ENDOGENOUS GROWTH: Schumpeter s process of creative destruction

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1 Jon Vislie Ocober 20, Lecure noes, ECON 4350 ENDOGENOUS GROWTH: Schumpeer s process of creive desrucion Joseph Schumpeer mde erly conribuions wih permnen influence on our undersnding of he role of R&D; process nd produc innovions, invenions, imiions, produc developmen ec., issues we believe ffec he echnologicl developmen o lrge exen. The modern growh models building on Schumpeer s insigh re highly endogenous in he sense h he growh res emerging from hese models re derived from bsic decision principles. We will presen simple version of Schumpeer s ide of he process of creive desrucion, bsed on he work by Aghion & Howi A Model of Growh Through Creive Desrucion, Economeric 992 (Mrch); pp As in ll models of economic growh following he rdiionl neoclssicl se-up, he objecive hs been o undersnd he echnologicl progress s n imporn engine o economic growh. Some models wihin he re of endogenous economic growh relied hevily on lerning by doing, echnologicl spillovers/exernliies nd incresing reurns (exernl o he firms) due o he non-rivlry of knowledge. During he producion nd insllion of new mchines, one lerns more how o opere hem ec. The incresed knowledge ws seen s n uninended by-produc of cpil ccumulion, nd ws no ken ino ccoun when he gens mde heir invesmen decisions. This lerning by invesing genered n exernliy, s more knowledge ccrues o he gens free of chrge, in public good-fshion. The incresed knowledge will be diffused perfecly in he economy; no propery righ is needed s his civiy is no delibere pr of he decision-mking. (One wy he diffusion cn ke plce is hrough he mobiliy of key personl beween firms wihin he sme indusry.) The AK-model ws n exmple or specil cse where we impose some lerning or echnologicl spillovers. Knowledge is included in humn cpil h is reed s n ordinry cpil objec. We were ble o derive, under some resricive ssumpions, mcro producion funcion wih overll incresing reurns o scle nd incresing mrginl produciviy of cpil, wih growh re h ws incresing over ime. Wihin he re clled Schumpeerin growh focus is more on how knowledge is creed nd used. Focus is on innovion, he incenives o innove nd he implicions which re reled o he process of creive desrucion ; lso found in he puy-cly model of Leif Johnsen wih scrpping nd invesmen in new plns. Schumpeer emphsised he role of compeiion in his process. The model hs

2 2 perhps more obvious policy implicions hn some of he oher models we hve looked upon; specil emphsis on indusril policy or suppor like subsidies o promoe innovion desired speed, nd lso he role of good educionl sysem. One focus is on he relionship beween growh nd compeiion clim hs been h here is n inverse relionship: he more compeiive environmen, innovion would be discourged; hence growh would be reduced. Such n inverse relionship hs been difficul o deec from d. In he simplified version of he creive-desrucion-model we consider, we ll deec such n inverse relionship. In he version of creive desrucion we consider here, indusril innovions improve he quliy of producs: lower-quliy producs re driven ou by higherquliy producs (Greshm s lw which here is heory of obsolescence) nd progress crees gins nd losses, hrough he process of creive desrucion. More effecive producion processes replce old nd less effecive ones, bu h lso implies some desrucion. This cn be envisged s we move up quliy-ldder s progress is mde. Ech new innovion cn be seen s n upwrd sep on he ldder; ech poin in ime we move upwrds is rndom, bu once n innovion kes plce, he upwrds jump in quliy is of some given size. The process cn be illusred s: #3 #2 g # g Innovion # is inroduced poin in ime. This innovion will se he bes sndrd in some producion process, unil he nex innovion occurs, some uncerin fuure poin in ime; 2. (Hence he lengh of he period beween wo innovions 2 is rndom vrible.) Once n innovion is inroduced, he quliy is rised by fixed fcor g. The newes mehod will replce he old one, nd will domine unil he nex innovion kes plce.

3 3 The expeced growh re of he economy depends on he economy-wide moun of reserch, brough ino dynmic model wih forwrd-looking gens. When firm conemples underking some reserch civiy, he pyoff from his civiy is he period over which he resercher cn enjoy being monopolis, by hving monopoly ren in he nex period (enforced by some pen lws). The emporry monopoly period hs rndom durion or lengh, unil he nex innovion occurs, rendering he knowledge underlying he presen monopoly ren obsolee. The likelihood of geing one s own mehod or ide obsolee opr overhrown, depends on reserch effor exered by ouside firms, compeing o become he nex innovor, cpuring he subsequen monopoly ren. This is he process of creive desrucion, mking he expeced presen vlue of he rens negively ffeced by fuure reserch civiy or reserch produciviy (modelled s he Poisson rrivl re of he nex innovion). Aniciping more reserch in he fuure will discourge curren reserch. The incenive or crro o lloce resources on reserch for firm is he expeced monopoly profi h he firm migh cpure. The likelihood from desroying someone s monopoly power, for hen o be in emporry monopoly-posiion, is he driving force inducing or encourging creive civiy like innovions. Consider he he following model: We hve economy wih L persons (skilled lbour), ech person hving one uni of lbour, supplied inelsiclly; hence L is he lbour supply ech poin in ime. This lbour cn be used eiher in reserch or in ordinry mnufcuring. Oupu of some consumpion good is genered by using n inermedie good s he sole inpu. The oupu of his finl good per uni of ime is given by he producion funcion y Ax, where x is he (mos producive) inermedie good used s inpu (neglecing physicl cpil), wih 0. A is prmeer indicing he produciviy or quliy of he inermedie inpu. We hve lbour mrke for skilled lbour. In producing he inermedie good, only lbour is used, in n moun m, in one-o-one-mnner; i.e. xhm ( ) m; liner producion echnology. The moun of people enering reserch is n; hence we hve: ( L) L m n i) The R&D-sge R&D is modelled s process of improving he quliy or produciviy of he inermedie inpu. Through innovive civiies here is flow of new invenions mnifesed s beer-quliy vrieies of he inermedie good used s inpu h will replce older vrieies. This process is modelled s incresing he echnologicl prmeer A in he producion funcion by he consn fcor g from one

4 4 innovion o he nex. Ech innovion will herefore improve he quliy of he inermedie inpu from A o ga, wih g > mesuring he size of he innovion. Ech resercher llocing one uni of lbour o R&D will ener loery ( sochsic R&D-process). Suppose h during shor inervl of imed, eiher one or no innovion will occur. Ech innovion will give n increse in A equl o g. Wih men rrivl re 0, which cn be seen s he probbiliy per uni of ime of hving n innovion, he probbiliy h n innovion will occur in he shor ime inervl of lengh d, is d. Hence he probbiliy h n innovion will no occur is d. (As n pproximion: Le Z denoe he number of innovions king plce during some fixed ime inervl, disribued ccording o Poisson, wih ( d) d 2 Pr ( Z on 0, d) e d ( d 2 ( d)...) d.)! When n persons lloce heir lbour ime on reserch, ech hving he sme rrivl re, hen he probbiliy h n innovion occurs in he ime inervl of lengh d, will be nd. We cn consider s mesure of he produciviy of he reserch echnology. Wih probbiliy nd here will be n innovion or new inermedie inpu, mesured by jump g during some shor inervl of ime. Afer innovion #, he inpu is x, wih higher produciviy hn he previous one; A ga. m x y Ax L n g wih prob. nd during, d The innovion mens h one discovers n improved version (or higher quliy) of he inermedie inpu. We ssume h ech successful innovor hs imelimied monopoly power; lsing unil he nex innovion occurs, by some oher firm. (This period migh be considered s he period over which one hs n effecive pen unil new innovion kes over.) A remrk on he sochsic reserch process Suppose h some rndom even Z is governed by Poisson process, wih known rrivl re u 0. This mens h during some given ime period, of lengh T, he

5 5 number of innovions h is expeced o ke plce per uni of ime is u. We know z ( ut) ut h Pr( Z z) e, wih EZ ut VrZ. Then we know lso h he z! lengh of ime you hve o wi for Z o occur will be exponenilly disribued wih prmeer u which is hen he probbiliy per uni of ime h he even will occur or he flow probbiliy of he even. Le be he rndom de of innovion. The probbiliy for he innovion o occur before T is hen given by P( T): FT ( ). Then for he innovion no o occur r prior o or before T+d consiss of wo disjoin nd independen oucomes: no innovion in [0,T] nd no innovion in [T,T+d]. The ls probbiliy is ud, becuse ud is he probbiliy for he even o occur in he smll inervl of lengh d. If QT ( ) FT ( ) is he probbiliy for no innovion before T, we hve, when muliplying he wo probbiliies: QT ( d) QT ( ) QT ( d) QT ( ) ( ud) uqt ( ). d Le d 0, nd ssume differenibiliy, hen we ge: Q( T) d Q( T) Q( T) uqt ( ) uuse. (ln QT ( )), o give: QT ( ) d QT ( ) c ut ln QT ( ) cut QT ( ) e. Becuse Q(0), we hve QT ( ) e u. Hence: The u probbiliy for he even o occur before is: F( ) Q( ) e, wih u probbiliy densiy F ( ) f ( ) ue. The wiing ime in Poisson process wih prmeer u is exponenilly disribued, wih expeced wiing ime s given by u. *** A some sge during he process of innovions, when is he number of innovions h so fr hve been relized, he moun of reserch underken by n innovor, mus obey some equilibrium, free enry or rbirge condiion. The expeced gin from going for innovion #+ for some person is V w, where w is he wge under hese circumsnces, fer innovion # hs occurred. (This is he wge h is pid in he mnufcuring indusry fer innovion # hs occurred.) In equilibrium we herefore hve: ( A) w V A he mrgin, person is indifferen beween llocing his lbour beween he wo civiies. The reurn from working in he mnufcuring secor, producing he inermedie good for he finl-good-secor, mus in equilibrium be equl o he

6 6 expeced reurn from doing reserch, which, wih some probbiliy, mkes me monopolis for some uncerin period of ime. Hence, he curren wge hs o be blnced gins he discouned expeced reurn from using lbour in reserch o become he innovor #(+). In equilibrium his wge mus be equl o he discouned expeced mrginl gin from obining he prize (or monopoly ren) V ; muliplied by which is he probbiliy per uni of ime for successful innovion. Ech innovion crees monopoly for he innovor when selling x o he finl good secor, s emporry monopolis. An innovor blnces his or her mrginl reurn in he wo compeing civiies. The wo opions mus hve equl expeced mrginl reurn. If I win he rce, I will be monopolis unil new innovion desroys my monopoly posiion. How cn we clcule he vlue of innovion #+? This depends on he lengh of he period over which I cn rep he profi flow from his innovion. This lengh is rndom nd ffeced by he ouside (or subsequen) firms rying o become he new innovor: For fixed monopoly period 0,, nd some ime-invrin discoun re r, he presen discouned vlue of he profi flows is given by r r e v ( ) e d. r 0 The poin in ime when new innovion kes plce,, is no fixed bu rndom n vrible, being exponenilly disribued ( n ) ; i.e. wih densiyn e. (To ny fesible oucome of he lengh of he monopoly period; (0, ), we ch posiive densiy, which is depending on he subsequen choice of reserch effor by ouside firms. Fuure innovions underken by ouside firms will desroy my monopoly posiion.) We hen hve when V is he expeced presen discouned vlue of being innovor #(+), hving pen so s o opere s emporry monopolis:

7 7 n ( ) ( ) r n r n V v n e d e e d 0 0 n n ( rn) e e d r n 0 0 n n n 0 0 n n ( rn) e e r n r n 0 0 r n r r n r r n r r r n r n From which we ge: n V ( r n ) V rv n V V r r (*) (**) The second pr, (*), sys h ech poin in ime, s long s he pen is cive, he expeced reurn of hving he pen (like reurn on some sse or cpil objec) is equl he curren monopoly profi flow, minus he expeced cpil loss from being overhrown by new innovor. The new innovion occurs wih probbiliy n ; or wih probbiliy n he innovor #(+) will be replced by subsequen innovion; #(+2); so n V is he expeced cpil loss per uni ime of being overhrown by #(+2). The erm (**) shows h he presen expeced vlue of he monopoly posiion is he nnuiy of n infinie srem of he monopoly profi minus he nnuiy of he cpil loss due o new innovion. The equliy V shows he expeced presen vlue of hving r n monopoly posiion, where he discoun fcor is being reduced due o r n compeiion from subsequen innovions. The fuure ges lower weigh. The denominor in cn be inerpreed s n obsolescence-djused ineres r n re, nd will show he impc of creive desrucion. The more reserch is expeced o follow he innovion #(+), he shorer is he likely durion of he monopoly period, which will reduce he vlue of innovion. The creive desrucion elemen is cpured by replcing n old monopolis by new one, desroying he ren h moived he previous innovor or previous creion.

8 8 ii) The sge fer innovion #. The monopolis wih innovion #, will sell he inpu x o he compeiive finlgood or consumpion good indusry s monopolis, fcing demnd funcion derived from he decision-mking problem in he compeiive indusry. We hen hve: The finl good secor is compeiive; wih price se equl o one. If pying p per uni of x used s inpu in he mnufcuring secor, where p is mesured in unis of he finl good, hey will choose x so s o: Mx Ax px; wih firs-order condiion Ax p, which is he inverse demnd funcion fcing he supplier of he inermedie good, s given by vlue mrginl produciviy. The supplier of his inermedie good or inpu is he emprry or preliminry winner of he innovion cones; wih rndom lengh of he monopoly period, selling his or her oupu used s inpu in he producion of he finl good, s monopolis. If wge per uni of lbour fer innovion #, is w, hen innovor #, wih emporry monopoly, will solve he following problem: He or she cn sell he innovion or inermedie good s monopolis, price p( x) Ax s long s he monopoly posiion is no overhrown. When using m x, we hve : Mx x p( x) xwxax wx. 2 2 We hen ge: w Ax p w x Ax 2 2 x Arg mx x Ax wx : w w where : is he produciviydjused wge, nd wih wx. Boh x nd will be declining in. A A 2 We hve x : X( ) dx, wih 0 d. Le A X( ). We inser nd ge: 2 2 ( ) A( ) A( ) : A ( ) d. We esily see h 0, d where X( ) is lbour used in he producion of he inermedie good s funcion of he produciviy-djused wge.

9 9 iii) Equilibrium We now hve wo equions h chrcerise he equilibrium, when using h A ga : ( L) L X ( ) n w A ( ) g( ) ( A) w : r n A A r n A r n r n Consider sedy-se or blnced growh equilibrium; wih SS ( A) g X( ) g ( ) r nˆ r nˆ SS ( L) L nˆx( ) X( ) L nˆ nd n nˆ : ( A ) SS ( L ) SS ˆn L n Then: r g ( L nˆ ) g L SS ( A) nˆ nglr (,,,, ) 0 r nˆ g Assume h he higher is ˆn, he higher is he expeced growh re in his economy when growh iself is sochsic. r g L From nˆ nglr (,,,, ), we cn derive relion beween expeced g growh nd he prmeers of he model:

10 0 A higher discoun re r will reduce growh. The vlue of fuure monopoly ren will hen go down; hence he incenive o do reserch is wekened. A higher pool of skilled lbour will increse expeced growh, s he wge or opporuniy cos of doing reserch will go down; nd lso he fuure srem of profi will be higher. This clls for insiuionl rrngemens wih good educionl sysem providing sound knowledge bou growh-promoing subjecs; like mhemics, physics, chemisry, biology, medicine. A more producive reserch echnology (higher ) will hve posiive impc on expeced growh. A higher will increse he role of creive desrucion ( lower vlue of he pen), which, ce. pr., should hve negive impc on expeced growh. However, in in opposie direcion, here is he impc on he mrginl cos of producion. The ler effec domines. An increse in he size of he innovion (g goes up), will increse he nex period s monopoly profi; sronger incenive o do reserch. (We hve r g r nˆ L g( ) L L will be incresing in g.) Require good g g( ) pen sysem nd inellecul propery righs. The bsolue vlue of elsiciy of demnd in he finl good secor using he inermedie good sold by he monopolis, is Elx : p. If higher compeiion mens more elsic demnd curve fcing he monopolis, hen more compeiive environmen should be ssocied wih pproching one. p We hve from p( x) Ax A, h x ( ) ( ), so h A p px ( A) p kp kp. The closer is one, he more elsic is demnd, or he higher is he degree of compeiion. ( A( ) x becomes smller s goes o one.) Produc mrke compeiion is bd for R&D, nd hence for growh. More produc mrke compeiion will reduce fuure monopoly rens h cn be reped by successful innovor; hence he incenive o underke R&D is wekened.