Rewards versus Intellectual Property Rights

Steven Shavell and Tanguy van Ypersele *

1. Introduction

Two basic means of stimulating innovative activity are compared in this paper. One is a system of rewards paid by the government to innovators. According to this system, innovations would pass immediately into the public domain, becoming freely available to all. The other approach is the familiar system of intellectual property rights that we employ, notably, patent and copyright protection, under which the government confers to innovators exclusive rights to market the goods and services that embody their intellectual works.

Our main conclusion is that the intellectual property rights system does not enjoy any fundamental advantage over the reward system. Indeed, an optional reward system - under which an innovator can choose between a reward and intellectual property rights - is superior to the intellectual property rights system in the model we examine.

These findings derive from the primary virtues of reward systems: that incentives to innovate are provided without granting innovators monopoly power over price; and that the magnitude of research incentives may be selected by government. A principal difficulty with reward systems, however, concerns the government's need for information to calculate rewards. To motivate our analysis, we first review a significant historical episode about the patent system and rewards. Although a fairly well-developed patent system had emerged as early as the 1400's in Venice and had spread through much of Europe and the New World by the end of the 18 th century, the system came under strong attack in the next century, especially during the period 1850 - 1875.1 Criticism of the patent system reflected dislike of monopoly power, both because it harms consumers who have to pay high prices and because it can hinder improvements and subsequent innovations if patent holders disallow that.2 Many economists disapproved the patent system, and in some countries, such as Germany, the economics profession was virtually unanimous in its opposition to patent.3

Reward systems were widely discussed as an alternative method of spurring innovation (and they had been used to a not inconsiderable extent 4 ). For example, Robert Macfie, a member of Parliament in England and an influential champion of rewards, set out a proposal for a government-financed reward system to replace patent, the London Economist pressed for adoption of a reward system, and economists examined rewards in professional journals, books, pamphlets, and conferences.5 Opinion was, however, divided on the virtues of rewards (criticism of patents did not imply endorsement of rewards). The chief argument against rewards concerned difficulties in their administration; it was typically expressed by John Stuart Mill, who maintained that patent is preferable "because it [patent] leaves nothing to anyone's discretion; because the reward conferred by it depends upon the invention's being found useful, and the greater the usefulness, the greater the reward..." 6

As a consequence of the criticism of patent, and also of the possible utility of rewards as an alternative, many countries in Europe prepared to reform or abolish patent, and some actually did so: England established a series of royal commissions from the 1850's to the 1870's to investigate the patent system; Chancellor Bismarck recommended abolition of patent in Prussia in 1868; Holland repealed its patent system in 1869; Switzerland, which had no patent law, rejected legislation to adopt it in 1863. Nevertheless, Europe ultimately embraced patent, but for reasons that may perhaps be regarded as more politically accidental than indicative of a substantive policy judgment favoring that system.7

In any case, today, intellectual property rights provide the principal legal financial stimulus for innovation.8 Rewards are little employed; their payment appears to be limited to inventions in the area of atomic energy and to certain other exceptional cases, although they were provided to inventors in the former Soviet Union.9

Modern economic literature reflects our reality and takes the general optimality of intellectual property rights largely as a given; the possibility of rewards is paid relatively little attention, despite the history we have summarized, and despite the seeming appeal of the topic to the intellect of the economist.10 There have been few papers written in economics journals this century on reward. Two exceptions are Polanvyi (1943) and Wright (1983) (neither of whom, however, mention the 19 th century controversy). Polanvyi recommends, in a sustained and insightful but informal argument, that rewards be adopted to foster innovation and to avoid the social losses associated with patent monopoly power; he offers reasons why informational difficulties facing the government in determining awards should not prove insurmountable. Wright is the first to consider a formal model of innovation in which innovators possess superior information to the government, and he finds that rewards are better than patents if the government's information is sufficiently good. Also, Kremer (1997), in an interesting, related paper, suggests that the government avoid social losses associated with patents by purchasing them at a price that it obtains from an auction process. (Governments have in fact occasionally purchased patents, and proposals for this to be done programmatically have sometimes been advanced.11 ) Another related paper is Scotchmer (1997); although she does not investigate rewards, she analyzes and characterizes the optimal form of patent system assuming that innovators possess superior information to the government.12

In this paper, we examine a simple model in which a potential innovator knows the demand curve for the product innovation he might produce but the government knows only the probability distribution of demand curves (this captures the notion that the government has difficulty in determining the value of an innovation). We first compare the patent system (for concreteness, we refer to patent rather than to intellectual property rights in general) to the reward system.13

Under the patent system, the innovator's incentive to invest in research is the monopoly profits he would earn, and if he produces the innovation, he then sells the innovation at the monopoly price. There are two familiar deviations from first-best behavior under the patent system. First, incentives to invest in research are inadequate, because monopoly profits are less than the social surplus created by an innovation.14 Second, if an innovation results, there is a deadweight loss in social welfare due to monopoly pricing; too little is sold because the monopoly price set by the innovator exceeds marginal cost.

Under the reward system, the innovator's incentive to invest in research is the reward he would receive.15 If the innovator produces an innovation, it will be available to competitors, so will sell at marginal cost (perfect competition in the product market is assumed). Because there is no deadweight loss from monopoly pricing, the only type of deviation from first-best behavior under the reward system involves the incentive to invest in research. This deviation could be in either direction. If the social surplus from the demand curve exceeds the reward, there will be an inadequate incentive to invest, and if the surplus from the demand curve is less than the reward, there will be an excessive incentive to invest. Either possibility may occur, as the optimal reward equals the expected surplus over the distribution of possible demand curves.

From the foregoing, it is apparent that the comparison between the patent and the reward systems can be resolved into two elements. On one hand, the reward system is superior to patent in that deadweight loss due to monopoly pricing is avoided under reward. On the other hand, the incentive to invest in research is imperfect under both systems, but in different ways. Under the patent system, the incentive to invest is always inadequate because monopoly profits are less than social surplus; but the incentive to invest is linked to actual social surplus because the innovator knows the demand for the potential innovation.16 The latter means, for example, that if the innovation would be very valuable, the innovator would invest a great deal in research, knowing that monopoly profits would be high. Under the reward system, the incentive to invest is governed by the reward and thus is not systematically inadequate; yet the incentive to invest is not linked to actual surplus but only to the reward. In particular, if the innovation would be very valuable, the innovator would invest only in accordance with the reward, which will equal the expected surplus from all possible innovations.

Because patent effectively harnesses the private information of the innovator about the value of an innovation, incentives to innovate might be superior under patent to those under reward, even though the incentives under patent are always less than first-best. This leads to the possibility that patent could be superior to reward, despite the deadweight loss due to monopoly pricing. Reward, however, could be superior to patent, both because of a better average incentive to innovate (as the optimal reward equals expected surplus) and because of avoidance of the deadweight loss from monopoly pricing. Analysis of patent versus reward does not lead one to think that there exists any general argument favoring the patent system over the reward system.

We next consider the optional reward system, under which an innovator may choose between a patent and a reward.17 This system unambiguously dominates patent. The explanation is suggested by two observations. First, if social welfare is improved relative to patent when the innovator chooses reward, then the optional system must be superior to patent, since there is obviously no difference between the systems when the innovator chooses patent. Second, social welfare plausibly can be improved when the innovator chooses reward, for deadweight loss is then eliminated, and potential problems with overinvestment in research can be addressed by the government's selecting an appropriately moderate level of reward.

Although the optional reward system is superior to the patent system, and the patent system might be superior to the (mandated) reward system, when the reward system is superior to patent, it might also be superior to the optional reward system. The reason that reward may be superior to optional reward is similar to that why reward may be superior to patent. Conversely, the reason that optional reward may be superior to reward is similar to that why patent may be superior to reward.

After analysing the patent, reward, and optional reward systems in our model, we discuss briefly a number of issues not considered in the model including: the government's ability to obtain information about demand (especially through observation of quantity sold) for the purpose of determining rewards; the race to be first to innovate; improvements to innovations; administrative costs; the financing of rewards through income taxation and possible associated distortionary costs; and the actual potential of reward systems for raising welfare.

2. The Model

A risk-neutral (potential) innovator may invest in research which will result in an innovation with a probability that depends positively on the research investment. Let

If there is an innovation, a new product18 can be produced at a constant per-unit cost; define

Regarding the demand curve for the product, let

where

We assume that at ta, monopoly profits, deadweight losses from monopoly pricing, and social surplus (these are described below) are positive,19 and that they increase with t.20

We suppose that the function p(k), the cost c, the demand curves d(q;t), and the density g(t) are common knowledge for the innovator and the government. The innovator alone knows t.21

Social welfare is assumed to be the expected value of the utility individuals obtain from the innovation product, minus production costs, and minus research investment.

2.1 First-best outcome.

If there is an innovation, the first-best quantity, denoted q*(t), is such that the height of the demand curve is c, that is, d(q*(t),t) = c. Thus social welfare exclusive of research investment is the social surplus,

q*(t)

s*(t) = ò(d(q;t) - c)dq. (1)

0

Consequently, the first-best research investment is that which maximizes

p(k)s*(t) - k, (2)

so that

p¢(k)s*(t) = 1 (3)

identifies the first-best k. If k(z) denotes the k that would be chosen if z is the payoff from an innovation,22 then the first-best k is written k(s*(t)). First-best social welfare as a function of t is thus

W*(t) = p(k(s*(t))s*(t) - k(s*(t)). (4)

Figure 1 shows s*(t) and k(s*(t)).23

2.2 Patent regime.

Under the patent regime (exemplifying intellectual property rights) the innovator has the exclusive right to sell the product resulting from an innovation. Hence, if he innovates, he will sell the monopoly quantity and charge the monopoly price. Specifically, let

where this quantity is determined by the condition, marginal revenue equals marginal cost, dq(q;t)q + d(q;t) = c. The monopoly price is d(qm(t)). Let

Knowing that an innovation would yield p(t), the innovator will choose k to maximize

p(k)p(t) - k (5)

so will choose k(p(t)).

Let us compare the outcome under patent to the first-best outcome. Now qm(t) < q*(t),

so that the social surplus under patent falls short of first-best social surplus s*(t) by the deadweight loss

q*(t)

l(t) = ò(d(q;t) - c)dq. (6)

qm(t)

Hence, social welfare under the patent regime given t is

WP(t) = p(k(p(t)))[(s*(t) - l(t)] - k(p(t)). (7)

This may be compared to first-best social welfare given t:

W*(t) - WP(t) = {[p(k(s*(t)))s*(t) - k(s*(t))] - [p(k(p(t))s*(t) - k(p(t))]} + p(k(p(t)))l(t). (8)

The first term, in braces, is clearly positive, and represents the welfare loss from inadequate investment in research under monopoly: because the monopolist's profit p(t) is less than first-best social surplus s*(t), he underinvests in research, k(p(t)) < k(s*(t)). The graph of k(p(t)) is shown in Figure 1. The second term is the expected deadweight loss due to monopoly pricing. In summary, we have

Proposition1.Under the patent system, there are two sources of welfare loss relative to first-best welfare: insufficient investment in research; and insufficient quantity of the innovation product sold, with accompanying deadweight loss, due to monopoly pricing.

These points are, of course, standard,24 but are set out so that we can contrast patent to reward.25

2.3 Reward regime.

Under the reward regime, the government gives a reward to the innovator if he succeeds with an innovation, and it is assumed that the innovation information is placed in the public domain and made available to a competitive production industry. Hence, it is assumed that the product will be sold at a price of c, so that zero profits will be made from production and total quantity produced will be q*(t). Let

r = reward paid by government for an innovation.

The innovator's incentive to innovate is due entirely to the reward, since he makes no profits from sales. He will thus choose research investment to maximize

p(k)r - k, (9)

so will choose k(r).

It follows that if - contrary to our assumption - the government were to possess perfect information about the demand curve t, the government could achieve a first-best outcome for each t by setting the reward r equal to s*(t): the innovator would then choose k(s*(t)), the first-best investment in research; and the quantity produced is always optimal, q*(t), under the reward system.

Because our assumption is that the government does not know t, the reward r must be independent of t. Social welfare as a function of the fixed reward is

tb

WR(r) = òp(k(r))s*(t)g(t)dt - k(r) = p(k(r))E(s*) - k(r), (10)

ta

where E(s*) is the expected value of s*(t); see Figure 1. It follows that (10) is maximized if r = E(s*).26 That is, the optimal reward r* is the expected social surplus from an innovation.27

We can now compare social welfare under the reward system to first-best social welfare. The difference beween the two is that research investment is the constant k(E(s*)) under the reward system, whereas investment depends optimally on t, equals k(s*(t)), in the first-best situation. Under the reward system, research investment k(E(s*)) is excessive relative to the first-best when s*(t) is below E(s*) and is inadequate when s*(t) exceeds E(s*).

To summarize this section,

Proposition 2. Under the reward system, the optimal reward r* equals the expected value of social surplus, E(s*), from an innovation. There is one source of welfare loss relative to first-best welfare: incorrect investment in research, which will be excessive or inadequate depending on whether actual surplus falls below or exceeds E(s*). There is no deadweight loss due to monopoly pricing if there is an innovation.

Note that the information the government requires to calculate the optimal reward is the density g(t) of demand curves d(q;t) and the production cost c (in order to compute the surplus for each demand curve). The government does not need to know the probability function p(k).

2.3 Patent versus reward.

If we subtract social welfare under patent from that under reward, we obtain

tb

WR(r) - WP= WR(r) - òWP(t)g(t)dt

tb

= ò{[p(k(E(s*)))s*(t) - k(E(s*))] - [p(k(p(t)))(s*(t) - l(t)) - k(p(t))]}g(t)dt. (11)

ta

The integrand in the second line reflects the two differences between reward and patent that we noted in the Introduction. First, under reward, there is no deadweight loss from insufficient production, whereas there is under patent. This constitutes an advantage of the reward system and tends to make the integrand positive (note that l(t) is subtracted from s*(t) in the second term). Second, under reward, the research investment is a constant k(E(s*)), whereas under the patent, research investment depends on t, and equals k(p(t)). This difference may favor either patent or reward, for when s*(t) is sufficiently close to its mean, E(s*), investment will be closer to its first-best level under reward than under patent, where it is inadequate for all t; but where s*(t) is very different from E(s*), investment may be closer to first-best under patent than under reward.

Figure 1 helps to clarify the comparison. Let t* be the t such that s*(t) = E(s*(t)). As shown in the Figure, reward is superior to patent for t in a region around t*. For t sufficiently close to t* and within this region, reward is superior to patent for the double reason that investment is closer to first-best than under patent and deadweight monopoly pricing loss is eliminated; elsewhere in the region, reward is superior to patent even though investment is farther from first-best than under patent, because reward eliminates pricing deadweight loss. For t outside the region, patent is superior to reward because investment is sufficiently closer to first-best under patent than under reward as to overcome the deadweight loss due to monopoly pricing. This suggests that if enough probability mass is distributed close to t*, reward will be superior to patent, whereas if enough mass is not close to t*, patent will be superior to reward.28 Hence, we have

Proposition 3. Either the reward system or the patent system may be superior to the other.

The foregoing discussion also leads to two observations about the comparison between reward and patent.

First, if the information that government has about demand is sufficiently good, then the reward system will dominate patent. Specifically, if the probability mass is sufficiently concentrated about E(s*), it follows from (11) that reward will dominate patent.29 This is because the research investment under reward will tend to be superior to (and higher than) that under patent and deadweight loss from monopoly pricing will be avoided.

Second, if the need for well-calibrated incentives to invest in research is sufficiently attenuated, then the reward system will dominate patent, because the factor of the elimination of deadweight loss from monopoly pricing will be of dominating importance. One way to make this notion precise is to consider the family of research investment functions p(kl), where lis a positive parameter. Note that the need for incentives to invest in research becomes small as lgrows large because the probability of innovation can be made high at low cost as lgrows large: for any k > 0, p(kl) ®as l®¥, where = lim p(k) as k ®¥. And indeed, inspection of (11) shows that reward will be superior to patent if lis sufficiently high.30

Additionally, we observe that the information the government needs to make the comparison between patent and reward is not only the density g(t), the demand curves d(q;t), and the production cost c, but also the probability function p(k).31

2.4 Optional reward regime.

Under the optional reward regime, the innovator can choose whether to take the government reward r (in which case the innovation information is placed in the public domain) or instead to obtain a patent. Hence, the innovator will choose the reward if and only if r ³p(t); he will choose patent when the demand curve is such that monopoly profits would be high, as is illustrated in Figure 2. Note that if r < p(ta), then the innovator will always behave the same way - choose patent and obtain p(t) - so that in determining the optimal reward, we can restrict attention to r ³p(ta). Now let t(r) denote p-1 (r) for r in [p(ta), p(tb)] and let t(r) = tbfor r > p(tb). Then social welfare under the optional reward system is

WO(r) = ò[p(k(r))s*(t) - k(r)]g(t)dt + ò[p(k(p(t)))(s*(t) - l(t)) - k(p(t))]g(t)dt. (12)

The derivative of (12) is

WO¢(r) = k¢(r)[p¢(k(r))E(s*1/2t £t(r)) - 1]G(t(r)) + t¢(r)p(k(r))l(t(r))g(t(r)), (13)

where G is the cumulative distribution function of g and E(s*1/2t £t(r)) is the expected value of s*(t) conditional on t £t(r). The first term in (13) reflects the inframarginal effect of raising the reward: the influence of the increase in research investment in cases where the innovator chooses the reward. Note that the term in brackets, [p¢(k(r))E(s*1/2t £t(r)) - 1], is the expected net return from more investment in such cases. The second term in (13) is the marginal effect of raising the reward: just inducing the innovator to accept the reward rather than to obtain a patent. In this circumstance, the innovator, by accepting the reward, does not alter his research investment (since the reward just equals his monopoly profits); the only change is that the monopoly pricing deadweight loss l(t(r)) is eliminated, explaining that factor in the second term.

Now the second term in (13) is non-negative (it is clear that t¢(r) is non-negative). Hence, if the first term in (13) is positive, (13) will be positive. The first term will be positive if [p¢(k(r))E(s*1/2t £t(r)) - 1] is positive, and that will be so if and only if r < E(s*1/2t £t(r)). This in turn certainly will be true for r £s*(ta), because s*(ta) < E(s*1/2t £t(r)) for any r. Thus (13) must be positive for r £s*(ta), which implies that the optimal r, denoted r**, must exceed s*(ta).32 We therefore have

Proposition 4.Under the optional reward system, the innovator chooses the reward when monopoly profit would be lower; otherwise he chooses patent. The optimal optional reward, r**, exceeds the minimum social surplus, s*(ta).

We observe that if r** ³p(tb), then the optional reward will always be chosen, so the outcome is equivalent to that if r** were a mandatory reward.

2.5 Optional reward versus patent.

We can immediately show the following.

Proposition 5.The optional reward system is superior to the patent system.

This result is really a corollary of Proposition 4. In particular, as we observed, the patent system is equivalent to an optional reward system with r = p(ta), because then the patent would always be chosen. But since r** > s*(ta), we know that r** exceeds p(ta); hence, the optimal optional reward system must be superior to the patent system.33

Although the above paragraph demonstrates the result, it is perhaps best understood by considering why the optional reward system with a reward of s*(ta) is superior to patent (and a fortiori why the optional reward system with the optimal reward must be superior to patent). If the reward is s*(ta), the reward will be chosen by the innovator whenever monopoly profits are less than this amount, that is, the reward will be chosen when t is in the interval

[ta, t(s*(ta))); see Figure 2. For any t in this interval, it is apparent that the choice of reward over patent must increase social welfare: the deadweight loss due to monopoly is eliminated; and since the innovator chooses research investment of k(s*(ta)) instead of k(p(t)), and k(p(t)) < k(s*(ta)) < k(s*(t)), the increase in research investment also raises social welfare. Because, then, social welfare is higher under patent whenever the reward is chosen and is the same as under patent when the reward is not chosen, social welfare must have risen.

2.6 Optional reward versus reward.

We have yet to compare the optional reward system to the reward system, which is of a mandatory nature. We have

Proposition 6. Either the optional reward system or the reward system may be superior to the other.

That the optional reward system may be superior to reward is clear: the patent system may be superior to reward, according to Proposition 3; and whenever the patent system is superior to reward, the optional reward system must be superior to reward, for optional reward is superior to patent, according to Proposition 5.34 The explanation is essentially that under optional reward, when the demand curve is high, patent will be chosen and incentives to invest will thus not be dulled by a too-low-under-the-circumstances reward. This investment-incentive advantage of optional reward may be more important than the disadvantage of deadweight loss from patent monopoly-pricing.

That the reward system may be superior to optional reward is possible for related reasons. When the demand curve is high and patent is chosen under optional reward, the investment-incentive advantage of optional reward may be less important than the disadvantage of deadweight loss from patent monopoly-pricing. Reward, being mandatory, prevents the potential problem that patent would be chosen when the demand curve is high.35

3. Discussion

We comment here on a number of issues that were omitted from the model and on its interpretation.

An alternative system: patent and reward. A policy that we did not consider is one in which an innovator always obtains a patent and is also given a reward. This system is superior to patent, since the problem of underinvestment is alleviated by payment of a reward. (The optimal reward would equal the expected value of the difference between social surplus and monopoly profits at the monopoly quantity - the social surplus not captured by the patent holder.) The system might or might not be superior to reward or optional reward, for reasons analogous to those relating to the comparison between patent and reward.

Government's ability to obtain information about the value of innovations. As we stressed in the analysis, the government's knowledge about the social value of innovations, embodied in its probability distribution over demand curves, is important to the performance of the reward system and to that of the optional reward system (even though the latter dominates patent no matter how poor the government's knowledge). In fact, one supposes that the government could obtain significant information about demand. Most obviously, the government can base its rewards on sales data, which should be relatively easy to obtain.36 (Note that if rewards are based on sales, the government should not fear that it would be flooded by claimants for rewards with inferior or meaningless innovations - they would not generate products that would pass the market test.) The government could also attempt to measure more about the demand curve than sales at the market price; for example, it could undertake surveys to determine the character and frequency of use of computer software, musical recordings, cinematic and television productions. As events unfold and information flows to the government, it could appropriately supplement rewards, perhaps on an annual basis. In past proposals for reward systems, payments based on sales and other information that government receives have sometimes been discussed (see especially Polanvyi (1943), at pp. 67-69). It would be a gross mistake to envision the reward as having to be premised on the government's estimate of valuation at the time an innovation is registered.

Government's information versus innovators'.We have just mentioned the ability of government to obtain information about demand, but we have not considered how good innovators' information is and its relation to government's. In this regard, two comments should be made, which together suggest that the factor of innovators' superiority of information may be less important than it initially appears to be. First, innovators' information will often be substantially imperfect early on, when they are deciding on research investment - the crucial period for assessment of reward systems versus intellectual property rights systems. Second, if rewards are based on sales and other ex post evaluations of worth, then innovators will anticipate a reward that is based on information that reflects actual demand fairly well. Hence, the reward system will function accordingly well, and it will be irrelevant that the government's ex ante information about demand might be very poor in relation to innovators'.

The latter point about ex post and ex ante information can be put more sharply. Suppose, as is not implausible, that the government's ex post, sales-related information about product demand is as good as innovators' ex ante information, when innovators are deciding on research investment. Then innovators enjoy noinformational advantage that favors intellectual property rights, and mandatory rewards (not just optional rewards) are unambiguously superior to intellectual property rights.37

Race to be first. The optimal magnitude of the reward would be affected in practice by a consideration that we did not study in our model: the race among potential innovators to be the first to innovate. As is emphasized in the literature on patent, this race leads to the possibility of overinvestment in research because the private return to being first exceeds its social value.38 Likewise, under a reward system, there would be a race to be first, and it might lead to excessive investment in research, lowering the optimal reward. Because the race to be first is a factor that afflicts both systems, and because the information needed to address it under either seems to be of the same character, consideration of the race to be first does not seem to bear on the comparison between reward and patent.

Administrative costs. Under a reward system, administrative costs would be incurred by the government in deciding upon rewards, and there would be litigation about rewards between innovators and government, as well as between innovators who contest each other's rewards. However, there would also be a savings in administrative costs relative to the patent or copyright systems: under these systems, intellectual property rights have to be protected by the state, parties often make efforts to determine if their rights have been violated and also to ascertain if they are violating someone's else's rights, and litigation costs are incurred in disputes over rights; but under the reward system, there are no intellectual property rights to generate such costs. On a priori grounds, one cannot say whether the administrative cost savings of the reward system would outweigh the administrative costs that the reward system would entail.39

Tax-financing cost of a reward system. Reward systems have to be financed, and we presume through income taxation, but that involves a labor-supply-related distortionary cost, something that was not considered in our model. Hence, the potential case for reward is less strong than is suggested by our analysis. However, there are reasons to believe that financing innovation through income taxation involves lower distortionary cost than financing innovation through the grant of intellectual property rights. Notably, we know from the tax literature that raising funds through income taxation is superior to doing so through commodity taxation (which is essentially equivalent to granting intellectual property rights); this conclusion presumes that the income tax can be adjusted in an optimal way to raise funds.40 If one takes the view that the income tax cannot be optimally adjusted, then there is still some basis for believing that the income tax involves less distortion than intellectual property rights: income taxation is equivalent to a uniform tax on all goods, whereas intellectual property rights involves concentrated taxes in the form of monopoly prices on just a subset of goods; and raising a given amount through a uniform tax on all goods generally involves less deadweight loss than through a tax on a subset of goods.

Subsequent innovations. We did not discuss the issue of subsequent innovations, that is, improvements to innovations or new innovations depending on past ones. Under the intellectual property rights system, subsequent innovations may be stymied by refusal of holders of property rights to allow improvements; there may be breakdowns in bargaining between the holders and innovators.41 A famous example of this occurred when James Watt, holder of an early steam engine patent, denied licenses to improve it to Jonathan Hornblower and Richard Trevithick, who had to wait for Watt's patent to expire in 1800 before they could develop their high-pressure engine. 42 Under a reward system, this would not have been the case, for Watt's steam engine would have been in the public domain, and Hornblower and Trevithick would have been free to improve it immediately. Indeed, as noted in the Introduction, this was one of the arguments in favor of the reward system emphasized in the 19 th century debates.43

Further merits of the optional reward system. The optional reward system not only has the theoretical advantage that it is superior to intellectual property rights, it has the practical, political advantage that industry should not object to it, as it can only raise firms' profits. Moreover, the fear that government would act suboptimally, and give unduly conservative rewards, would be less an issue under an optional reward scheme because innovators can always obtain intellectual property rights. Indeed, just because of innovators' option, the government's temptation to pay too little might be checked under an optional reward system. Thus, were there an interest in actual adoption of a reward scheme, an optional version seems the best type to propose. (As noted earlier, the plan set out by Polanvyi (1943) was mainly optional in nature, as are schemes for the government to offer to purchase patents.)

Importance of the advantages of reward systems. To appreciate the possible advantages of reward systems, it is helpful to consider areas of innovation where the social losses due to intellectual property rights are likely to be high, namely, where the difference between price and production cost (after innovation) is large. Such areas of innovation may be exemplified by development of pharmaceuticals, computer software, and recorded music and visual products. Here, prices are often substantial in relation to production cost; drugs may sell for many times their marginal production cost, the price of computer software is generally nontrivial even though its marginal production cost is essentially zero (it can be downloaded from the Internet), and similar statements can be made about CD recordings, cable TV broadcasts, and first-run movies. In a regime with rewards, drugs would be far cheaper and more widely used, all computer software would be free, and electronically recorded materials would be inexpensive, arguably engendering significant increases in consumer welfare. Moreover, there would also be potential gains from enhanced incentives to innovate, as profits from patent and copyright may fall far short of consumer surplus. For example, Kremer (1997) suggests that studies of the social versus the private returns from research indicate that private profits from research might well be less than one third of the social returns. Because optimal rewards would reflect the social returns, rewards would increase overall incentives to invest.

4. Conclusion

Reward systems, or optional reward systems, appear on reflection to hold great promise as alternatives to our system of intellectual property rights, because there is no necessity to marry the incentive to innovate to conferral of monopoly power in innovations. As such, serious study of the possibility of reward systems, with a view towards their implementation at least on an experimental, partial basis, is worth contemplating.

References

Macfie, R.A., The Patent Question in 1875,London: Longmans, Green, and Co., 1875.

Polanvyi, Michael, "Patent Reform," Review of Economic Studies, Winter 1943,11, 61-76.

Sinnot, John P., World Patent Law and Practice,Vol. 2M, New York: Matthew Bender, 1988.

Tirole, Jean, The Theory of Industrial Organization, Cambridge: MIT Press, 1988.

Notes

* Harvard Law School and the National Bureau of Economic Research; and the Department of Economics, Tilburg University, the Netherlands, respectively. Shavell acknowledges research support from the John M. Olin Center for Law, Economics, and Business at Harvard Law School; van Ypersele acknowledges research support from the Belgian American Educational Foundation and the Catholic University of Louvain (UCL). We are grateful to Illoong Kwon for research assistance and to ? for comments on the paper.

1 On the history of patent, see Dutton (1984), Machlup (1958), MacLeod (1988), and, especially, Prager (1944). For an account of the 19 th century European debate about patent, see Machlup and Penrose (1950); and see also Chapter 1 of Dutton (focusing on Britain in the 19 th century) and Chapter 10 of MacLeod (focusing on Britain in the 18 th century). For materials relating to the patent debate, see Macfie (1869), Macfie (1875), and Macfie (1883).

2 Another criticism was that innovators did not actually receive much of the profits from patents because businesses to which they sold their rights made the lion's share; thus, it was argued, patents did not really provide a strong motive to innovate. A quite different criticism was that patents were not needed to induce innovators: on one hand, they could often earn enough to induce innovation merely by being first to market; on the other, they often were motivated by fame and honor, so financial incentives were not necessary. On the criticisms made of patent, see Macfie (1869), Macfie (1883), and Machlup and Penrose (1950).

3 See Macfie (1883) at p. 141 and Machlup and Penrose (1950) at p. 4.

4 See MacLeod (1988), at pp. 191-196, who notes that at least eight acts authorizing rewards for specific inventions were passed by Parliament between 1750 and 1825, that substantial sums were granted by Parliament to specific inventors (such as £30,000 to Edward Jenner for his smallpox vaccine), and that many organizations (especially industry groups) instituted reward schemes.

5 Macfie's proposal is reproduced in Macfie (1869) at pp. 84-87. Machlup and Penrose (1950) at p. 19 describe the attention given to rewards by the Economistand state that reward proposals "were discussed in the professional journals and conferences almost everywhere."

6 Mill (1872) at p. 563.

7 See Machlup and Penrose (1950) at pp. 3 - 6. They suggest that the victory of patent was associated with the weakening of the free-trade movement (which was occasioned by the economic depression of the 1870s), as the free-trade movement was closely linked politically to the anti-patent forces.

8 For a description of, and materials on, intellectual property rights protection, see, for example, Goldstein (1993).

9 The United States Atomic Energy Act (1946) established a Patent Compensation Board to grant financial rewards for innovations relating to atomic energy that are of military value (the government does not allow such innovations to be sold on commercial markets). The English patent laws allow for a patent to be infringed upon by the state if it has a "Crown use" for the patented good, in which case compensation, that is, a reward, is to be paid; see Halsbury's Laws of England (1994), at pp. 270-273. The former Soviet Union made rewards to individual innovators; notably, an innovator might obtain a percentage (on a sliding scale, from 17% to .5%, but subject to an absolute ceiling) of the cost savings achieved by a process innovation; see Sinnot (1988) at pp. 44-51.

10 This is not to say that the possibility of rewards is entirely ignored; for example, in his classic essay, Arrow (1971) mentions the intrinsic appeal of rewards at p. 153. However, the lack of importance of rewards in the economic literature is indicated by how little space is devoted to the topic in the chapters on innovation in several well-known books on industrial organization: Scherer (1980) spends only a page (see p. 458) on rewards; Scherer and Ross (1990), a later edition of Scherer (1980), does not mention rewards; and Tirole (1988) discusses rewards in 1/2 of a page (see p. 401).

11 For example, as Kremer (1997) notes, the French government purchased the patent for the Daguerrotype in 1839. A proposal for England to purchase patents routinely was made in 1851 in England; see Macfie (1883) at p. 33.

12 She demonstrates that the optimal patent system must take the form of a patent renewal system, in which patentees are able to extend the length of their patents by paying fees for renewals. Such systems have the feature that they implicitly make use of innovators' private information (notably, innovators with more valuable patents will be the ones who will tend to purchase longer extensions).

13 As mentioned, Wright (1983) also compares patent and reward, but his analysis is somewhat difficult to interpret, in part because his model includes a complicating issue - the race among multiple potential innovators to be first to innovate (on which we comment later). The chief contributions of our paper are (a) that it clarifies the comparison between patent and reward through use of a simple and natural model of innovation with just one potential innovator, and (b) that it investigates the optional reward system and shows it to be superior to patent.

14 However, for reasons going outside our model, there could be an excessive incentive to invest in innovation research; namely, the race to be first to innovate and the business-stealing aspect of innovations may produce too great an incentive to innovate. But as we suggest in Section 3, taking this point into account would not affect the qualitative nature of our conclusions.

15 The reward need not be paid ex ante - when the invention is recognized by the government; it could be based on ex post data - on sales and other information; see Section 3.

16 This point is related to Mill's statement above, although he and other critics of reward were concerned not only about government's lack of information but also about abuse of its authority and the rights of inventors.

17 Such a system was proposed by Polanvyi (1943). Note too that a system in which the government offers to buy patents is of this type.

18 Were we to study process innovations (see, for example, Chapter 10 of Tirole (1988)) instead of product innovations, the general nature of our results would not be altered.

19 Thus, we are implicitly supposing that the government's information is good enough to screen out innovations with no value (or with no expected value). This assumption makes sense if the government devotes positive resources to screening innovations (something that happens under our patent system), and it is also justified if the government obtains information from sales of innovations, as discussed in Section 3.

20 We will consider the following example below: p(k) = (exp[.1k] - 1)/exp[.1k]; c = 5; kinked demand curves (used for computational convenience) given by d(q;t) = min (.5t - .05q +5, 200t - 20q - 1800), so that the kink occurs at q = 10t - 90.476. The parameter t is in [ta, tb] = [10, 20] and is distributed according to the truncated normal distribution with mean 15 and variance 4. That is g(t) = (1/(8p) 1/2 )exp[-(t - 15) 2 /8] + .0012419.

21 The assumption that the innovator has perfect information about demand (since he knows t) and that the government does not is the simplest way to reflect the idea that innovator possesses superior information about demand. A more realistic assumption is that the innovator's information about demand is not perfect but still is better than the government's. Were this the assumption, the qualitative nature of our results would not be altered. Indeed, we can reinterpret the model we are about to examine as follows: let t be a signal, observed only by the innovator, of the true demand curve whose parameter is, say, u (so there is a probability distribution of u conditional on t). The reader can then verify that under this interpretation, essentially nothing in our arguments needs to be altered to demonstrate our conclusions. (For example (and referring to notation to be defined), p(t), monopoly profits under patent, would be interpreted as expected monopoly profits, s*(t) would be interpreted as the expected value of s*(u) given t, p(t) would be less than s*(t), and so forth.)

22 That is, k(z) is determined by p¢(k)z = 1. Note that k(z) is increasing in z (implicitly differentiate p¢(k)z = 1 with respect to z to obtain k¢(z) = -p¢(k)/(zp²(k)) > 0).

23 In the example that we mentioned, s*(t) = 2.5t 2 - 204.139 and k(s*(t)) = 10ln[.1s*(t)].

24 See, for example, Chapter 10 of Tirole (1988).

25 In the example, p(t) = 45.238t - 409.3, l(t) = .51076, and k(p(t)) = 10ln[.1 p(t)].

26 Specifically, p(k)E(s*(t)) - k is maximized over k if k = k(E(s*(t)), so r must equal E(s*(t)).

27 In the example, the optimal reward is E(s*) = 367.62, and k(E(s*)) = 10ln[36.762].

28 In the example, reward is superior to patent; but if the distribution in the example is modified from the truncated normal to the uniform distribution, patent is superior to reward. Specifically, in the example, social welfare under reward is 321.57 and under patent it is 321.51, so reward is better. When the distribution of t in [10, 20] is uniform, social welfare under reward is 332.84 and under patent it is 334.04, so patent is better.

29 This follows from continuity considerations and the fact that at t*, the integrand is positive, for at t*, [p(k(E(s*)))s*(t) - k(E(s*))] = [p(k(E(s*)))E(s*) - k(E(s*))] > p(k(p(t*)))E(s*) - k(p(t*))] > p(k(p(t*)))(E(s*) - l(t*)) - k(p(t*))].

30 It is clear that as l®¥, k(E(s*)) and k(p(t)) both approach 0, and p(k(E(s*))) and p(k(p(t)) both approach . Hence, the integrand in (11) approaches l(t) > 0.

31 The government will need the same information to compute the optimal reward under the optional reward system, and to make comparisons between that system and the other systems.

32 In the example, r** = 327.2, and this exceeds s*(ta) = 45.35. Social welfare given the optimal optional reward is 321.62.

33 In the example, social welfare under the optimal optional reward system is, as we noted, 321.62, whereas social welfare under the patent system is 321.51.

34 It is also possible for optional reward to be superior to reward when reward is superior to patent. This is the case in the example, where social welfare under the optional reward system, being 321.62, exceeded social welfare under the reward system, namely, 321.57.

35 We can modify the distribution over t in our example to illustrate that reward may be superior to optimal reward. Let t be uniformly distributed at height 9 over the subinterval [14.95, 15.05] and uniformly distributed at height 1 over the subinterval [17.9, 18]. In this case, reward turns out to be superior to optional reward; under reward, social welfare is 336.218, and under optimal optional reward, social welfare is 336.214. The reason that reward is superior may be explained roughly by two observations: (a) reward functions well because 90% of the probability mass is in a concentrated region, about 15; (b) reward is superior to patent even for t in the high region, [17.9, 18], due to the deadweight loss from monopoly pricing, but patent is chosen in that region under optimal optional reward.

36 In terms of our model, this means that the distribution of demand curves would be a conditional distribution, of all curves that pass through the observed quantity and price pair.

37 In terms of our model, we are supposing that the t that the innovator observes ex ante is a signal of the demand curve (see footnote 21), and that the government observes t (or even a better signal) ex post. Therefore, the reward can be a function of t, and be set equal to s*(t). Hence, the reward system is superior to patent: investment under the reward system will be k(s*(t)), which is second best (socially optimal given t), and production of the good will be first-best; whereas under the patent system, investment will be only k(p(t)) and there will be a deadweight loss due to monopoly pricing.

38 See Chapter 10 of Tirole (1988).

39 In considering this paragraph, the complicating factor that administrative costs are really endogenous should be borne in mind. We can imagine an intellectual property rights system that is less expensive than the one we have, and we can imagine a reward system that involves low administrative costs because it bases rewards on a simple formula, such as a percentage of sales revenues.

40 The point that income taxes are superior to commodity taxes is presented, for example, in Stiglitz (1987). The proof, which assumes separability of utility of consumption goods and of leisure, can be sketched as follows (this, however, is not the argument Stiglitz employs). Let us show that any revenue raised by commodity taxes can instead be raised in a Pareto superior manner, through a suitable increase in the income tax that does not involve any additional distortion in work effort. Denote by a(y) the commodity tax revenue obtained from individuals with income y. Now eliminate the commodity tax and raise the income tax at each y by the amount a(y). Then it is clear that if an individual were to continue to earn y, his utility would rise. Hence, it is possible to raise the income tax by a(y) + b(y), where b(y) > 0, so as to leave the individual who earns y with exactly the utility he enjoyed under the commodity tax. By this construction, the utility an individual obtains as a function of y will be the same as under the commodity tax, so no individual's labor decision will change, yet the government will raise greater funds (the integral of the b(y)). The excess funds can be distributed to make all persons better off. This construction, under which additional income taxes are raised without distorting work effort, is closely related to that of Kaplow (1996), who shows that there need not be any distortionary cost associated with raising greater income tax revenues to finance a government program.

41 To some degree, this problem can be addressed by legal rules that force the right holder to allow an innovator to make and sell an improved product; this is what compulsory licensing rules of patent law do.

42 See Scherer (1980) at p. 452.

43 See, for example, Macfie (1875), who states at p. 5 "when an invention is patented, the reward being monopoly, a stop is put to improvement....If we substituted for monopoly a sensible system of grants in money, thus preserving a pecuniary stimulus to publish inventions, I predict that almost every new machine or process would be studied, scrutinized, and subjected to such an amount of diversified and intelligent thought that...it would be greatly perfectionated."