Partha Dasgupta * 
The Welfare Economics of Knowledge Production
Oxford Review of Economic Policy, 4 (4,) 1988
HHC: Index and page numbers added
Carl Christian von Weizsäcker begins his excellent book on entry barriers by classifying economic activity into three classes, or levels as he calls them: the exchange of goods, the production of material commodities, and the creation of knowledge. (See von Weizsäcker, 1980.) He is prompted into developing this classification, rather than some other, because these three levels are on the whole easy to distinguish, and because they are in an order of increasing distance from the consumption of material goods and services. Von Weizsäcker in fact proceeds to demonstrate in his book that this distance has a marked influence on the organization of the economic activity in question
Von Weizsäcker’s classification is time honoured. But until recently much of the focus of analytical economics had been on the first two levels: those of exchange and production of material goods and services. The analytical economics of knowledge had been on the whole an impoverished sibling. All this has changed over the past decade or so, and the microeconomic analysis of technological change is an active field of research. But as in all other types of enquiry it would appear rapidly to have acquired an internal history. A number of the early papers in the field (e.g. Kamien and Schwartz, 1978; Levin, 1978; Loury, 1979; Dasgupta and Stiglitz, 1980a, b) analysed the characteristics of strategic behaviour on the part of profit-maximizing firms when they compete not only in the production of goods and services, but also in the development of new products and new ways of manufacturing old products; what one would want to call technological competition. Now, for reasons that are well understood today, the theory of perfect competition is of no use here.  Even if technological competition were fierce, the resulting industrial structure would be oligopolistic, as the recent literature on these matters has made clear. Moreover, in order to understand the structure of industries we must trace back to the possibilities facing inventors and developers, to their underlying motivation, and to the background
* University of Cambridge
1. Over the years I have gained much from discussions on the matters covered in this essay with Paul David, Eric Maskin, and Joseph Stiglitz, with each of whom I have collaborated on several occasions. The material in Section H is based largely on Dasgupta and David (1988), which also develops a thesis concerning the historical origins of science and technology as social institutions In writing this essay I have also benefited greatly from the instructions that John Vickers has given me
2. See Schumpeter (1976) for an early elaboration of this viewpoint.
incentive structure. The recent literature on the microeconomics of technological change has clarified a number of these issues. Nevertheless, it is unfortunate that the literature has been dominated by matters concerning patent races, at the expense of pretty much all else.
In this essay I want to redress the balance, even if only by tiny bit, and talk of other matters. Specifically I want to study the sorts of social institutions which can, at least in principle, sustain an efficient leve1 of inventive and innovative activity. Plainly, the characteristics of such institutions will depend upon the nature of the produced commodity in question, namely knowledge. It is best then to start with that
Knowledge is not a homogeneous commodity. There are different kinds of knowledge and no obvious natural units in which they can be measured. Indeed, each piece of knowledge is a separate commodity. It is indivisible, in the sense that once a certain piece of knowledge has been acquired there is no value to acquiring it again: the wheel does not need to be invented twice. The same piece of information call be used over and over again, at no cost (Marx, 1970; Arrow, 1962). For my purpose here it does not matter whether we think that certain kinds of knowledge possess intrinsic worth in the Aristotelian sense, or whether we value knowledge solely in functional terms.  What is of critical importance is that knowledge and more specifically information, can be jointly consumed and used by as many as care to. Thus, if one person gives another person a piece of information this does not reduce the amount of information held by the first possessor, although of course the benefit to each typically will depend upon whether and in what manner the other makes use of this piece of knowledge. In short, knowledge has the hallmark of a public good, a durable public good.
In what follows I shall for simplicity of exposition assume that the cost at transmitting knowledge is negligible when compared to its production cost. This is not as wild an assumption as it might appear at first blush, especially today, because transmission costs are to be distinguished from the costs incurred in educating people to interpret the knowledge and to make use of it. This latter is what one would call the cost of education of learning, of absorption, of processing and so forth. Plainly the greater the number of people who can make use of transmitted knowledge the greater is the social value of that knowledge.  Plainly also, not all knowledge can be communicated, especially problem-solving skills, more generally knowledge that is acquired through practice on the part of the researcher. I am not considering this kind of knowledge here for they are embodied in the researcher. We would call such knowledge the researcher’s skill or acquired ability. Models of learning (by doing) with the incomplete spillover capture this kind of person-specific knowledge. (See Dasgupta and Stightz 1988)
Given this, one seeks to identify resource allocation mechanisms, more grandly socio-economic institutions, which can in principle produce and allocate knowledge in an efficient manner. The qualification should be noted. As in all theories of institutional design, I am here interested in a thought-experiment. So I assume that it is possible costlessly to design and establish an entire socio-economic institution, supporting it with a background of attendant rules, norms, rights, and backing them with the force of the
3. In the context of education policy such a distinction matters greatly, and the education literature has consistently displayed a tension between these two aspects, most especially in debates over the choice of course curricula. This tension has on occasion been diffused, as in the writings of John Dewey, who in his philosophy tried to fuse the two by appealing to a sort of Aristotelian view of the development of a person. Nevertheless, the tension is a real one. But for the most part this distinction does not affect the arguments in this essay.
4. Throughout, I am thinking of knowledge as a ‘good’, unlike pollution. Thus I am ignoring the kinds of knowledge that are used for purposes of waging war. This would involve a different set of considerations regarding public policy.
law. As it happens, modern resource-allocation theory suggests that there are three possible institutions. As it also happens there are analogues of each in the world as we know it I shall elaborate upon them in turn.
The first consists in the government engaging itself directly in the production of knowledge allowing free use of it (recall that transmission costs are assumed negligible) and financing the production cost from general taxation. This was at the heart of Professor Samuelson’s classic analysis of the efficient production and allocation of public goods (Samuelson, 1954)  Government research and development (R & D) laboratories which publicly disclose their findings such as for example agricultural research establishments, are an approximation of such an arrangement. It is as well to note that the volume of public expenditure for the production of knowledge and the allocation of this expenditure for different kinds of knowledge are in this institutional set-up public decisions.
The second resource-allocation mechanism which in principle can produce knowledge in an efficient manner is one where production is undertaken by private agents, who in turn are subsidized for their effort by the public purse. Thus, the subsidies are financed by general taxation. A crucial feature of this arrangement is that private producers are denied exclusive rights to the knowledge they produce. Once knowledge is produced under this arrangement it is freely available to all. This is the Pigovian solution to the problem posed by public goods, and more generally, by externalities (see Pigou, 1932; Baumol and Oates, 1975; Dasgupta and Heal, 1979). In albeit imperfect forms this arrangement characterizes much research in public entities, such as state funded universities, where a good deal of the research output is prohibited from being patented, and where salaries and promotions - the production subsidies - are paid out of public funds.
These two resource allocation mechanisms resemble one another greatly, but there are important differences, at least in theory. I am thinking of the Pigovian solution as a decentralized mechanism, one where production decisions are made by private agents, and whose work is subsidized by the government. (The subsidies are the shadow costs of production.) And I am characterising the Samuelsonian solution as a command mode of planning: the decision of what to produce and how much to produce is made by the government. Of course, where the second fundamental theorem of welfare economics holds there is no serious difference in the implementability of these two resource allocation mechanisms. Nevertheless, they represent different methods of planning.
Each of these institutions reflects a non-market mechanism for resource allocation. The third and final institution to consider is therefore the market mechanism itself. Admittedly, we are discussing the production of a public good, a commodity which can be consumed jointly. But this does not mean that private appropriation of benefits is necessarily impossible. For some types of knowledge, what one might call the output of basic research (see Section III), private appropriation may prove difficult. For other types it may to a large extent be possible. I want to think now of those sorts of knowledge to which private ownership can be legally assigned and whose ownership can be enforced. By ownership I mean the right to control the use of the public good. Suppose then that society grants producers of new knowledge
5. The social cost-benefit rule, it will be recalled, is the equality of the marginal rate of transformation between the public good and a numeraire private good and the sum of the private marginal rates of indifferent substitution between these two goods.
property rights to discoveries and inventions, and allows them to engage in trade should they wish to, vja licensing or outright sale. In the world as we know it, patents, trademarks, and copyrights are an embodiment of such ownership.
Clearly, the value of a given piece of knowledge is different for different people. Therefore, if production under the market mechanism is to be efficient the owner must set different prices for different buyers, since efficiency demands that the marginal cost of production of this knowledge equals the sum of the fees charged by the producer to all buyers. At an efficient market equilibrium the quantity demanded by each buyer equals the total amount which is produced and is on offer. This was Lindahl’s proposal for the supply of public goods; to establish a competitive market mechanism for it. (See Musgrave and Peacock, 1968.)
One problem with the suggestion, as Arrow (197 1) noted, is this. Since Lindahl prices are ‘named’ prices, one for each buyer, each of the Lindahl markets for a given piece of knowledge is thin, essentially a bilateral monopoly. This is scarcely a propitious environment for the emergence of efficiency prices. Furthermore, the enforcement of property rights is difficult, particularly on the output of fundamental research, for the findings of such research have possible applications in wide varieties of fields, and it can be exceptionally difficult to detect a violation of property rights. In other words, the economic benefits of knowledge are often difficult to appropriate privately and therefore to market efficiently. This is so even when patent and copyright protection gives one transferable legal rights to exclude others from using that knowledge. Matters are easier in the case of more narrowly restricted knowledge of new technical processes and practical devices. This partly explains why it is a commonplace today to see A paying B a licence fee for using B’s patent on the manufacture of a new product, or on a new process for manufacturing an old product. 
There is in fact an additional difficulty in applying Lindahl’s theory of public goods directly to the case of knowledge. As we noted earlier each piece of knowledge is a distinct entity. Producing the same piece of knowledge more than once is of no use.  Different pieces of knowledge differ from one another in their detailed characteristics, and each piece can be thought of as a unit of the commodity with that characteristic. We are then in the realm of product differentiation, and unless strong assumptions are made, such as for example that the space of product characteristics is closed and bounded we cannot in general ensure that competitive equilibria with full appropriability is efficient.  The point is a familiar one, that firms can locate themselves in the ‘neighbourhood’ of other firms in terms of the characteristics of the knowledge they produce, or more accurately, the characteristics of the research programmes they pursue. We would then expect that firms face downward-sloping demand curves in the market for knowledge, even in a large economy unless, of course, fairly strong assumptions are made regarding the potential size of firms. I conclude that on a-priori grounds there are inefficiencies associated with the market mechanism, even when appropriability poses no problems. 
But this is only one side of the ledger. The other side is the fact that if they are to function well the two non-market mechanisms we noted earlier require an enormous quantity of centralized information, not only about private demand for knowledge but also about research possibilities open to individuals and
6. Private firms often do not rely on patents which involves disclosure of their discoveries and they rely instead on secrecy. This involves a different type of risk, in that a rival may at a future date discover the same thing and exploit it with the backing of a patent. I am ignoring the practice of secrecy here only because I am considering Lindahi markets, which by definition cannot be established if firms keep their discoveries secret.
7. By this I don’t of course mean that repeating an experiment to confirm one’s own or others’ findings is useless. That is a different matter altogether
8. Even in a large economy. For an analysis of the efficiency properties of monopolistic competitive industries, see e.g., Hart (1979)
9. There are a number of other problems with this mechanism in the market for knowledge. I do not go into them here. But see Dasgupta (1988)
firms. This tension, induced by the fact that the market mechanism and each of the various non-market planning mechanisms suffers from different types of weaknesses, has been a pervasive feature of the literature on science and technology policy.
As noted earlier each of the three allocation mechanisms we have outlined is to be found in economies as we know. They have developed over a long period, traceable in the European context at least, to the Renaissance patronage system. (For a development of this historical thesis, see Dasgupta and David, 1988.) They work in imperfect ways, as the foregoing discussion predicts they would, but they try and capture the essential features of the idealised social constructs. They have not risen and grown out of pure design, they have instead evolved over several hundred years.  Nevertheless, it is a useful exercise to study the argument by design, as we have done. It makes clear the central features of the organizations that have evolved over time, and are to be found today. Moreover, the fact that they co-exist requires explanation, and the argument by design gives us a lead as to why they do; why in fact we do not see the dominance of one of them. It has to do with differing characteristics of different kinds of knowledge.  I argue this next.
The analysis of Section II suggests that von Weizsäcker’s three-level classification of economic activity is too coarse. One would want to classify knowledge into types to see whether there is at least a tendency for the market and non-market mechanisms to produce specific types. As it happens there is a classification which is of use for this purpose: basic and applied knowledge. In his classic article, Arrow (1962), thought of: basic research as that kind of activity, the output of which is used only as an informational input into other inventive activities. By way of contrast, applied research is the kind of activity whose informational output is an input in the production of commodities - von Weizsäcker’s intermediate level.
There are, of course, other classification schemes that are similar in spirit, though some are misleading. Thus it is a commonplace to think of science as being concerned with basic research and technology with applied research. On occasion one distinguishes abstract from concrete knowledge, and on other occasions the search for principles from the seeking of applications. And so forth. It would be out of place here to discuss connections between these classification schemes. The basic-applied research distinction is adequate enough for my purposes.
The distinction is an analytical one and in actual practice it is not clear cut. Moreover, the intention of a researcher is often quite different from his actual performance. Much basic knowledge has been acquired as an accidental outcome of what is applied research. For example, the immediate motivation behind Pasteur’s research around 1870 was to solve certain practical problems connected with fermentation in the local wine industry. He was successful in this. But the by-product of his research is what made him immortal. The history of science and technology is littered with instances of this.
These are happy accidents, a bonus as it were, and although they are not rare, the immediate target of the researcher is in such cases the solution to an applied problem. The fact that there are happy accidents does
10. For example, the first systematic use of patents began in Venice in 1474, when the Republic promised privileges of ten years to inventors of new arts and machines. The rule of priority in science was institutionalized in the seventeenth century, with the rise of parliaments of scientists, specifically the Royal Society of England (1662).
11. In an early discussion the late Michael Polanyi, (Polanyi, 1943-4), suggested that the patent system should be abolished, that it should be replaced by a system where inventors are rewarded out of public funds and that potential users should have unrestricted access to the inventions. Polanyi was thus arguing (by design) that an imperfect Pigovian solution is superior to an imperfect Lindahl solution.
not rule out the desirability of conducting basic research, that is, where the goal itself is basic knowledge. In his oft-cited essay Arrow (1962) advanced the argument that the more basic the character of the research the more in need it is of public funding. He argued this from two observations. First, the intended output of basic research (we are calling it basic knowledge) is more difficult to appropriate than applied knowledge (which is to be taken to mean knowledge applicable directly to the production of material commodities). We have already touched upon this.
The second observation is more controversial. Arrow argued that the value of basic research is more conjectural than that of applied research and is therefore more likely to be undervalued by private individuals and firms. The idea here is that private firms and individuals are likely to be more risk averse than they would be if acting collectively through the government, and so may avoid undertaking basic research to any large extent because of its greater uncertainty. A related idea is that basic research involves on average a longer gestation lag than applied research. If private rates of discount exceed social rates, either because of myopia or because of imperfect capital markets, there is a case for the provision of public assistance to basic research.
These arguments have had an influence on public policy towards basic research, both in Western Europe and in the United States.  While the share of basic research expenditure incurred by the Federal Government in the United States has been declining in recent years, it is still about two-thirds of the total. (See National Science Foundation, 1986.) In a recent interesting essay Rosenberg (1988) provides evidence to indicate that these arguments are also correct. For example, he notes that the most successful basic research laboratories in the private sector have been in firms that have strong market positions, such as Bell Labs., IBM, Dupont, Dow Chemical, Eastman Kodak, etc. Being large and enduring they can absorb risk and take the long view. Their research success has been to a large extent due to the close intellectual proximity maintained between the basic research laboratories and the development and production wings of these firms.
It was noted earlier that even though the transmission cost of knowledge may below, the cost of absorbing the information, of interpreting it and using it fruitfully may well be very high. This is often the case with research output at the frontiers of science and technology. Firms wishing to make use of the latest findings that are publicly available need to have scientists who can make it possible for them to do so. A good portion of the ‘technology’ of their being able to do so consists in their pursuing basic research! This provides one reason why private firms conduct basic research. 
All this is to see basic knowledge as an accidental outcome of applied research, or as being tied to applied research. In fact, of course, many of the most creative leaps that humankind has made have been made by thinkers chasing an intellectual problem thrown up internally by their subjects of specialization. If one had asked the late Professor Paul Dirac what he was doing when attempting to write down the relativistic quantum field equation for the electron, he would have answered that he was attempting just that. The avenues along which basic knowledge grows are many and varied, and typically unpredictable. It is for this reason one hears the argument that a part of the public subsidy for research ought to be earmarked for creative persons rather than projects. Creative people can be relied upon to choose promising problems. That is what makes them creative. One reason behind the astonishing success of the Cavendish Laboratory at Cambridge immediately after the Second World War was that its then Director pursued this policy.
The direction which these considerations point at then is this. Centralized information about promising
12. See Mowery (1983) for a good discussion of the influence these arguments have had on public policy towards basic research in the United States.
13. A related reason is the large demand of governments for equipment connected with warfare. Private firms conduct basic research in these fields so as to be able to compete against one another for government contracts.
avenues of research, both applied and basic, is by the nature of things necessarily sparse. Such diverse and specialized knowledge is dispersed among professionals in their fields; scientists, technologists, market analysts, and so on. R & D decisions have to be decentralized. For reasons that we have explored, much basic research needs to be funded publicly, along Pigovian lines, where persons and teams are funded but where the choice of research programmes and strategies are left to the researchers themselves. Of course, the detailed organization of decisions that ought to be established is a complex matter, as current discussion on the subject in the United Kingdom shows. Here I have for obvious reasons been painting the organizational structures in broad strokes, in terms of prototypes
The matter is different for applied research. Appropriability of applied knowledge is easier. Moreover, a good deal of applied research addresses the development of products and manufacturing processes, involving less in the way of an advancement of one’s understanding of basic principles. There is then a supposition that on average applied research, as we have defined it here, is intellectually less enticing. Thus for example the oft-made claim that many scientists hanker after knowledge for its own sake is one made about those who are attracted to basic research. For these reasons as well there is an a-priori case for relying in the main on the private sector for applied research by instituting intellectual property rights, such as patents, copyrights, and trademarks.  There is then the question of efficient property rights and the desirability of preventing excessive duplication of R& D in the private sector. In the next two sections I go into these issues.
At first blush the structure of efficient property rights is obvious. The Arrow-Debreu theory tells us that if it is costless to establish markets, each and every commodity ought to be supported by a competitive market in a private ownership economy. There is then an immediate problem in using the theory when knowledge is treated as a commodity.  For suppose that given any knowledge base there are constant returns to scale in the production of commodities. Since R & D involves the expenditure of resources, production of commodities, including knowledge, must involve increasing returns to scale. Thus in particular firms must be allowed to earn profits from their production activities in order to recoup their R & D expenditure. Patents are designed to allow that to happen, to prevent competition in the producer market. But the problem is that it is not clear what a patent means.
We noted in Section II that the right way to think of the production of knowledge is to think about the economics of product differentiation. Inventions and discoveries differ by way of the characteristics of the information associated with them. A statement made with 95 per cent confidence is different from what is verbally the same statement made with 90 per cent confidence. Not by much perhaps, but they are by no means the same. A patent provides a protected sphere around the characteristics of the invention made by the patent holder. We should therefore be interested not only in the optimal duration of patents, but we should also be interested in the optimal tightness of patents, or in other words, the size of the protected sphere. In addressing this question I shall elaborate upon an argument put to me by Professor Carl Shapiro of Princeton University.
14. It should be noted that English and American patent laws, as forerunners of modern patent laws elsewhere, expressly forbade patenting a ‘fact of nature’. The problem is that it is not clear what is a fact of nature. This was illustrated recently in the litigation over the Stanford University and the University ofCalifomia at Berkeley patcnts on recomhinant DNA. Under United States Law, a patent can be awarded to cover ‘.., any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof. The duration of a U.S. patent is 17 years from the date of issue.
15. I am ignoring oft-cited problems connected with the fact that research often throws up unthought of possibilities, more specifically surprise events, so that the information partition not only becomes finer with discoveries, it contains elements not included previously. These issues are pertinent not only to the Arrow-Debreu theory but to decision theory in particular and economics in general.
Purely for the sake of expositional ease I suppose that knowledge characteristics can be aggregated adequately into a scaler number. We then have a natural metric, providing us with a distance measure between any two pieces of information. Without loss of generality I suppose that the state of knowledge at the initial date (t=O) is zero. For simplicity I assume that the cost of producing knowledge of measure y (y≥0) is k(y). (This cost can be thought of as being the expenditure of a numeraire commodity, say income.) The greater the extent of the invention, the greater is the cost. Thus k’(y) ≥ 0.  We may think of y as the extent of a cost reducing invention, or an index of the quality improvement of an existing product.
Denote by x the size of the protected sphere around the discovery. The interpretation is that when a discovery is made the discoverer is protected from entry by rivals into the region consisting of points within a distance x from the discovery, y. (It should be remembered that when the discoverer of y announces it rivals can, unless prevented by law, make use of y without having to incur k(y).) Let T be the duration of this protection, the patent length. Let B(x, y) denote the flow of social benefits and P(x, y) the flow of private profits to the discoverer. Making standard assumptions we would conclude that Bx(x, y) < 0, By(x, y) >0, Px(x, y)> 0, Py(x,y) >0, and P(0,y)= 0 for all y. In what follows I ignore income effects. The government is to choose x, y and T with a view to maximising the present value of social benefits, subject to the constraint that the present value of profits earned by the inventor is non-negative.  Let r (>0) be the social rate of discount, assumed without loss of generality to be equal to the discount rate of the private sector. It follows that the government’s problem is: Choose x (≥0), y (≥0) and T (≥0) so as to maximise
Subject to the constraint
To have a non-trivial problem suppose that it is socially beneficial to have some discovery. It is then a trivial matter to confirm that the optimal values of x and y satisfy the pair of conditions
P(x,y) = rk(y) (2)
and Px(x, y) [By(x, y) - rk.’(y)]= Bx(x, y) [Py(x, y) - rk’(y)]; (3)
and that theoptimal value of T is infinity. In other words, the patent issued should be a permanent one, but the protected sphere defining the patent on y should be of the smallest size consistent with the researcher being willing to undertake the research (condition ). Putting it slightly differently, the intellectual property should be a free-hold, but the property should be defined as narrowly as is compatible with incentives on the part of the private sector to produce the property.
An immediate implication of conditions (2) and (3) is that the size of the optimum protected sphere is not invariant to the kind of discovery we are studying. This follows at once from the fact that both the social benefit function, B, and the private profit function, P, depend upon the type of knowledge production we are considering. What is invariant is the optimum length of the patent. This invariance result should be contrasted with the results in Nordhaus (1969), Dasgupta and Stiglitz (1980b), Stoneman (1987) and Dasgupta (1987), which argue that the optimum patent length is finite and that it is dependent upon the type of discovery being studied. I shall presently try and explain why we are obtaining such strikingly different results.
16. As usual, for simplicity of exposition I assume that the discovery is made instantaneously. I ignore uncertainty in the R & D process since this will raise additional matters. For an analysis of this last see Dasgupta (1987). See also Section V.
17. Thus, the government is a Stackleberg leader. I suppose for simplicity of exposition that competition among potential inventors leads in equilibrium to a single agent carrying out the R & D at a pace which the government can choose so long as it does not yield negative present value profits.
Why do we not see the policy implied by (1) put into practice? There are several reasons. Here I want to concentrate on one which brings out quite sharply a feature of knowledge production which is not captured in (1). It has to do with private learning and it carries with it the implication that the solution of (1) is not implementable in short, it is inconsistent with incentives.
Let x* and y* denote the solution to (1). By hypothesis, the initial state of knowledge is zero. (This, as we noted, is merely a normalization, of no significance.) But y*>0. Thus the optimum solution envisages a discrete change in the state variable, namely the state of knowledge. Consider the agent who has made the discovery. Assume for the moment that the agent does not disclose his finding. Thus, the state of knowledge of this agent is y*, that of all others is still nil. But now the cost of discovering all pieces of knowledge in the neighbourhood of y* is tiny for the agent in question and is approximately k(y*) for each of the others. The knowledgeable person has a great advantage over the rest. So then when the discoverer applies for a patent he will seek a patent not only on y*,but on all pieces of knowledge in the neighbourhood of y*, the size of the neighbourhood depending upon how easy it is for the discoverer to scan around the discovery y*. In general when this learning effect is large, the neighbourhood the discoverer can scan pretty much costlessly exceeds x*. One concludes that when a discoverer applies for a patent he applies for a patent on an entire region in the space of knowledge characteristics. It follows that in general x* is not implementable: the protected sphere cannot be made as small as the government might ideally like. From this it follows at once that the optimum patent length is finite. 
Research projects have uncertain yields. No one who launches a programme of research can be certain of the outcome. Each project possesses an irreducible element which is specific to the team conducting it which is another way of saying that in characterizing a project one must include the minds that are directing and conducting it. Thus, apart of the uncertainty concerning output is what one might call ‘team-specific’. It follows from this that the uncertainties faced by two research teams can never be fully and positively correlated.  They would not be fully and positively correlated even if, acting as separate teams, they were to pursue what is otherwise the same programme of research.
It can be argued that private firms competing for a patent pursue overly correlated projects (Dasgupta and Maskin1987). This they tend to do even when they are neutral to risk. The intuition behind this result makes clearer the effect of the institution of patents on R & D races. As we noted earlier, patents aim at awarding all private profits to the winner of the race, the more comprehensive a patent the greater is the flow of profits to the winner. If a firm were to choose a research project which is less correlated with the project chosen by its rival, it would bestow a positive externality on the rival. Specifically, the likelihood that the rival is successful when the firm in question is not, would increase. This is socially desirable (because cet. par. society does not care who wins the patent, so long as a good discovery is made), but it is not picked up in the firm’s private calculation. As our intuitions about externalities would suggest, this means that there is excessive similarity among the research projects pursued by private firms engaged in a patent race.
18. Nordhaus (1969) and Stoneman (1987) explored the optimum lengths of patents when, as in (1) above, the R & D process involves no uncertainty. This enabled them to postulate that in equilibrium there is a single agent engaged in R & D. Dasgupta and Stiglitz (1980b) explored some of the additional problems that arise if firms face independent uncertainties regarding their R & D technologies. In equilibrium the number of firms in this sort of situation is not unity and one has to correct for the fact that the number of active firms is also affected by the patent length. The result in Dasgupta and Stiglitz (1980b) concerning the length of optimum patents is valid only if the patent holder is a perfectly discriminating monopolist. Dasgupta (1987) corrects the erroneous statement in the earlier paper that it does not depend upon this assumption.
19. They can, of course, be fully and negatively correlated if they are involved in, say, testing mutually exclusive hypotheses.
Entry into patent races can be a cause of waste. If entry is relatively costless there can be a dissipation of expected rents from inventions, as firms chase an invention knowing that there is some chance of winning the patent. It is possible to show that under a wide class of cases, patent competition results in firms pursuing an excessive number of parallel research projects. (Loury, 1979; Dasgupta and Stiglitz, 1980a, b.) This is another way of saying that the market can sustain excessive duplication. 
This is a special kind of market failure, and it is not easy to see how it can be corrected for by R & D taxes. In order to impose such corrective taxes the government needs to be able to monitor a firm’s R & D programme in specific details. (How else is the government to judge that it has chosen an overly duplicative programme?) This the firm rightly will not wish to allow, because this would disclose information and would dilute the firm’s prospects of appropriating the benefits from its R & D effort. The discussion of Section II is relevant again. Disclosure (of one’s R & D project) dilutes the incentives for undertaking R & D in the first place. One concludes that the prescription of an externality tax is incompatible with incentives.
I would argue that these possibilities on their own provide some justification for the encouragement of joint R & D ventures among private firms. They are different from the argument that is most often put forward in popular writings, that joint ventures enable firms to pool their R & D risks and thereby enable them to undertake projects which otherwise would not be undertaken. 
The distinction between basic and applied research is somewhat blurred in a joint venture, for the reason that such programmes are highly targeted towards commercial goals. But in principle one can ask about the appropriate mix of co-operation and competition, even at the R & D stage. For example, one can imagine firms cooperating in basic research; that is, pooling their research laboratories and sharing the output of basic research, and then competing at the development stage once the basic research is completed. On the other hand, one often sees in practice an agreement to share the costs and output of R & D (both basic and developmental), to be followed by competition in commodity production. Then there are examples, such as EUREKA, where the venture is joint all the way from research and development to the product market, what I shall call a vertically integrated joint venture.
In a closed economy an analysis of a vertically integrated joint venture may seem in effect an analysis of pure monopoly. But this would not be correct. When firms enter a joint venture they do not become a single firm. Their R & D laboratories will co-operate but they will not become a single laboratory. This makes the analysis of joint ventures difficult even when they are vertically integrated. Nevertheless, many of the ingredients of any such analysis are embedded in the discussions of Sections II and III.
Within joint ventures a distinction should be made between two polar cases: (i) those where the venture not only allows firms to co-ordinate their policies, it also commits them to share their newly discovered knowledge; and (ii) those where the only gain is a co-ordination of policies. The key feature underlying (ii) is that the extent to which knowledge is shared is not subject to control: a certain ‘fraction’ of each firm’s R & D output spills over to the rival firm whether or not they agree on a joint venture. The distinction therefore is based on the extent to which the firms’ R & D laboratories are combined by the venture. Underlying (i) is the assumption that the laboratory outputs are common property. Underlying (ii) is the hypothesis that they are kept separate, but that their funding is determined by a joint policy.
20. We emphasise the use of the term ‘excessive’ because it is often desirable socially to have several parallel research projects in operation, just as it is desirable to hold a diversified financial portfolio.
21. Within the European Economic Community members are engaged in large scale operations, such as RACE (Research in Advanced Telecommunication Technology for Europe Programme). EUREKA (European Research Coordination Agency: ESPRIT (European Strategic Programme for R & D in Information Technologies); and in the United States by MCC (Microelectronics and Computer Technology Corporation).
Our earlier discussion is directly applicable to (i) and in fact it is (i) which is most often alluded to in the literature. A central gain, both to the firms involved and to society, is the sharing of knowledge. As against this is a possible loss to society occasioned by the fact that a joint venture implies greater monopoly power. The gain from shared knowledge is absent from (ii), because by hypothesis the extent to which knowledge is made common is unaffected by the venture, although of course the amount of knowledge each firm produces is affected. 
In a recent interesting note d’Aspremont and Jacquemin (1987) have analysed the implications of joint ventures with (ii) as the background situation. There is no uncertainty postulated, R & D is directed at process innovations and the R & D technology is assumed to enjoy no scale economies. It is supposed that a certain amount of knowledge spills across the firms’ R & D laboratories in an exogenous manner. (This last is what makes the venture one of pure co-ordination case [ii])
Knowledge spillovers are a form of positive externality. So it might be thought that a joint venture must necessarily involve greater R & D expenditure: the venture after all internalizes the externality. But this would be wrong. The point is that if the joint venture were to be restricted to a co-ordination of R & D expenditure, the firms would expect to compete in the product market once R & D were completed. The firms would know in advance that after the completion of R & D there will be no jointly agreed production policy. Given this, they may well choose to agree on a lower R & D expenditure level, lower than, that is, the level that would emerge it they were not to have a joint venture
Clearly then the answer depends upon the extent of knowledge spillover. If this is large a joint R & D venture would be expected to result in greater R & D expenditure and indeed even greater output production. This can be shown to be the case. (See d’Aspremont and Jacquemm, 1987) In fact it can be shown that if knowledge spillovers are large a vertically integrated joint venture would be expected to sustain even greater R & D expenditure than a mere R & D joint venture. Where a vertically integrated joint venture is restrictive is at the production stage, and consumers can end up paying a higher product price even though production costs are lower because of the integrated nature of the venture. The greater surplus is captured by what is in effect a monopolist and distributed to shareholders. A joint venture, whether restricted to the R & D stage or whether integrated fully, does not produce the first-best efficient outcome. But if spillovers are large an R & D joint venture can be closer to it than unbridled competition.
These results are congenial to intuition. They also indicate that our broad brush discussion of the welfare economics of knowledge production has probably been along the right lines. The tension we noted earlier in this essay, between the need for co-ordination and sharing of produced knowledge the paucity of centralized information about R & D possibilities and dilution of private incentives to produce knowledge if it is to be shared, is at the heart of the basis upon which public policy has to be geared.
22. A good deal of the urgency expressed within the EEC and the USA about having joint ventures in R & D, especially in high technology industries, is the competitive threat from Japan. In the text I shall ignore such gains from joint ventures and ask whether there are gains to a society in having R & D ventures even if it were to face no competitive threat from outside.
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