Economic Growth & Development: Part 4 Vertical Innovation Models. By Kiminori Matsuyama. Updated on , 11:01:54 AM

Transcription

1 Economic Growh & Developmen: Par 4 Verical Innovaion Models By Kiminori Masuyama Updaed on :0:54 AM Page of 7

2 Inroducion In he previous models R&D develops producs ha are new ie imperfec subsiues of he exising producs The economy grows hrough expanding variey We now sudy models where a newly developed produc is a perfec subsiue of he exising produc The new produc is a beer or improved version of he old one which i is going o replace Producs are verically differeniaed The economy grows hrough ualiy improvemen Each produc has is own life-cycle I firs replaces older vinages bu i will evenually be replaced by a new produc in he fuure Temporary monopoly power Suble welfare implicaion On one hand innovaors do no value he monopoly profi earned by he producer of he old vinage ha is successful innovaion will desroy; his works in he direcion of over-invesmen On he oher hand hey also know ha he reurn o innovaion is only emporary; his works in he direcion of underinvesmen These models may also be inerpreed as models of process innovaions Each innovaion comes up wih a new way of producing he goods a a reduced cos Page 2 of 7

3 Page 3 of 7 ab-euipmen Version: Acemoglu Ch4 Final Good Producion: X Y where 0 d x X v I A coninuum of indusries ν [0] each producing a paricular line of inermediaes Iν: The range of ualiy available for produc line ν a ime : he ualiy index of each produc x ; he unis of he produc used of ualiy in produc line ν a ime Wihin each produc line producs of differen ualiy are perfec subsiues I urns ou ha in euilibrium only he produc of highes ualiy available denoed by is used a each momen We also assume β = /σ and index ualiy such ha ζ β = d x Y 0

4 n Qualiy adder : 0 n ; # of successful innovaions beween 0 and in produc line ν a random variable Wihin each produc line a new innovaion improves he ualiy by facor of λ > R&D and Producion Technologies for Inermediaes: R&D is cumulaive in he sense ha i builds on he experiences of previous R&D Only wih currenly available i is feasible o inven ualiy Invesing Z unis of he final good generae a flow rae of success Poisson Z arrival rae eual o 2 Only new enrans conduc such R&D no by he incumben which currenly produces The incumben has weaker incenives because i would replace is own produc hus desroying he profis ha hey are currenly making Arrow s replacemen effec 3 Once invened one uni of produc of ualiy can be produced wih unis of he final good Assume ζ 2 = ζ 3 = We need some resricion on ζ ζ 2 and ζ 3 o ensure he BGP; ζ β = ζ 2 = ζ 3 = is one such resricion bu no he only one Page 4 of 7

5 Demand for an inermediae: x x p / Monopoly pricing: Each ualiy leader has ualiy advanage of and cos disadvanage of 3 over he previous leader In order o replace he previous / leader is price mus saisfy p x / / / p x This consrain is no binding if λ is sufficienly large he drasic innovaion case such ha In his case he leader ses p x Normalize Then p x x and for all ν & as long as i remains he ualiy leader / Q Y X Q & w Q where growh Q d is he average ualiy across secors which is he engine of 0 Page 5 of 7

6 Value of a Qualiy eader: Even if each produc is forever proeced by paen is value is desroyed when i is replaced by innovaion of a beer produc r V V z V where z Z / is he flow rae a which a successful innovaion akes place in ν a R&D Innovaion: Free enry V / and V / if z 0 Noe: Innovaors make zero profi This means ha when hey innovae across secors hey are indifferen abou how much hey inves in each secor Page 6 of 7

7 Evoluion of Q: suppose z z for all ν a In an inerval of ime z secors experience one innovaion which will increase heir ualiy by λ The measure of secors experiencing more han one innovaion is o Q Q z Q z o Q z Q Since z z z Z z Q Z Q Z No aggregae flucuaion because here are many a coninuum of secors Characerizing BGP: look for BGP along which r r such ha Q / Q Y/ Y C/ C r / 0; From he aggregae resource consrain Y C X Z C Z C z z z > 0 Q Q Q Page 7 of 7

8 Page 8 of 7 Free Enry: V V Valuaion of a Firm: z r z r V Combining hese z r z Q Q g r r 0 g From z Q C Q z C For he exisence we need

9 Noes: Again he scale efficiency and ase parameers have he growh effecs Saring from any Q 0 > 0 here is an euilibrium pah along which he economy grows a he consan rae g Bu I am no convinced ha his is he only euilibrium pah alhough Acemoglu assers ha i is The opimal growh is also a balanced growh pah Unlike he horizonal innovaion models he opimal growh rae can be higher or lower han he growh rae in he euilibrium balanced growh pah Tax Policy on R&D spending: By discouraging R&D his increases he value of an incumben as Since V r z V r r z g z r g Hence i reduces he growh rae Page 9 of 7

10 Aghion-Howi Model: Acemoglu Ch42 Page 0 of 7

11 Innovaion by Boh Incumbens & Enrans: Acemoglu Ch43 So far R&D is done only by enrans This model allows R&D boh by incumbens and enrans The lab-euipmen version Ch4 is modified as follows: A small incremenal improvemen inkering can be done only by incumbens The parameers are also changed so ha incumbens grow in size as hey improve he ualiy of heir producs o obain he firm size dynamics A drasic innovaion is done only by enrans in euilibrium Again incumbens have no incenives o do so in euilibrium due o he Arrow s replacemen effec Final Goods Producion: Index ualiy such ha ζ β = β Y 0 x d Inermediae Inpus Producion: Once invened one uni of produc of ualiy can be 3 3 produced wih = unis of he final good where ζ 3 = 0; ie i is eual o = independen of Page of 7

12 Small ualiy improvemen inkering: R&D available only o incumbens: n Qualiy adder : s where λ > n ; # of successful improvemen beween s and > s in produc line ν a random variable s is he dae a which his incumben ook over his produc line by making a drasic innovaion Tinkering upgrades he curren ualiy level o he nex level Invesing z unis of he final good by he incumben generaes a flow z v success rae Poisson arrival rae eual o z wih ζ 2 = 2 Drasic innovaion Creaive desrucion: R&D pursued only by enrans: For he curren ualiy a successful drasic innovaion leads o Each uni of he final good invesed by an enran in R&D generaes a flow success rae of zˆ / where zˆ is he oal R&D spending by all enrans divided by so ha he flow success rae is zˆ zˆ z is sricly decreasing This capures exernal diminishing reurns which each enran akes as given The negaive exernaliies are mild so ha z z is sricly increasing Assume lim z z 0; lim z 0 z o ensure he inerior soluion Page 2 of 7

13 x Demand for an inermediae: x p Monopoly pricing: Each incumben has a leas ualiy advanage of 3 over he previous leader bu no cos disadvanage because of Hence he / leader mus se is price such ha p x / Assume ha he innovaion by enrans is drasic enough ha / Then he leader ses is monopoly price unconsrained p x / x and for all ν & Y Q X Q and w Q where Q d is again he average ualiy across secors 0 Page 3 of 7

14 Value of an Incumben producing : Keep he noaion simple by V V ; r V V max{ z V V z} zˆ zˆ V z0 R&D by Enrans Creaive Desrucion: zˆ V wih zˆ 0 There is always some R&D by enrans since lim z 0 z R&D by Incumbens Tinkering: V V ; V V if z 0 Evoluion of Q: suppose z z and zˆ zˆ for all ν and Then Q z Q zˆ zˆ Q z zˆ zˆ Q o Q / Q z zˆ zˆ Page 4 of 7

15 Balanced Growh Pah: e us look for he BGP where r r such ha C/ C r / g 0 zˆ zˆ > 0 and z z > 0 V v Posiive R&D by Incumbens V Valuaion of a Firm r V zˆ zv ˆ V r zˆ zˆ ; Free Enry by Enrans z ˆ V r zˆ zˆ r zˆ zˆ zˆ zˆ zˆ g We also have: g Q / Q z zˆ zˆ which deermines z Page 5 of 7

16 Again for he exisence of his BGP we mus verify: Incumbens have an incenive o do R&D r r Effecs of λ & κ: From zˆ zˆ g and z ˆ zˆ zˆ zˆ g ; zˆ zˆ zˆ g More creaive desrucion reduces he growh rae This is because i reduces he incremenal innovaion by he incumbens: zˆ zˆ and g z from g z zˆ zˆ Indeed Acemoglu Proposiion 46 show ha while axaion on R&D spending by incumbens are growh-reducing axaion on R&D spending by enrans are growhenhancing in srong conras wih he baseline model of Ch4 My parial inuiion: Encouraging R&D by he enrans discourages R&D by he incumbens while encouraging R&D by he incumbens will no discourage R&D by he enrans because hey do R&D o become incumbens Acemoglu also discusses he model s implicaion on firm size dynamics Page 6 of 7

17 Sep-By-Sep Innovaion: Acemoglu Ch44 Page 7 of 7