis from he facor inpu are presen independen of he ype innovaion ha period, his erm is no of ineres when i comes o deermining he ype of innovaion aciviy. The deerminan of he innovaion aciviy looks as follows, Π I = II DI ( φ) Π + φπ 1 where II ID ( Π ) > E 1( Π ) II ID ( Π ) E ( Π ) if E 1 φ = (3) 1 if E 1 1 which implies ha only one ype of innovaion will occur a each period. The profis from incremenal innovaions are deermined by variables already known a 1, so he expeced profis equal he acual profis. Profis from incremenal innovaion evolve according o Equaion (4). Π II = pµδ B S (4) 1 1 The incremenal profis are hence a funcion of previous periods resource socks ( S 1 ) on which he innovaion can be applied, previous periods echnological opporuniies ( B 1 ), he capabiliy of enrepreneurs o urn he opporuniies ino incremenal innovaions (δ ), he effec of incremenal innovaions on he resource sock ( µ ) and he price level ( p ). The coss are for simpliciy assumed o be zero since hey are relaively small compared o he coss of drasic innovaions. The profis from drasic innovaions are highly simplified. In realiy he acual profis are uncerain, and migh even be negaive, even hus he expeced profis migh be consan. However, in his model he expeced profis equal acual profis as a simplificaion. This does no change he resuls excep for leaving ou he possibiliy of very high or negaive growh during he emporary drasic innovaion period. The profis from drasic innovaions can herefore be expressed as in Equaion (5). Π ID = Π * (5) 16
where Π * is a consan. In Secion 5.2 we will discuss how his profi level migh be affeced by price changes. To make he dynamics clearer we will look a how he level of Π I is deermined by he naure of innovaion in he previous period, 1. Firs we need o deermine he level of B and S a 1, depending on he naure of innovaion a 2. By subsiuing B 1 and S 1 ino he expressions in Equaion (4) we ge he profis from incremenal innovaion a as presened in Equaion (6). Π I pµδ = pµδ [( 1 δ ) B 2 ][ S 2 µδb 2S 2 γ ( 1+ ϕ 2 )] [ B + D ][ S + λd γ ( 1+ ϕ )] 2 1 2 1 2 if incremena l innovaiona -1 if drasicinnovaiona -1 (6) The profis from exracion a are for sure lower han a -1 if -1 was an incremenal innovaion period. period of drasic innovaions a -1 can give posiive effecs on he profis if he drasic innovaion was successful enough, i.e. if D is large enough o ouweigh he facor inpu. In his las case, we see ha a paradigm shif boh increases he echnological opporuniies, B, and he physical quaniy of resources, S. We can now deermine he breakeven poin beween he differen innovaion periods by equaing heir profis, i.e. Π II = Π his breakeven poin is S * and is described in Equaion (7). ID. The sock of familiar resources a S* = Π * pµδ B 1 (7) The breakeven poin for he familiar resource sock increases wih profis from drasic innovaions ( Π *) bu decreases wih he price of he resource ( p ), he effecs on he quaniy of resources from incremenal innovaions ( µ ), he capabiliy of urning echnological opporuniies o innovaions (δ ) and he level of echnological opporuniies ( B 1 ). 1 Hence, he shif can be induced in a siuaion wih abundan 1 Noe ha he criical level could as well has been expressed in erms of B *. In he echnological opporuniy model B * was a consan bu now his criical level is affeced by he sock of resources, 17
resources if here is a lack of echnological opporuniies. This is he case of a echnological opporuniy induced shif. This shif can be delayed because of a large resource sock, since even small progresses in incremenal echnology give high payoffs wih abundan resources. However, if here is a lo of echnological opporuniies he criical level is low and he shif occurs a a low sock of resources. In his case we have a resource induced shif. This comes ou logically by he assumpion ha profis from incremenal innovaions in he naural resource secor is dependen on how much resources ha are lef on which o apply he new echnology. 3.3 Economic Growh very simplisic income funcion for he naural resource secor is presened in Equaion (8). ln F F ( Π Π ) I y ln y 1 + Π Π 1 = ln y 1 + Π + 1 = (8) where y is he level of income from he naural resource secor. Hence, economic growh is deermined by profis eiher from incremenal innovaions or from drasic innovaions, and from changes in he facor inpu. Economic growh, innovaion cases is described in Equaion (9). g, in he wo g g = g II DI = p = Π ( µδb 1S 1 + γϕ ( 1 2 )) + pγϕ ( ) * 1 2 if if Π Π II II > Π Π DI DI (9) where II g is economic growh under periods of incremenal innovaions and g DI economic growh under periods of drasic innovaions. Noe ha 1 2 = δ B 2 if period -1 was an incremenal innovaion period and if period -1 was an drasic innovaion period. 1 2 = which changes over ime. I is acually he produc ( )* BS ha is he consan criical level in his model. 18
Hence, independen on he innovaion period here migh be an effec on from an increased facor inpu effec due o a higher knowledge sock. During incremenal innovaion periods here is also a posiive bu decreasing effec on from decreases in B and S. This is he exogenous growh model s decreasing reurns picure. However, here is also a posiive effec on g g g from he profi of he drasic innovaion. The sochasic success oucome of he same drasic innovaion deermines he poenial incremenal growh nex period. This increase in growh poenial induced by a small B or S, follows he endogenous growh idea. new period of exogenous growh can now begin. Hence, long run growh is in his sense endogenously driven. 4 RESULTS In his secion we will analyze he resuls from he dynamics presened in he previous secions by simulaions, and discuss he possibiliies of sagnaion. The effecs depend o a large exen on he uncerain oucome of he paradigm shif, i.e. on he success ( D ) from he drasic innovaion period. Figure 2 gives and example of how he dynamics of S migh look like depending on he oucome of and Figure 3 illusraes he cycles of D (see Equaion (2)), g (see Equaion (9)) during he same period. 11 Noice firs ha he drasic innovaion occurs a differen levels of he resource sock, i.e. he value of S * changes depending on he amoun of echnological opporuniies lef a ha momen. This reflecs he fac ha a drasic innovaion is eiher echnological opporuniy induced or resource induced. We will sar by analyzing wha happens during a period of drasic innovaions and laer he implicaion of his on he following period. 11 For all simulaions we have used δ =, 5, µ =, 2, λ = 2, γ = 4, ϕ =, 5, p = 1, Π * = 3, B 6, S 4, 1 and Y 1. = = RND = ( 1 + 5)( 1+ 5δ ) = D where RND is a random number beween and 1. lernaive assumpions will be discussed in Secion 5. = 19
Figure 2: The dynamics of he familiar resource sock and drasic innovaions. 3 25 2 D 15 1 5 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 1 9 8 7 6 5 S 4 3 2 1 D S Period Figure 3: Economic growh in he naural resource secor and drasic innovaions. 3,1 25 2 D 15 1 5,8,6 g,4,2 D g 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2, Period If he drasic innovaion was successful, in he sense ha i conribued enough o he echnological opporuniies B and he resource sock S by a large D, he economy will be saved from he criically low levels of S and a new era of economic growh is saring. Wha acually happens is ha he higher D increases S direcly by λ D, and B lower he criical level S * since S * = Π * pµδ B 1. Boh hese effecs increase he possibiliies for incremenal innovaions (see period 2, 5, 7, 1, 12, 16 and 19 in figure 2 and 3). 12 If however he drasic innovaion only led o a small paradigm shif hen S will only increase slighly and maybe no even exceed he new lower criical level S * (see period 1). In ha case he resource paradigm was no large enough o compensae for he decrease in S from he facor inpu effec, which coninues independen on he innovaion period. 12 During he period of incremenal innovaions S decreases and S * increases, closing he gap of hese kind of innovaions. 2
So, wha happens he period following a drasic innovaion period? The economy will coninue wih a period of incremenal innovaions if S > S *, since incremenal innovaions hen have higher expeced profis. This incremenal innovaion period will normally lead o a new drasic innovaion once he criical level S * is reached again. However if he resource sock is relaively low in he beginning of he period and he exracion rae very high here migh be a case where he incremenal innovaions in combinaion wih he facor inpu deplee he sock and economic growh in he naural resource secor ceases. This will be called he exracion sagnaion case and is discussed furher in Secion 5.1. If however S < S *, here will be a new period of drasic innovaions immediaely afer he preceding one since expeced profis from drasic innovaions sill are higher han profis from incremenal innovaions. Hopefully his new drasic innovaion is more successful so ha a period of incremenal innovaions is profiable again. However, since here is always exracion in erms of he facor inpu, S will coninue o decrease during he drasic innovaion periods and he gap beween he acual level of S and he criical level S * increases. Low expeced success of drasic innovaion will herefore increase he possibiliies of geing rapped in a siuaion where he needed size of he drasic innovaion increases, making i harder and harder o exceed S * again. This process will coninue unil S is exhaused and he growh rae in he naural resource indusry drops o zero This will be called he echnological sagnaion case and is discussed furher in Secion 5.1. The evoluion of above is presened in Figure 4. and Y (see equaion (8)) during he period illusraed increases wih B 1 δ during periods of incremenal innovaion and is consan during drasic innovaion periods. Y increases during boh periods. Remember ha a higher affecs boh he expeced success of he drasic innovaion and he facor inpu. We will herefore have a non-decreasing effec on he probabiliy of drasic innovaion success and he facor inpu over ime. The size of hese ineremporal effecs depends o a large exen on he abiliy o innovae, δ, as we will see in he nex secion. 21
Figure 4: The dynamics of he knowledge sock and he income level. 14, 12, 1, 8, Y 6, 4, 2,, 1 2 3 4 5 6 7 8 9 11112131415161718192 Period 18 16 14 12 1 8 6 4 2 Y 5 NLYSIS 5.1 Effecs of Changes in δ crucial variable is δ, he abiliy o urn echnological opporuniies ino innovaions. ssume ha δ increases for example because of an improved educaional sysem. The direc effec is a higher rae of incremenal innovaions, given he echnological opporuniies. This also means ha he addiive effec on increases. Boh hese effecs will increase he depleion rae of he resource opporuniy sock, S, during incremenal innovaions. Technological opporuniies are exploied in a faser rae, which increases he rae of exracion and discoveries each period, and he higher increased δ is in his sense bad for he resource sock. inensifies he facor inpu effec over ime. Hence, an There are however oher effecs as well. higher δ will, given he size of D and a cerain ime inerval, increase he number of drasic innovaions ( S * is reached more imes), which in urn increases he oal amoun of echnological opporuniies over he oal inerval. higher δ will also increase he probabiliy of a drasic innovaion success ( D ), increasing he amoun of echnological opporuniies each period. The success will also increase over ime since δ also affecs Hence, boh in a sociey wih a low and high δ we could expec a susainable resource sock, as long as he drasic innovaions are fruiful. The only difference is. 22
ha he frequency and ampliude of he cycles wih a high δ is larger han wih a low δ. There is however oher imporan differences in he wo cases. s menioned since he echnological opporuniies add o he knowledge sock while used up, an increased δ will also increase. Moreover, he oal number of innovaions, and hence innovaion profis, will be higher during a given ime inerval and he income from he facor inpu effec increases as increases. Boh hese effecs increase he income level. Hence, in a sociey wih a high δ we could expec a susainable resource sock wih high flucuaions, a large knowledge sock and a high level of income. In a sociey wih a low δ here could also be a susainable resource sock bu wih low flucuaions, a small knowledge sock and a low level of income. The analysis above referred o increases or decreases of δ in a cerain inerval. If we insead urn o he exreme cases we will arrive a he sagnaion scenarios. oo high δ will drive he secor o he exracion sagnaion case, and a oo low δ will drive he resource secor ino he echnological sagnaion case. Wih a very high δ he possibiliy of unsuccessful drasic innovaions becomes negligible, especially over ime since increases dramaically. However, he speed of depleion of S increases also drasically, boh because of he direc effec on incremenal innovaions and he indirec effec on he facor inpu, and hence he probabiliy of exracion sagnaion increases. Figure 5 gives an example of resource exhausion in he shor run because of a high δ. Figure 5: The dynamics of he familiar resource sock in he exracion sagnaion case. δ =, 8. 6 5 4 D 3 2 1 14 12 1 8 S 6 4 2 D S 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 Period 23
s menioned in he previous secion; a sequence of unsuccessful drasic innovaions will also lead o sagnaion. Wih a very low δ he probabiliy of a successful drasic innovaion is also very low, and hence he probabiliy of echnological sagnaion herefore increases. Since no echnological opporuniies are used up during drasic innovaion periods here is no increase in ha oherwise had increased he probabiliy of a larger D, which may have compensaed for he increased gap beween S * and S. Figure 6 gives an example of resource exhausion in he long run because of a low δ. Figure 6: The dynamics of S in he echnological sagnaion case. δ =, 2. 2,5 2 1,5 D 1,5 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 16 17 18 19 2 Period 4 35 3 25 2 S 15 1 5 D S Figure 7 illusraes he effecs of differen δ on he change of he sock of familiar resources, knowledge, and income during 2 periods. 13 very low δ, S is close o zero, i.e. he resource sock has decreased significanly, because of he high probabiliy of echnological sagnaion. If he probable oucome of an unsuccessful drasic innovaion has occurred here will be a new drasic innovaion period and if his period coninues he resource sock is driven owards depleion in he long run by he facor inpu effec. Noe ha since δ is low he depleion rae is also low, which means ha he sock migh no be compleely exhaused afer he 2 periods. Neiher or Y increases much because of resriced amouns echnological opporuniies. Then here is he normal inerval where an increased δ means a larger sock of boh and Y wih a susainable S, alhough wih inensified cycles. very high levels of δ, S approaches zero again reflecing he high probabiliy of resource exhausion 13 Noe ha i is he change in he sock over he whole period ha is examined. Hence, as long as he value is larger hen one, he sock has grown. 24
in he shor run because of oo inensive exracion. Even hough δ is large, which usually means ha and Y increases subsanially, he effec on hese socks declines slighly since he number of periods is lower if an exracion sagnaion case occurs. Figure 7: Effecs of he innovaion abiliy on he growh of he familiar resource sock, he knowledge sock and he income level. 1,2 14 1 12,8 1 8 gs,6 g,gy 6,4 4,2 2,1,2,3,4,5,6,7,8,9 1 Dela gs g gy For each value of d we run en simulaions and he poins in he figure represens he average value from hese. gx = X T X is represening he change in he sock during he hole period, where X =, Y, S, i.e. he sock of knowledge, income or familiar resources. X is he average of he firs hree periods and X T is he average of he hree las periods. 5.2 Effecs of Changes in p In he basic analysis we reaed resource prices as consans. In his secion we will discuss how he resource cycles will be affeced if we assume he naural resource price increases as he resource becomes exhaused, i.e. p S < (Hoelling, 1931). Le us firs look a he effecs on profis from he facor inpu effec. In he basic analysis γ was a consan bu now we assume ha γ p < since efficiency echnology and recycling aciviies on he demand side probably would increase as he price of he resource increases, and hereby decreasing he demand for he resource. Changes in profis as S declines hen looks as follows, Π S F γ > > 1 p γ p = γ + p ( 1 ϕ 1 ) if (1) p S 1 < p γ < 1 1 25
Hence, as S declines he profis from he facor inpu effec will eiher increase or decrease depending on he elasiciy of demand. If we assume ha he demand hrough he facor inpu effec is only slighly affeced by he price, i.e. he percenage decrease in he quaniy of demanded resources will be smaller han he percenage increase in he price, he effec on he profis would be posiive. rgumens supporing his are ha his demand is conneced o he maerial demand buil up in he economy during a long ime and he probabiliy of look-ins is high. Oher argumens in favor of his are ha people are confiden in coninued echnological progress in he resource secor and ha ha here is a myopic behavior leading o a posiive discoun rae (Kraukraemer, 1998). If we insead assume ha he resource efficiency echnologies are highly sensible o price changes, i.e. he percenage decrease in he quaniy of demanded resources will be larger han he percenage increase in he price, he effec on profis from a resource decline. Now we urn o he effecs on innovaions. s S changes he profis from incremenal innovaions changes according o Equaion (11) if we include price effecs. Π S II 1 = p p + S 1 S 1 S 1 p µδ B 1 > if > 1 (11) p S 1 We will conclude ha he profis from incremenal innovaions decline as he resource sock declines since we assume he price elasiciy in his case o be elasic. The exra exracion made possible by he incremenal innovaion is no ye a lock-in since he economy has no ye buil a sociey wih his need. When i comes o he profis from drasic innovaions, which we unil now have reaed as consan, i is possible o assume ha he revenue is posiively affeced DI by a price change, i.e. Π p >. We assume his since he higher he price of he prevailing sock of familiar resources he larger marke shares for he new familiar resources creaed by he drasic innovaion, which migh be refleced in he revenue o he drasic innovaor. Hence, he profis from drasic innovaions will increase as S 1 DI decreases, Π S 1 <, if we include he price effec. 26