Chapter 5: The Schumpeterian Model

1 Chapter 5: The Schumpeterian Model Philippe AghionUfuk AkcigitPeter HowittMay 21, IntroductionThis Chapter develops an alternative Model of endogenous growth, in which growth is generatedby a random sequence of quality-improving (or vertical ) innovations. The Model grew out ofmodern industrial organization theory1, which portrays innovation as an important dimension ofindustrial competition. This Model isSchumpeterianin that:(i)it is about growth generated byinnovations;(ii)innovations result from entrepreneurial investments that are themselves motivatedby the prospects of monopoly rents; and(iii)new innovations replace old technologies: in otherwords, growth involvescreative the past 25 years,2 Schumpeterian growth theory has developed into an integrated frame-work for understanding not only the macroeconomic structure of growth but also the many mi-croeconomic issues regarding incentives, policies and organizations that interact with growth: whogains and who loses from innovations, and what the net rents from innovation are; these ultimatelydepend on characteristics such as property right protection, competition and openness, education,democracy and so forth and to a di erent extent in countries or sectors at di erent stages of de-velopment.

2 Moreover, the recent years have witnessed a new generation of Schumpeterian growth Very Preliminary. Please do not circulate. In class use only. Please report all typos/mistakes to Tirole (1988).2 The approach was initiated in the fall of 1987 at MIT, where Philippe Aghion was a rst-year assistant professorand Peter Howitt a visiting professor on sabbatical from the University of Western Ontario. During that year theywrote their " Model of growth through creative destruction" (see Section below); which was published as Aghionand Howitt (1992). Parallel attempts at developing Schumpeterian growth models include Segerstrom, Anant andDinopoulos (1990) and Corriveau (1991).1 New Growth EconomicsChapter 5 Aghion et focusing on rm dynamics and reallocation of resources among incumbents and new models are easily estimable using micro rm-level datasets, which also bring the richset of tools from other empirical elds into macroeconomics and endogenous growth.

3 Subsequentchapters will describe each of these applications in great Model of growth with vertical innovations has the natural property that new inventionsmake old technologies or productsobsolete. This obsolescence (or creative destruction ) featurein turn has bothpositiveandnormativeconsequences. On thepositiveside it implies a negativerelationship between current and future research, which results in the existence of a unique steady-state (or balanced growth) equilibrium. On thenormativeside, although current innovations havepositive externalities for future research and development, they also exert a negative externality onincumbent producers. Thisbusiness-stealing e ectin turn introduces the possibility that growthbeexcessiveunder laissez-faire, a possibility that did not arise in the endogenous growth modelssurveyed in the previous this Chapter , we describe the basics of the Schumpeterian framework. In particular, presents a simple discrete time version of the Schumpeterian growth Model .

4 Section thenpresents a continuous time version of the one-sector Schumpeterian Model . Section then extendsthe continuous time Model to multiple A toy (myopic-agents) version of the Schumpeterian modelIn this section we develop a simple version of the Schumpeterian growth Model with discretetime and where individuals and rms live for one period. The basic Model abstracts from capitalaccumulation is a unique nal good in this economy,Yt;which is used forconsumptionCt;intermediate good productionXt;and R&DRt:Therefore the resources constraintof this economy is simplyYt=Ct+Xt+Rt:3 See Klette and Kortum (2004), Lentz and Mortensen (2008), Akcigit and Kerr (2010), and Acemoglu, Akcigit,Bloom and Kerr (2013)4 The implications of introducing human and physical capital accumulation are explored in Chapter preliminary notes, Please do not circulate!2 New Growth EconomicsChapter 5 Aghion et The production technologyThere is a sequence of discrete time periodst= 1;2;:::Each period there is a xed numberLofindividuals, each of whom lives for just that period and is endowed with one unit of labor serviceswhich she supplies inelastically.

5 Her utility depends only on her consumption and she is risk-neutral,so she has the single objective of maximizing expected consume only one good, called the nal good, which is produced by perfectly competi-tive rms using two inputs - labor and a single intermediate product - according to the Cobb-Douglasproduction function:Yt= (AtLt)1 y t( )whereYtis output of the nal good in periodt,Atis a parameter that re ects the productivityof the intermediate input that period andytis the amount of intermediate product used. Thecoe cient lies between zero and one. The economy s entire labor supplyLis used in nal-goodproduction. As in the neoclassical Model , we refer to the productAtLas the economy s e ectivelabor supply. We normalize the price of the nal good to unity without loss of any intermediate product is produced by a monopolist each period, using the nal good as aninput, one for one. Let us denote the amount of nal good used for intermediate-good productionbyXt:Then the production function is simplyyt=Xt:( )That is, for each unit of intermediate product, the monopolist must use one unit of nal good InnovationGrowth results from innovations that raise the productivity parameterAtby improving the qualityof the intermediate product.

6 Each period there is one person (the entrepreneur ) who has anopportunity to attempt an innovation. If she succeeds, the innovation will create a new versionof the intermediate product, which is more productive than previous versions. Let us denote lastVery preliminary notes, Please do not circulate!3 New Growth EconomicsChapter 5 Aghion et s productivity asAt 1:Speci cally, the productivity of the intermediate good in use will gofrom last period s valueAt 1up toAt= At 1, where >1. On the other hand, if she fails thenthere will be no innovation attand, in this case, another randomly chosen monopolist will producethe intermediate good with the old productivity that was used int 1, soAt=At 1. HenceAt=8> <>: At 1if entrepreneur is successful,At 1if entrepreneur fails.( )In order to innovate, the entrepreneur must conduct research, a costly activity that uses the nal good as its only input. As indicated above, research is uncertain, for it may fail to generate anyinnovation.

7 But the more the entrepreneur spends on research the more likely she is to cally, we assume to innovate fromAt 1up toAt= At 1with probabilityzt;one mustspend the amountRt=c(zt)At 1( ) nal good on simplicity, assume a quadratic R&D cost:c(zt) = z2t=2;( )where is a parameter which inversely measures the productivity of the research of eventsNow we can summarize the timing of events in this Model : step 0 Periodtbegins with the initial productivityAt 1which is inherited from the previousperiod (cohort), step 1a randomly chosen entrepreneur invests in R&D by chosing(zt;Rt), step 2innovation (success/failure) is realized, and productivity evolves according to( ); step 3production of the intermediate good(yt)takes place, step 4production of the nal good(Yt)takes place, step 5consumption(Ct)takes place, and preliminary notes, Please do not circulate!4 New Growth EconomicsChapter 5 Aghion et Solving the modelThe Model is solved by backward induction: in each periodt;we rst compute the equilibriumproduction and pro t of a successful innovator; then, we move back one step and compute theoptimal innovation intensity by the rm selected to be an Equilibrium production and pro tsWe start from step 4.

8 The nal good producer maximizes the following objective functionmaxyt; Ltn(AtL)1 y t wtLt ptyto:Therefore we can express the inverse demand for intermediate goodytand labor aspt=@Yt=@yt= (AtL)1 y 1t;( )andwt= (1 )A1 tL y t;where we already imposed thatLt=L:Now we move to step 3. The monopolist with productivityAt, taking the demand( )asgiven, maximizes her expected pro t (At), measured in units of the nal good: (At) = maxyt;ptfptyt ytgsubject to( )whereptis the price of the intermediate product relative to the nal good. That is, her revenue isprice times quantityptytand her cost is her input of nal good, which must equal her outputyt:Substituting the constraint( )into the objective function we get (At) = maxytn (AtLt)1 y t yto;( )Very preliminary notes, Please do not circulate!5 New Growth EconomicsChapter 5 Aghion et implies an equilibrium quantity:5yt= 21 AtL;( )and equilibrium pricept=p=1 :Note that the equilibrium price is above the marginal cost (which is equal to one) since 2(0;1).

9 The additional margin on top of the marginal cost is called the price markup which is governed bythe inverse of :As !1;the markup vanishes the price becomes equal to the marginal , the equilibrium pro t is: (At) = AtL;where (1 ) 1+ 1 ( )that are both proportional to the e ective labor supplyAtL:Substituting from ( ) into the production function ( ), we see that nal output will beproportional toAtL:Yt= 2 1 AtL( )Therefore the growth rate of this economy will be equal to the growth rate of the Equilibrium innovation intensityIn step 2, for any given innovation ratezt;At=8> <>: At 1with probabilityzt,At 1with probability1 now move back to step 1 and consider the innovation investment decision of the entrepreneurwho has the opportunity to innovate at datet:If the entrepreneur attsuccessfully innovates, she5 The rst-order condition for the maximization problem is: 2(AtL)1 y 1t 1 = 0from which ( ) follows directly. Substituting from ( ) into ( ) yields ( ).

10 Very preliminary notes, Please do not circulate!6 New Growth EconomicsChapter 5 Aghion et become the intermediate monopolist that period, because she will be able to produce a betterproduct than anyone else. Otherwise the monopoly will pass to someone else chosen at random,who is able to produce last period s product. Thus the entrepreneur will choose the innovationintensityzttomaxztfzt ( At 1) c(zt)At 1gor equivalently tomaxztfzt L c(zt)g:where we used( ):The rst order condition is simply:c0(zt) = L;which, once combined with( )yields the equilibrium innovation intensityzt=z= L= :( )The following assumption ensures that the innovation ratezis between zero and 1 The parameters of the Model satis es the following condition(1 ) 1+ 1 L < GrowthThe rate of economic growth is the proportional growth rate of nal good (Yt=L), which accordingto equation ( ) is also the proportional growth rate of the productivity parameterAt:gt=At At 1At 1It follows that growth will be random.