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Endogenous Technological ChangePaul M. RomerThe Journal of Political Economy, Vol. 98, No. 5, Part 2: The Problem of Development: AConference of the Institute for the Study of Free Enterprise Systems. (Oct., 1990), pp. S71-S102.Stable URL:http://links.jstor.org/sici?sici B2-8The Journal of Political Economy is currently published by The University of Chicago Press.Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtainedprior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content inthe JSTOR archive only for your personal, non-commercial use.Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained athttp://www.jstor.org/journals/ucpress.html.Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academicjournals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers,and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community takeadvantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org.http://www.jstor.orgWed Jan 9 14:30:43 2008

Endogenous Technological ChangePaul M. RomerUnluerszty of Ch cagoGrowth in this model is driven by technological change that arisesfrom intentional investment decisions made by profit-maximizingagents. T h e distinguishing feature of the technology as an input isthat it is neither a conventional good nor a public good; it is a nonrival, partially excludable good. Because of the nonconvexity introduced by a nonrival good, price-taking competition cannot besupported. Instead, the equilibrium is one with monopolistic competition. The main conclusions are that the stock of human capitaldetermines the rate of growth, that too little human capital is devoted to research in equilibrium, that integration into world marketswill increase growth rates, and that having a large population is notsufficient to generate growth.I. IntroductionOutput per hour worked in the United States today is 10 times asvaluable as output per hour worked 100 years ago (Maddison 1982).In the 1950s, economists attributed almost all the change in outputper hour worked to technological change (Abramovitz 1956; Kendrick 1956; Solow 1957). Subsequent analysis raised our estimates ofPrepared for the conference "The Problem of Economic Development: ExploringEconomic Development through Free Enterprise," held at the State University of NewYork at Buffalo, May 1988. I have benefited from the comments of many seminar andconference participants and two discussants (Rob Vishny, Buffalo, May 1988, and DaleJorgenson, National Bureau of Economic Research Economic Fluctuations meeting,July 1988). Discussions with Gary Becker, Karl Shell, Robert Lucas, Gene Grossman,and Elhanan Helpman were especially helpfill. Research assistance was provided byDanyang Xie. T h e original work was supported by National Science Foundation grantSES-8618325. It was revised while I was a visitor at the Center for Advanced Study inthe Behavioral Sciences and supported by NSF grant BNS87-00864.[ J u u n i n l ?/ P o / i l i , n i Econuniv, 1990, \ol. 18. no, 5 , pt. 21Q 1990 hr l'hr L'nlverslty of Chic,igo. All lights reseried 0022-3808190198O5-0 115 11. 0

S72JOURNAL OF POLITICAL ECONOMYthe importance of increases in the effective labor force and the effective stock of capital in generating growth in output per worker (Jorgenson, Gollop, and Fraumeni 1987), but technological change hassurely been important as well. The raw materials that we use have notchanged, but as a result of trial and error, experimentation, refinement, and scientific investigation, the instructions that we follow forcombining raw materials have become vastly more sophisticated. Onehundred years ago, all we could do to get visual stimulation from ironoxide was to use it as a pigment. Now we put it on plastic tape and useit to make videocassette recordings.The argument presented in this paper is based on three premises.The first is that technological change-improvement in the instructions for mixing together raw materials-lies at the heart of economicgrowth. As a result, the model presented here resembles the Solow(1956) model with technological change. Technological change provides the incentive for continued capital accumulation, and together,capital accumulation and technological change account for much ofthe increase in output per hour worked.The second premise is that technological change arises in large partbecause of intentional actions taken by people who respond to marketincentives. Thus the model is one of endogenous rather than exogenous technological change. This does not mean that everyone whocontributes to technological change is motivated by market incentives.An academic scientist who is supported by government grants may betotally insulated from them. The premise here is that market incentives nonetheless play an essential role in the process whereby newknowledge is translated into goods with practical value. Our initialunderstanding of electromagnetism arose from research conductedin academic institutions, but magnetic tape and home videocassetterecorders resulted from attempts by private firms to earn a profit.T h e third and most fundamental premise is that instructions forworking with raw materials are inherently different from other economic goods. Once the cost of creating a new set of instructions hasbeen incurred, the instructions can be used over and over again at noadditional cost. Developing new and better instructions is equivalentto incurring a fixed cost. This property is taken to be the definingcharacteristic of technology.Most models of aggregate growth, even those with spillovers orexternal effects, rely on price-taking behavior. But once these threepremises are granted, it follows directly that an equilibrium with pricetaking cannot be supported. Section I1 of the paper starts by showingwhy this is so. It also indicates which of the premises is dropped ingrowth models that do depend on price-taking behavior. The argument in this section is fundamental to the motivation for the particu-

TECHNOLOGICAL CHANGES73lar model of monopolistic competition that follows, but it is moregeneral than the model itself.In the specific model outlined in Section 111, a firm incurs fixeddesign or research and development costs when it creates a new good.It recovers those costs by selling the new good for a price that ishigher than its constant cost of production. Since there is free entryinto this activity, firms earn zero profit in a present value sense.The conclusions of the model follow directly from this specification.On the basis of results from the static theory of trade with differentiated goods (see, e.g., Helpman and Krugman 1985), one shouldexpect that fixed costs lead to gains from increases in the size of themarket and therefore to gains from trade between different countries. Perhaps the most interesting feature of the equilibrium calculated for the model constructed here is that increases in the size ofthe market have effects not only on the level of income and welfarebut also on the rate of growth. Larger markets induce more researchand faster growth.The analysis also suggests why population is not the right measureof market size and why the presence of a large domestic market incountries such as China or India is not a substitute for trade with therest of the world. T h e growth rate is increasing in the stock of humancapital, but it does not depend on the total size of the labor force orthe population. In a limiting case that may be relevant for historicalanalysis and for the poorest countries today, if the stock of humancapital is too low, growth may not take place at all.These implications of the model are taken up briefly in the finalsections of the paper. Section I11 describes the functional forms thatare used to describe the preferences and the technology for themodel. It defines an equilibrium that allows for both monopolisticcompetition and external effects arising from knowledge spillovers.Section IV offers a brief intuitive description of a balanced growthequilibrium for the model. Section V formally characterizes the equilibrium. Section VI describes the welfare properties of the equilibrium. Section VII discusses the connection implied by the modelbetween trade, research, and growth. Algebraic details of the derivations are placed in the Appendix.11. Rivalry, Excludability, and NonconvexitiesEconomists studying public finance have identified two fundamentalattributes of any economic good: the degree to which it is rivalrousand the degree to which it is excludable (Cornes and Sandler 1986).Rivalry is a purely technological attribute. A purely rival good has theproperty that its use by one firm or person precludes its use by an-

S74JOURNAL OF POLITICAL ECONOMYother; a purely nonrival good has the property that its use by one firmor person in no way limits its use by another. Excludability is a function of both the technology and the legal system. A good is excludableif the owner can prevent others from using it. A good such as the codefor a computer program can be made excludable by means of a legalsystem that prohibits copying or by means of encryption and copyprotection schemes.Conventional economic goods are both rivalrous and excludable.They are privately provided and can be traded in competitive markets. By definition, public goods are both nonrival and nonexcludable. Because they are nonexcludable, they cannot be privately provided or traded in markets. Public goods can be introduced into amodel of price-taking behavior by assuming the existence of a government that can levy taxes. Basic scientific research is an example of apublic good that could be provided in this way and that is relevant formodeling growth.Rivalry and excludability are closely linked because most rivalgoods are excludable. (A parking space in a shopping center parkinglot is an example of a good that is effectively nonexcludable becausethe cost of enforcing excludability is too high relative to the value ofthe good.) The interesting case for growth theory is the set of goodsthat are nonrival yet excludable. The third premise cited in the Introduction implies that technology is a nonrival input. The secondpremise implies that technological change takes place because of theactions of self-interested individuals, so improvements in the technology must confer benefits that are at least partially excludable. Thefirst premise therefore implies that growth is driven fundamentally bythe accumulation of a partially excludable, nonrival input.T o evaluate these claims, it helps to have a specific case in mind.The example of a nonrival input used in what follows is a design for anew good. T h e vast majority of designs result from the research anddevelopment activities of private, profit-maximizing firms. A designis, nonetheless, nonrival. Once the design is created, it can be used asoften as desired, in as many productive activities as desired.In this sense, a design differs in a crucial way from a piece ofhuman capital such as the ability to add. T h e design is nonrival butthe ability to add is not. The difference arises because the ability toadd is inherently tied to a physical object (a human body) whereas thedesign is not.' T h e ability to add is rivalrous because the person who'T h e original version of this paper used the terms "embodied" and "disembodied" torefer to the difference between an intangible such as the ability to add, which is tied to aspecific person, and an intangible such as a design, which is not. This choice of terminology is not used in this revision because embodiment has another meaning ingrowth theory and because the notion of rivalry already exists in the public financeliterature.

TECHNOLOGICAL CHANGES75possesses this ability cannot be in more than one place at the sametime; nor can this person solve many problems at once. As notedabove, rivalry leads to a presumption that human capital is also excludable. Thus human capital can be privately provided and traded incompetitive markets. In contrast, the design is nonrival because it isindependent of any physical object. It can be copied and used in asmany different activities as desired.Like any scientific concept, nonrivalry is an idealization. It is sometimes observed that a design cannot be a nonrival good because it isitself tied to the physical piece of paper or the physical computer diskon which it is stored. What is unambiguously true about a design isthat the cost of replicating it with a drafter, a photocopier, or a diskdrive is trivial compared to the cost of creating the design in the firstplace. This is not true of the ability to add. Training the secondperson to add is as costly as training the first. For simplicity, thearguments here will treat designs as idealized goods that are not tiedto any physical good and can be costlessly replicated, but nothinghinges on whether this is literally true or merely close to being true.Nonrivalry has two important implications for the theory ofgrowth. First, nonrival goods can be accumulated without bound on aper capita basis, whereas a piece of human capital such as the ability toadd cannot. Each person has only a finite number of years that can bespent acquiring skills. When this person dies, the skills are lost, butany nonrival good that this person produces-a scientific law; a principle of mechanical, electrical, or chemical engineering; a mathematical result; software; a patent; a mechanical drawing; or a blueprintlives on after the person is gone. Second, treating knowledge as anonrival good makes it possible to talk sensibly about knowledge spillovers, that is, incomplete excludability. These two features of knowledge-unbounded growth and incomplete appropriability-are features that are generally recognized as being relevant for the theory ofgrowth. What thinking about nonrivalry shows is that these featuresare inextricably linked to nonconvexities.If a nonrival input has productive value, then output cannot be aconstant-returns-to-scale function of all its inputs taken together. Thestandard replication argument used to justify homogeneity of degreeone does not apply because it is not necessary to replicate nonrivalinputs. Suppose that a firm can invest 10,000 hours of engineeringtime to produce a design for a 20-megabyte hard disk drive for computers. Suppose that it can produce a total-of 2 trillion megabytes ofstorage per year (i.e., 100,000 units of the drive) if it builds a 10million factory and hires 100 workers. If it merely replicates the rivalinputs-the factory and the workers-it can double its output to 4trillion megabytes of storage per year.Suppose that the firm could have invested 20,000 hours of en-

S76JOURNAL OF POLITICAL ECOXOMYgineering time in the design work instead of 10,000 hours and, bydoing so, could have designed a 30-megabyte hard disk drive thatcould be manufactured with the same factory and workers. When thefirm doubles all its inputs, it uses a 20,000-hour design, two factories,and 200 workers and produces 6 trillion megabytes of storage peryear, three times the original output.More formally, if F(A, X) represents a production process thatdepends on rival inputs X and nonrival inputs A , then by a replicationargument, it follows that F(A, AX) AF(A, X). This replication argument assumes that X is an exhaustive list of the rival inputs. Becausethe focus here is on national economies, the argument neglects integer problems that may be relevant for a small market that gets stuckbetween n and n1 plants. The fact that it may not be possible toactually replicate all the inputs in the list X has no bearing on thisargument about the properties of F(.).If A is productive as well, it follows that F cannot be a concaveproduction function because F(AA, AX) AF(A, X). Because of theproperties of homogeneous functions, it also follows that a firm withthese kinds of production possibilities could not survive as a pricetaker. If disk drives sold for marginal cost, annual revenue for thefirm would just equal interest payments on the capital and wage payments to workers. More generally, since F(A, X) X . (dF/dX)(A,X),it follows that aF (A, X) X ' dF (A,X)F(A, X) A . dAaxIf all inputs were paid their value marginal product, the firm wouldsuffer losses.This point has been made many times before (Schumpeter 1942;Arrow 19626; Shell 1966, 1967, 1973; Nordhaus 1969; Wilson 1975).Previous growth models have avoided this difficulty in various ways.Solow (1956) treats A as an exogenously provided public input (i.e.,an input that is both nonexcludable and nonrival). Shell (1966, 1967)treats it as a public input that is provided by the government. In eachcase, the factor A receives no compensation, and every individualfirm is assumed to be free to exploit the entire stock of A. Thesemodels are consistent with the first premise, that technological changedrives growth, and the third, that the technology is a nonrival good,but they are inconsistent with the second premise. They both deny therole that private, maximizing behavior plays in generating technological change.In an attempt to make the evolution of A responsive to marketincentives, Arrow ( 1 9 6 2 assumed)that an increase in K necessarilyleads to an equiproportionate increase in knowledge through "learn-

TECHNOLOGICAL CHANGEs77ing by doing," but he still treats knowledge as a public good. Lucas(1988) assumed in effect that it is production of human capital ratherthan physical capital that generates this nonrival, nonexcludablegood. Both of these papers make the production of a nonrival, nonexcludable good an unintentional side effect of the production of aconventional good.The learning-by-doing formulation has the advantage that it makesthe rate of accumulation of nonrival knowledge endogenous, but it isunsatisfactory because it takes the strict proportionality betweenknowledge and physical capital or knowledge and education as anunexplained and exogenously given feature of the technology. It preserves the public-good character of knowledge assumed by Solow andShell but makes it a public good that is privately provided as a sideeffect. Like the other public-good formulations, it rules out the possibility that firms make intentional investments in research and development.This formulation has the additional difficulty that it is not robust.The nonrival input produced through learning by doing must becompletely nonexcludable. If it were even partially excludable, Dasgupta and Stiglitz (1988) show that decentralized equilibrium withmany firms would not be sustainable.In a partial equilibrium model of an industry in which firms faceupward-sloping cost curves, Shell (1973) proposed a model with pricetaking in which expenditure on research was compensated out ofquasi rents. Griliches (1979), again in an industry setting, made thisformulation more explicit. He assumed that the production functiontakes the form F(Anr,AE, X), where AE represents an excludable partof the benefits of research and development and Ah, represents thenonexcludable part. Since AE is excludable, it is accumulated intentionally. The nonexcludable part A,,, is created as a side effect ofproducing AE. He also assumed that the function F(.) is homogeneousof degree one in X a

Endogenous Technological Change Paul M. Romer Unluerszty of Ch cago Growth in this model is driven by technological change that arises from intentional investment decisions made by profit-maximizing agents. The distinguishing feature of the technology as an input is that it is neither a conventional good nor a public good; it is a non-

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