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Patent policy, investment and social welfare
Accepted Manuscript
Patent Policy, Investment and Social Welfare. James Bergin PII: DOI: Reference:
S0167-7187(18)30072-9 https://doi.org/10.1016/j.ijindorg.2018.08.007 INDOR 2473
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International Journal of Industrial Organization
Received date: Revised date: Accepted date:
5 May 2016 10 August 2018 24 August 2018
Please cite this article as: James Bergin, Patent Policy, Investment and Social Welfare., International Journal of Industrial Organization (2018), doi: https://doi.org/10.1016/j.ijindorg.2018.08.007
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James Bergin
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Patent Policy, Investment and Social Welfare.
Department of Economics & Finance City University of Hong Kong
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Hong Kong August 2018
Keywords: Patents, Investment, Innovation, Welfare. JEL Classification Numbers: D6, O3.
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Corresponding author: James Bergin.
Abstract
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This paper considers patent policy in an environment where firms are heterogeneous, differentiated by their technologies, and where the impact of policy varies across firms. More stringent (restrictive) patent policy
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reduces access to patented knowledge and affects both profitability and the innovation performance of a firm. This in turn changes a firm’s in-
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centives to invest in innovation. The paper studies circumstances where, comparing two firms where one has a technology weaker than the other
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(ranked lower in the technology comparison), the impact on the technologically weaker firm of such policy is either more or less severe than on the strong firm. In each case the consequence for investment in innovation is examined. The welfare implications of such policies are also considered. One feature of the paper is that the formulation allows for a broad and multidimensional description of technologies.
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Acknowledgement: Thanks are due to the editor and two anonymous referees
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for many helpful comments.
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Introduction
The purpose of patent law is to encourage innovation by attaching property rights to discovery, thus allowing the innovator to recoup investment costs. A
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patent allows the owner to fully exploit the innovation, with the right to pre-
vent its use by others. But exclusion creates incentives for those excluded — denying access to a technology may spur innovation. For example, reduced access to others’ discovery may make it more attractive for a firm to develop its
own technology. This paper examines how varying patent restrictiveness (the strength of patent protection) affects such investment incentives.
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In the environment here, a large number of firms invest in R&D each period to improve technology. Profitability and innovation success depends on a
firm’s own level of technological advancement, its level of investment, its access to other technologies and the distribution of competitors characteristics. Changes in patent restrictiveness affect access to other technologies and hence a firm’s profitability and innovation performance. Firms have different technolo-
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gies, and greater restrictiveness of access to IP (intellectual property) affects firms with different technologies differently, and this feeds through to investment incentives. The way in which this differential impact across firms occurs
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determines the firm’s investment response. Here, two environments are examined. In one, the impact on profitability and innovation success is greater for technologically weaker firms (reflecting greater dependency on outside innova-
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tion), so the advantage to being a better firm is heightened, motivating an increase in investment.1 Provided increased restrictiveness improves (or doesn’t
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weaken) the impact of investment in improving a firm’s technology, there is an incentive for each firm to invest in innovation. In a contrasting environment, weak technology firms rely less on outside technology; better firms suffer greater
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impact when access is reduced. So, increased restrictiveness lowers the relative value of having good technology (again in terms of profitability and capacity to 1 Here technologies are partially ordered. One firm may have a higher ranked technology than another, according to the ordering, but this need not be the case. (The technologies may not be comparable.) When two firms technologies are comparable, say that one is stronger (or weaker) than the other if, according to the ordering, it is ranked higher (or lower). When using the term ‘technologically weaker firm’, the implicit comparison is to a firm with a higher ranked technology.
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innovate). If, additionally, increased restrictiveness worsens (or doesn’t raise) the productivity of investment, with the relative benefit to being technologically good lower, each firm has lower incentive to invest leading to a decline in
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investment. These models are explored in sections 3.1 and 3.2, followed by a discussion of welfare.
The impact of varying patent restrictiveness (measured by patent length or breadth) in optimal patent design has been studied extensively. Nordhaus [1, 2] considered varying patent length and breadth to encourage cost reducing
innovation. There, breadth is the fraction of a cost reduction due to innovation
that does not become freely available after the patent is granted. Gilbert and
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Shapiro [3], Gallini [4], Denicolo [5], Kotowitz and Schure [6] and Takalo [7] consider various aspects of the design of patent policy, in particular the tradeoff between length and breadth. Whatever the perspective, increasing length or breadth imply a more stringent patent policy. Here in examining investment incentives, the distinction (between length and breadth) will be ignored and the term ‘restrictiveness’ used to denote a tighter or more stringent patent policy.
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An outline of the paper is as follows. Section (2) describes the key features of the model: profit, technology and it’s evolution. Section (3) gives the main and welfare.
The Model
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results relating investment to patent policy and section (4) discusses investment
Each firm has its own technology and invests each period. The investment deci-
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sion generates current cost but improves the technology of the firm in subsequent periods. The firm’s profit, which depends on its technology is determined each
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period in market equilibrium. Technology is protected by the patent regime, but firms may use technologies outside patent protection and may benefit from the presence of other patented technologies (by limited imitation, adaptation and so forth.) There are a continuum of firms and so there is a distribution of technologies at any period in time. This distribution evolves over time as firms invest in innovation. The technological evolution of the firm and the corresponding
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profit flow are described next.
2.1
Technology and Innovation
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Denote a firm’s technology by α P Λ, where Λ is the set of all possible technologies. The set of technologies is assumed to be an ordered space with (partial)
order ľ, so technologies may not be comparable. This contrasts with com-
mon practice of specifying technology space as univariate and fully ordered. There are two motivations for this. First, non-comparable technologies arise naturally, even when technology is characterized by a scalar.2 Second, multi-
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dimensionality of technology is commonplace (For example, DRAM memory chips are characterized by access time, refresh rate and other features.)3 When
α1 ľ α and α1 ‰ α, then α1 is a better (or higher ) technology. One attractive
feature of this general formulation is that the results, which focus on improvement of technology through investment, do not depend on technologies being comparable or ranked: to examine the firm’s incentives it’s just necessary to
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compare the firm’s better (post investment) technology with its pre-investment technology. (Perhaps a limitation of using a multidimensional technology space is that the generality may limit detailed analysis: a univariate specification
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with a tighter model specification could allow a more detailed evaluation of the different effects driving the results.4 ) A firm invests to improve its technology, α, drawing a better technology, α1 ,
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according to the distribution P . Investment leads to a distribution over better technologies with larger investment improving the distribution. As patent policy
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varies, the benefit to such investment does also and thus the incentive to invest. How such incentives are affected by patent policy is the central focus of the paper. The population of firms is given by a distribution over technologies, say
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2 For example, the most cost efficient technology may depend of the level of production — see remark (A) in the appendix for additional discussion. 3 To illustrate, let the technology space be Λ “ R2 “ tpα , α q | α ě 0, i “ 1, 2u, the 1 2 i ` non-negative orthant. Suppose that α1 “ pα11 , α12 q ľ pα1 , α2 q “ α if and only α1i ě αi , i “ 1, 2. Then, for example, α1 “ p4, 1q and α “ p3, 2q are not comparable. 4 For example, when tighter patent policy leads to increased investment, the welfare effect is ambiguous: tighter policy has a standard negative effect and increased investment a positive effect. Which effect is the more significant for welfare is a question that could be investigated with a tight parametrized model and univariate technology specification.
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µ P PpΛq, where PpΛq is the set of distributions on Λ. Distributions in PpΛq are
ordered in terms of first order stochastic dominance, written µ ě ν if µ first order dominates ν. (See the appendix for details.) Each firm’s technology evolves over
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time. The technology distribution history is µt “ tµτ u´8 τ “t “ pµt , µt´1 , . . .q “ pµt , µt´1 q. Call µt the ambient technology (at time t): it fully describes existing
technology at this time (Note that boldface µt denotes the current and past distributions.)
A firm, α, at time t invests i at cost rpiq to innovate on α. The technology
environment in which it operates is described by µt . A patent regime governs the firm’s access to technology and is characterized by a restrictiveness parameter,
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`, such that larger values of ` denote a greater restriction on a firm’s use of ambient technology. The exact manner in which variations in ` affect firm profitability and R&D performance is central to the paper. The pair pµt , `q
describes the IP structure facing a firm; and that along with the firm’s own technology, α, describe firm α’s knowledge environment. The firm’s technology evolves stochastically — depending on pµt , `q, the firms technology, α, and it’s by P p¨ | µt , α, i, `q.
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level of investment, i. Denote the distribution over α’s next period technology
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Throughout the discussion it is assumed that: (i) having a better technol-
ogy or investing more raises the probability of drawing a better technology, (ii) having less access to technology (through a more restrictive patent regime, `)
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lowers the probability of drawing a good technology, and (iii) better ambient technology (µt ) improves a firm’s ability to innovate. So, P pd˜ α | µt , α, i, `q
is weakly increasing in α, and i; and weakly decreasing in ` (in terms of first
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order stochastic dominance).5 Assumption (ii) captures the impact of patent restrictiveness on the firm’s ability to innovate, as the firm’s freedom to incorporate other technologies is reduced. (For example, when firms must create
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“work-arounds” to achieve a feature available in a patented technology.) Define µ1t ě µt coordinate-wise to mean that µ1t´j ě µt´j for all j ě 0. The kernel,
P pd˜ α | µt , α, i, `q, is assumed to be increasing in µt — in the sense that if µ1t
dominates µt coordinate-wise, then other things equal, a better distribution is 5 See
the appendix for formal definitions and further discussion.
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drawn conditional on µ1t than µt . Better technology in the population and better technology in the public domain improves the firm’s success in innovation. The next sections (2.2 and 2.3) describe the determinants of profit and formu-
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late the model of innovation. Following that, the firm’s optimizing problem and equilibrium behavior are considered (sections 2.4 and 2.5).
2.2
Profit and revenue
The variables, pµt , α, `q, affect a firm’s innovation distribution P , but also the in a simple single market model.
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firm’s profit π: πpµt , α, `q. To illustrate, example (2.1) derives a profit function
Example 2.1: Let firm α have cost given by pµt , α, `q, cpα1 , µt , `q ď cpα, µt , `q if α1 ľ α,
1 2 2 cpα, µt , `qq , where for any cpα, µ1t , `q ď cpα, µt , `q if µ1t ľ µt ,
and cpα, µt , `1 q ě cpα, µt , `q if `1 ě `. (See the appendix for other formu-
lations.) Firm α’s profit at price p is given by maxq pq ´ 21 cpα, µt , `qq 2 givş p p ing q “ cpα,µ with aggregate supply Qs pp, µt , `q “ cpα,µ µt pdαq. To t ,`q t ,`q ´1
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simplify, let cpα, µt , `q “ rϕpα, `qgpµt , `qs
where ϕpα, `q is a scalar quality-
efficiency index of technology (increasing in α), and g an increasing real val-
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ued function of µt reflecting the impact of ambient technology on a firm’s efficiency, and decreasing in `. Finally, suppose that demand is given by pd pQ, µt q “ dpµt qQ´β , β ą 0, where dpµt q measures the impact of ambient
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technology (such as quality). At the market clearing price profit is:
1 1 πpµt , α, `q “ γpµt , `qϕpα, `q “ rdpµt q2 gpµt , `q1´β ϕpµ ¯ t , `q´2β s 1`β ϕpα, `q, ϕpµ ¯ t , `q “ 2
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(1)
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˛
Example (2.1) is discussed in greater detail in the appendix. Later, a monotonicity property of the profit function will be used. It is convenient to introduce the condition here. (See section (3.1) for discussion.) Definition 2.1: Profit is non-decreasing in technology if πpµt , α, `q is nondecreasing in µt . 5
ż
ϕpα, `qdµt
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In example (2.1), considering µt , dpµt q is increasing µt , as is gpµt , `q1´β provided 0 ă β ă 1, while ϕpµ ¯ t , `q, the mean of the individual specific component
is increasing in µt . So, profit is nondecreasing in µt if the overall impact of the
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first two effects dominate (because of the functional form in equation (1)). Next, sections (2.3), (2.4) and (2.5) describes technology evolution, firms choices and equilibrium.
2.3
The Evolution of Technology
The investment strategies of firms in conjunction with the transition kernel,
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P , move the state of the system forward over time (from µt to µt`1 ). Firms investment strategies are represented by a joint distribution, τ , on pi, αq P I ˆΛ, written τ P MpI ˆ Λq. Consistency requires that τ have marginal µ on Λ. Let
the set of distributions on I ˆΛ consistent with µ be denoted Cpµq. Conditioning on α, τ pdi | αq, gives the distribution over investment of firm α. So, given the
current distribution on technologies, µt , if αt invests according to the strategy
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τt p¨ | αt q, then next period the aggregate distribution on technologies is given
by µt`1 .6
it ,αt
P p¨ | µt , αt , it , `qτt pdit | αt qµt pdαt q “
ż
it ,αt
P p¨ | µt , αt , it , `qτt pdit ˆ dαt q (2)
The Firm’s decision.
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2.4
ż
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µt`1 p¨q “
Let vpµt , τ t , α, `q be the present value at time t of the payoff flow to a firm, α, optimizing in each period from this point on, given the distribution up to
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the present, µt , and given a sequence of aggregate distributions τ t “ tτs u8 s“t . With discount rate δ, the firm’s optimization problem is expressed in a Bellman
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equation as:
vpµt , τ t , α, `q “ maxtπpµt , α, `q ´ rpiq ` δ i
ż
vpµt`1 , τ t`1 , α ˜ , `qP pd˜ α | µt , α, i, `qu (3)
6 This is a standard formulation. For example, see Jovanovic and Rosenthal [8], and Bergin and Bernhardt [9]). The appendix provides additional discussion.
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where µt`1 “ pµt`1 , µt q with µt`1 given by equation (2). The function v is
increasing in α: a firm with higher α can imitate the investment strategy of one
2.5
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with lower α and draw stochastically better technology.
Equilibrium.
With investment cost rpiq, if i is an optimal choice for α in equation (3) then (assuming an interior solution): ż
α ˜
vpµt`1 , τ t`1 , α ˜ , `qrP pd˜ α | µt , α, i1 , `q ´ P pd˜ α | µt , α, i, `qs “ 0
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“ 1 ‰ i Ñi i1 ´ i
´r1 piq ` δ lim 1
Assume r1 piq Ñ 8 as i Ñ 8 to ensure a finite solution. The first order condition for i is:7
´r1 piq ` δ
ż
α ˜
vpµt`1 , τ t`1 , α ˜ , `q∆i P p˜ α | µt , α, i, `q “ 0.
(4)
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The expected gain in the continuation payoff equals the additional investment cost. Assume the second order condition for an optimum is satisfied. In equilibrium, if i is chosen at α, the pair pi, αq must satisfy equation (4). Let Et be the
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set of such pairs, so that if pi, αq P Et , then i satisfies the first order condition
for α. Equilibrium requires that at each t, τt pEt q “ 1 and τt satisfies consistency. Establishing the existence of equilibrium is straightforward (Jovanovic
The Impact of Patent Restrictiveness on In-
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and Rosenthal [8], Bergin and Bernhardt [9])
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vestment.
What is the impact on investment of restricting access to patented intellectual property? Here, the impact varies, depending on the quality of the firm. The discussion considers two environments where the impact of the policy change def
∆i P pX | µt , α, i, `q “ limi1 Ñi i1 1´i rP pX | µt , α, i1 , `q ´ P pX | µt , α, i, `qs for each open set X Ď Λ of P p¨ | µt , α, i, `q positive measure. 7 With
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is either greater or less on lower (relative to higher) technology firms. In the first environment, low technology firms are assumed to be more dependent than higher technology firms8 on the use of technology protected by patent: restrict-
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ing access has greater impact on weaker firms, the advantage to being good becomes greater. Provided increased patent restrictiveness doesn’t reduce the
return (success) to investment, weak firms can become better with greater research effort. Put differently, firms can “substitute” investment to compensate
for reduced access to technology. In this environment, overall investment in
R&D increases (see theorem (3.1)). This case is developed in the next section. In the second case, called the complements case, this situation is reversed
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(section (3.2)).
Remark 3.1: In general a change in patent restrictiveness may entail several conflicting effects on investment incentives — clear-cut results obtainable only in the settings of sections (3.1) and (3.2). For example, if conditions pS ´ iq and pC´iiq below are both satisfied, then strengthening patent protection puts
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pressure on weak firms to raise investment in innovation, but the gain from investment in innovation is reduced, providing conflicting incentives.
Investment and Patented Knowledge as Substitutes.
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3.1
Increasing patent restrictiveness, `, affects both profit and innovation perfor-
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mance, but the impact varies depending on a firm’s current technology. If, for example, the (negative) impact is greater on the ability of a weak technology firm to innovate, compared to a high quality firm, then the relative advantage
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to being a good firm (having a good technology) has increased, and investing in technology improvement serves as a substitute for the patented technology. This impact bias against weaker technology firms is expressed by having those
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firms experience greater impact in terms of profitability ((S-i)(a)) and innovation success ((S-i)(b)), so the relative advantage of being a better firm is greater. If, in addition, increasing ` raises the marginal product of investment then it is easier for investment to compensate for the loss of access to patented technol8 So,
if α1 ľ α, α is more dependent on patented technology, as defined in section 3.1.
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ogy (S-ii). These conditions, (S-i) and (S-ii), and payoff monotonicity imply that this compensation takes place. (S-i) Increasing patent restrictiveness, `, or worsening technology, µ has a
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greater impact on weaker firms.
(a) An increase in ` or fall in µ impacts current profits of better firms less than weaker firms:
πpµ1 , α, `1 q ´ πpµ, α, `q, is increasing in α, for `1 ě `, µ1 ď µ
(b) An increase in ` or fall in µ worsens the technology draw of weaker
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firms more. For g increasing: ş ş gp˜ αqP pd˜ α | µ1 , α, i, `1 q´ gp˜ αqP pd˜ α | µ, α, i, `q, is increasing in α, for `1 ě `, µ1 ď µ
(S-ii) Increasing patent restrictiveness, `, raises the marginal productivity of investment for each α. For g increasing: ş ş gp˜ αq∆i P pd˜ α | µ, α, i, `1 q ě α˜ gp˜ αq∆i P pd˜ α | µ, α, i, `q, α ˜
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`
for `1 ě
Condition (S-i) captures how variations in patent restrictiveness affects firms
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differentially. To motivate the condition, suppose that increasing patent restrictiveness lowers firms profits. Then, with `1 ą `, ∆π “ π 1 ´ π “ πpµ, α, `1 q ´ πpµ, α, `q is negative. Condition (S-i)(a) requires that ∆π is increasing in α:
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if α1 is a better technology than α (α1 ľ α), 0 ą πpµ, α1 , `1 q ´ πpµ, α1 , `q ą πpµ, α, `1 q ´ πpµ, α, `q. Thus, reduced access to technology (`1 ě `) has greater
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(adverse) impact on the weaker firm. Under regime `1 the relative advantage to being a better firm has increased.9 Condition (S-i)(b) concerns the impact of patent tightening on innovation performance. Greater restrictiveness has no
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impact on a firm’s use of its own technology, but it restricts access to ambient technology. Given (S-i)(b), the impact is greater on weaker firms.10 Again, the effect is to increase the relative advantage to being good.
9 Alternatively, extra patent protection may increase the value of a firm’s IP (in terms of profit), so ∆π ą 0, and if the benefit is greater to better firms, then again ∆π is increasing in α (see the appendix for further discussion). 10 Implicitly, weak technology firms make greater use of innovation in the public domain. Reduced access affects them more.
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Condition (S-ii) asserts that the marginal productivity of investment for all firms is increased when access to patented technology is reduced (` increased). A firm’s marginal research productivity (given by ∆i P ) is measured by how
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P pd˜ α | µ, α, i, `q changes due to a small change in i. With assumption (S-ii),
the more technology is publicly accessible, the less the value to creating more technology. Conversely, the less technology is publicly available (as ` increases),
the higher the marginal productivity of investment. In statistical theory, this has a natural interpretation. The less data available, the greater the benefit
from additional data (for example, the reduction of the variance in the sample
estimator declines as the sample size increases).11 A similar idea appears in
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the literature on innovation and unit cost reduction. Gottschalk and Janz [11]
and Levin and Reiss [12] model production cost as dependent on the firm’s own innovation and the pool of industry knowledge. (Cost depends on both own R&D and outside R&D). There, the lower is the pool of industry available R&D, the greater the firm’s marginal reduction of unit cost from increasing it’s R&D investment. Conversely, the greater is the outside pool of R&D, the lower
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the marginal impact of the firm increasing it’s R&D investment to reduce it’s unit cost. Here, (S-ii) plays an analogous role: increasing ` reduces access to
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outside the pool of technology and raises the marginal product of the firm’s investment in terms of technology improvement. With monotonicity of profit in technology, conditions (S-i) and (S-ii) are shown to imply that increasing
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patent restrictiveness leads to increased investment. Theorem 3.1: Suppose that profit increases with technology improvement and assumptions (S-i) and (S-ii) are satisfied. Then increasing patent restrictiveness
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improves the aggregate distribution of technologies in successive periods. As noted already, under (S-i) and (S-ii), increasing ` incentivizes firms to raise
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investment. And this increases the quality of the aggregate distribution. Monotonicity of profit in µt ensures the increased investment incentive is not reversed by a payoff decline as the aggregate distribution improves.12 Further motivation for this result and theorem (3.2) are given in section (3.3) where positive
11 See Bikhchandani and Mamer [10] for discussion of the marginal valuation of information, measured with a loss-function. 12 Without this assumption it would still be reasonable to expect that even if the resulting
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or negative covariation between i and ` is viewed from the perspective of superor sub-modularity. Note that the impact on welfare is ambiguous. Raising ` increases investment which is welfare improving (because of positive externalities
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in investment), but the greater restrictiveness has the usual negative welfare effects by restricting usage.
3.2
Investment and Patented Knowledge as Complements.
A contrasting view of increasing patent restrictiveness is that the impact is great-
est on high technology firms.13 Suppose that is the case, and in addition, that
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increasing patent restrictiveness reduces the marginal product of investment.14
Together, these effects work to dis-incentivize investment in innovation: increasing patent restrictiveness reduces the value of being a good firm and lowers the productivity of investment in improving one’s technology. To express these conditions in the model, suppose instead that better firms are more dependent on patented knowledge to generate current profit (π) and innovate (P ), so that such
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knowledge is a complement to the quality of a firms’ technology.15 Suppose also that increasing patent restrictiveness removes from use knowledge that would otherwise raise the marginal product of investment. Conditions (C-i) and (C-ii)
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formalize these properties.
(C-i) Increasing patent restrictiveness, `, or worsening technology, µt , has a
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greater impact on better firms. (a) An increase in `, or fall in µ lowers profits of better firms more than
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weaker firms: πpµ1 , α, `1 q ´ πpµ, α, `q, is decreasing in α, for `1 ě `, µ1 ď µ
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improvement in the technology distribution dis-incentivizes investment by lowering profit, it would dampen but not fully offset the initial incentive to increase investment due to the ` increase. 13 For example, because better firms make greater use (than weak firms) of intellectual property created by others, so that greater limitation on access to that intellectual property has a bigger impact. 14 Suggesting that increased access to patented raises the marginal product of investment and that investment is complemented by patented technology. 15 Alternatively, regarding profit, suppose that increasing ` raises profit via extra protection for each firm’s innovation, but the extra restrictiveness benefits weak firms more, possibly because more peripheral technology held by weak firms becomes patent protected.
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(b) An increase in `, or fall in µ worsens the technology draw of better firms more. For g increasing: ş ş gp˜ αqP pd˜ α | µ1 , α, i, `1 q´ gp˜ αqP pd˜ α | µ, α, i, `q, is decreasing in α, for `1 ě
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`, µ1 ď µ
(C-ii) Increasing patent restrictiveness lowers the marginal productivity of investment for each α. For g increasing: ş ş gp˜ αq∆i P pd˜ α | µ, α, i, `1 q ď α˜ gp˜ αq∆i P pd˜ α | µ, α, i, `q, α ˜
`
for `1 ě
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Assumption (C-i)(a) asserts that when increasing restrictiveness lowers prof-
itability, the impact is greater on good firms.16 Assumption (C-i)(b) expresses a similar effect (greater negative impact on better firms), but in terms of the impact on innovation of increased patent restrictiveness. Finally, (C-ii) says that increasing patent restrictiveness lowers the marginal productivity of investment in generating innovation. Under these circumstances, with profit monotonicity,
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greater restrictiveness lowers investment.
Theorem 3.2: Suppose that profit increases with technology improvement and
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assumptions (C-i) and (C-ii) are satisfied. Then increasing patent restrictiveness worsens the aggregate distributions in successive periods.
Some motivating discussion.
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3.3
The previous sections give conditions under which variations in investment are
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positively or negatively associated with changes in the restrictiveness of patent policy. Changes in patent restrictiveness affect both profitability and the impact of investment on R&D which in turn alters optimal investment decisions.
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The combination of such effects generates the investment response to increased restrictiveness. Under the substitutes or the complements conditions, the impact on investment is unambiguous (either positive or negative covariation of restrictiveness and investment). 16 Or, if increased restrictiveness raises a firms profitability, the gain is relatively less for a good firm.
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To motivate those conditions, recall firm α’s optimization problem given by equation (3):
i
ż
( vpµt`1 , τ t`1 , α ˜ , `qP pd˜ α | µt , α, i, `q (5)
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vpµt , τ t , α, `q “ max πpµt , α, `q ´ rpiq ` δ
Simplifying the discussion, assume pµt , µt`1 , τ t`1 q as fixed, or alternatively assume that neither the profit function or transition kernel depend on the ag-
gregate distribution. In this case, write v¯pα, i, `q for the term inside t¨ ¨ ¨ u, so
firm α solves maxi t¯ v pα, i, `qu. The solution i, varies with ` and this co-variation of investment and restrictiveness of patent policy (positive covariation in the
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substitutes case; negative in the complements case) captures the investment response to variation in restrictiveness. This may be viewed from the perspective
of super or sub-modularity. Given α, the function v¯pα, i, `q is supermodular if v B B¯ B` t Bi u
ě 0 (and submodular if
B B¯ v B` t Bi u
ď 0). With supermodularity, increasing
` has α’s best response be to raise i. Under what circumstances will this be so? Essentially, the conditions on the profit and transition kernel in (S-i), (S-ii)
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lead to a supermodular payoff function v¯, and a positive association between investment and patent restrictiveness (and the conditions (C-i), (C-ii) to a sub-
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modular function).17 Further motivation in the appendix clarifies the specific mechanism and connection to the assumptions in greater detail.
Efficiency and Welfare
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This section notes some welfare implications of the model. First, equilibrium is
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inefficient: at any level of patent restrictiveness, investment is below the socially optimal level. Second, in the complements case increasing ` lowers welfare; in
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the substitutes case, the conclusion is ambiguous. Finally, for a general model of total social welfare, the optimal value of ` in a social planner problem is ` “ 0. Turning to overall welfare (consumer and producer), increased invest-
ment improves the aggregate distribution of technologies over time, so provided improved technology raises consumer welfare, the overall effect is unambigu-
17 The additional complication that must be addressed is the knock-on impact from the resulting aggregate investment change back to individual decisions.
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ously positive.18 When investment is chosen to maximize overall welfare for a given value of `, the optimal value of ` is 0. This is discussed next. Let TSpµt , `q be a measure of consumer and producer welfare (total surplus) at time t, which
TSpµ1t , `1 q ´ TSpµt , `q ě 0,
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depends on the distribution of characteristics and the patent policy (in examşQ ˜ µq ´ ps pQ, ˜ µ, `qsdQ). ˜ Assume that: ple 2.1, TSpµ, `q “ maxQ 0 rpd pQ, µ1t ě µt , `1 ď `
(6)
so that improving technologies or reducing patent protection on existing tech-
nologies raises current welfare. Maximizing the present value of total surplus,
V pµ, `q “
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less the investment costs gives the program:
max tTSpµ, `q ´
τ PCpµq
ż
rpiqdτ ` δV pµ1 , `qu
(7)
ş where µ1 “ pµ1 , µq, with µ1 determined from µ1 p¨q “ P p¨ | α, µ, i, `qτ pdi ˆ dαq.
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Lemma 4.1: Social welfare, V pµ, `q, is decreasing in `.
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So, if the social planner maximizes welfare by choice of investment (with `
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exogenous), welfare decreases in `. According to theorems (3.1) and (3.2), if investment and patented technology are substitutes, increasing ` raises investment; and if complements, increasing ` reduces investment. How does welfare
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in equilibrium compare with the socially optimal level V pµ, `q? Here, in equiş librium producer surplus at time t is PSpµt , `q “ πpµt , α, `qµt pdαq. Total surplus, TSpµt , `q, at time t is the sum of producer and consumer surplus de-
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termined by the equilibrium. In equilibrium, from period t, let µet`j be the resulting distribution at time t ` j and µt`j “ pµet`j , µet`j´1 , . . . , µet`1 , µt q. The
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welfare generated with equilibrium investment is then (from time t), VE pµt , `q “ ş ř8 j j“0 δ rTSpµt`j , `q ´ α rpit`j qµt`j pdαqs.
By definition, VE pµt , `q ď V pµt , `q. From lemma (4.1), V pµt , `q is decreasing
in `. Considering the complements case, the impact of increasing ` is to worsen
18 Note that the social welfare optimization problem must respect the same intellectual property rights as appear in the individual firm problem: it addresses the externality issues, subject to access to technology being restricted according to the patent strength, `.
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the negative externality and reduce investment (which is already below the socially optimal level). So in the complements case, welfare decreases. In the substitutes case there are two effects at work: the direct effect of increasing welfare improving. Summarizing these observations:
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` worsens the negative externality, but the resulting increase in investment is
Theorem 4.1: Let VE pµ, `q denote equilibrium total surplus, and let V pµ, `q
be surplus under the social planner as defined in equation (7). Then V pµ, `q ě VE pµ, `q and V pµ, `q is declining in `. In the complements case, VE pµ, `q declines in `; in the substitutes case, VE pµ, `q may not be monotonic in `.
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Thus, increasing ` unambiguously worsens welfare in the complements case. In the substitutes case the impact is ambiguous as increasing investment and greater restrictiveness have opposite effects on welfare.
Conclusion
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5
A common view of patent incentives is that the ownership right to exploit discovery motivates investment in R&D: the patent is a prize or reward (of monopoly
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rights) compensating for investment and effort. From a policy perspective, this views each patent in isolation. Here, innovation is viewed as a flow with R&D building on an existing pool of intellectual property, and where access and ability
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to use that pool provides an important incentive. Patent policy affects access to that pool and how firms leverage it directly for profit and as a means to support their R&D. This raises policy questions. For example, how does patent policy
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feed through to incentives? If tightening patent policy encourages investment, does it do so because the innovation reward is greater or because firms are forced
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to greater dependency on own innovation and hence need to improve their own technology? At a more detailed level, the paper highlights the asymmetric incentives that
the patent system creates for different firms to invest. If, for example, tighter patent policy lowers firms profits, but the impact is greater on weaker firms, then weaker firms have a relatively greater incentive to improve. However, the
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channels through which these effects work are complex and may conflict: tighter patent policy may increase the incentive to improve but lower the productivity of investment in R&D. Weaker patent protection may reduce the direct incentive
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to invest in R&D, but makes available a larger portion of exisiting technology. What effects discussed here are likely to be the most important in deciding if a more restrictive patent policy encourages investment by raising the relative reward gap between a firm and others with better technology?
At the level of generality of the model developed here, these questions are dif-
ficult to investigate but suggest a direction for research with a more specialized
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model where the key functions and parameters are more tightly formulated.
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References [1] Nordhaus, W. D., The Optimal Life of a Patent, Cowles Foundation Dis-
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cussion Paper No. 241. [2] W. D. Nordhaus, The Optimum Life of a Patent: Reply, American Economic Review 62 (358) (1972) 428–431.
[3] Gilbert, R. and Shapiro, C., Optimal Patent Length and Breadth, The Rand Journal of Economics 21, No. 1 (1990) 106–112.
[4] Gallini, N., Patent Length and Breadth with Costly Imitation, The Rand
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Journal of Economics 44 (1992) 52–63.
[5] Denicolo, V., Patent Races and Optimal Patent Breadth and Length, Journal of Industrial Economics 44, No. 3 (1996) 249–265.
[6] Kotowitz, Y. and Schure, P., The Optimal Patent Length, mimeo, Univer-
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sity of Victoria, Canada.
[7] Takalo, T., On the Optimality of patent Policy, Finnish Economic Papers
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14(1) (2001) 33–40.
[8] Jovanovic, B. and Rosenthal, R.W., Anonymous sequential games, Journal of Mathematical Economics (1988) 77–87.
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[9] Bergin, J. and Bernhardt, D., Anonymous sequential games: existence and characterization of equilibria, Economic Theory 5 (1995) 461–489.
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[10] Sushil Bikhchandani and John W. Mamer, Decreasing Marginal Value of Information Under Symmetric Loss, Decision Analysis 10 (358) (2013) 245–
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256.
[11] Gottschalk, S. and Janz, N., Innovation Dynamics and Endogenous Market Structure, Dew discussion paper 01-39, Centre for European Economic Research (2001).
[12] R. C. Levin, P. C. Reiss, Cost-Reducing and Demand-Creating R&D with Spillovers, The Rand Journal of Economics 19 (1998) 538–556. 36
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[13] Torres, R., Stochastic Dominance, Northwestern Discussion paper.
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Patent Policy, Investment and Social Welfare. James Bergin PII: DOI: Reference:
S0167-7187(18)30072-9 https://doi.org/10.1016/j.ijindorg.2018.08.007 INDOR 2473
To appear in:
International Journal of Industrial Organization
Received date: Revised date: Accepted date:
5 May 2016 10 August 2018 24 August 2018
Please cite this article as: James Bergin, Patent Policy, Investment and Social Welfare., International Journal of Industrial Organization (2018), doi: https://doi.org/10.1016/j.ijindorg.2018.08.007
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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James Bergin
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Patent Policy, Investment and Social Welfare.
Department of Economics & Finance City University of Hong Kong
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Hong Kong August 2018
Keywords: Patents, Investment, Innovation, Welfare. JEL Classification Numbers: D6, O3.
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Corresponding author: James Bergin.
Abstract
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This paper considers patent policy in an environment where firms are heterogeneous, differentiated by their technologies, and where the impact of policy varies across firms. More stringent (restrictive) patent policy
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reduces access to patented knowledge and affects both profitability and the innovation performance of a firm. This in turn changes a firm’s in-
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centives to invest in innovation. The paper studies circumstances where, comparing two firms where one has a technology weaker than the other
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(ranked lower in the technology comparison), the impact on the technologically weaker firm of such policy is either more or less severe than on the strong firm. In each case the consequence for investment in innovation is examined. The welfare implications of such policies are also considered. One feature of the paper is that the formulation allows for a broad and multidimensional description of technologies.
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Acknowledgement: Thanks are due to the editor and two anonymous referees
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for many helpful comments.
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1
Introduction
The purpose of patent law is to encourage innovation by attaching property rights to discovery, thus allowing the innovator to recoup investment costs. A
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patent allows the owner to fully exploit the innovation, with the right to pre-
vent its use by others. But exclusion creates incentives for those excluded — denying access to a technology may spur innovation. For example, reduced access to others’ discovery may make it more attractive for a firm to develop its
own technology. This paper examines how varying patent restrictiveness (the strength of patent protection) affects such investment incentives.
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In the environment here, a large number of firms invest in R&D each period to improve technology. Profitability and innovation success depends on a
firm’s own level of technological advancement, its level of investment, its access to other technologies and the distribution of competitors characteristics. Changes in patent restrictiveness affect access to other technologies and hence a firm’s profitability and innovation performance. Firms have different technolo-
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gies, and greater restrictiveness of access to IP (intellectual property) affects firms with different technologies differently, and this feeds through to investment incentives. The way in which this differential impact across firms occurs
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determines the firm’s investment response. Here, two environments are examined. In one, the impact on profitability and innovation success is greater for technologically weaker firms (reflecting greater dependency on outside innova-
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tion), so the advantage to being a better firm is heightened, motivating an increase in investment.1 Provided increased restrictiveness improves (or doesn’t
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weaken) the impact of investment in improving a firm’s technology, there is an incentive for each firm to invest in innovation. In a contrasting environment, weak technology firms rely less on outside technology; better firms suffer greater
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impact when access is reduced. So, increased restrictiveness lowers the relative value of having good technology (again in terms of profitability and capacity to 1 Here technologies are partially ordered. One firm may have a higher ranked technology than another, according to the ordering, but this need not be the case. (The technologies may not be comparable.) When two firms technologies are comparable, say that one is stronger (or weaker) than the other if, according to the ordering, it is ranked higher (or lower). When using the term ‘technologically weaker firm’, the implicit comparison is to a firm with a higher ranked technology.
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innovate). If, additionally, increased restrictiveness worsens (or doesn’t raise) the productivity of investment, with the relative benefit to being technologically good lower, each firm has lower incentive to invest leading to a decline in
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investment. These models are explored in sections 3.1 and 3.2, followed by a discussion of welfare.
The impact of varying patent restrictiveness (measured by patent length or breadth) in optimal patent design has been studied extensively. Nordhaus [1, 2] considered varying patent length and breadth to encourage cost reducing
innovation. There, breadth is the fraction of a cost reduction due to innovation
that does not become freely available after the patent is granted. Gilbert and
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Shapiro [3], Gallini [4], Denicolo [5], Kotowitz and Schure [6] and Takalo [7] consider various aspects of the design of patent policy, in particular the tradeoff between length and breadth. Whatever the perspective, increasing length or breadth imply a more stringent patent policy. Here in examining investment incentives, the distinction (between length and breadth) will be ignored and the term ‘restrictiveness’ used to denote a tighter or more stringent patent policy.
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An outline of the paper is as follows. Section (2) describes the key features of the model: profit, technology and it’s evolution. Section (3) gives the main and welfare.
The Model
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2
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results relating investment to patent policy and section (4) discusses investment
Each firm has its own technology and invests each period. The investment deci-
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sion generates current cost but improves the technology of the firm in subsequent periods. The firm’s profit, which depends on its technology is determined each
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period in market equilibrium. Technology is protected by the patent regime, but firms may use technologies outside patent protection and may benefit from the presence of other patented technologies (by limited imitation, adaptation and so forth.) There are a continuum of firms and so there is a distribution of technologies at any period in time. This distribution evolves over time as firms invest in innovation. The technological evolution of the firm and the corresponding
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profit flow are described next.
2.1
Technology and Innovation
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Denote a firm’s technology by α P Λ, where Λ is the set of all possible technologies. The set of technologies is assumed to be an ordered space with (partial)
order ľ, so technologies may not be comparable. This contrasts with com-
mon practice of specifying technology space as univariate and fully ordered. There are two motivations for this. First, non-comparable technologies arise naturally, even when technology is characterized by a scalar.2 Second, multi-
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dimensionality of technology is commonplace (For example, DRAM memory chips are characterized by access time, refresh rate and other features.)3 When
α1 ľ α and α1 ‰ α, then α1 is a better (or higher ) technology. One attractive
feature of this general formulation is that the results, which focus on improvement of technology through investment, do not depend on technologies being comparable or ranked: to examine the firm’s incentives it’s just necessary to
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compare the firm’s better (post investment) technology with its pre-investment technology. (Perhaps a limitation of using a multidimensional technology space is that the generality may limit detailed analysis: a univariate specification
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with a tighter model specification could allow a more detailed evaluation of the different effects driving the results.4 ) A firm invests to improve its technology, α, drawing a better technology, α1 ,
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according to the distribution P . Investment leads to a distribution over better technologies with larger investment improving the distribution. As patent policy
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varies, the benefit to such investment does also and thus the incentive to invest. How such incentives are affected by patent policy is the central focus of the paper. The population of firms is given by a distribution over technologies, say
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2 For example, the most cost efficient technology may depend of the level of production — see remark (A) in the appendix for additional discussion. 3 To illustrate, let the technology space be Λ “ R2 “ tpα , α q | α ě 0, i “ 1, 2u, the 1 2 i ` non-negative orthant. Suppose that α1 “ pα11 , α12 q ľ pα1 , α2 q “ α if and only α1i ě αi , i “ 1, 2. Then, for example, α1 “ p4, 1q and α “ p3, 2q are not comparable. 4 For example, when tighter patent policy leads to increased investment, the welfare effect is ambiguous: tighter policy has a standard negative effect and increased investment a positive effect. Which effect is the more significant for welfare is a question that could be investigated with a tight parametrized model and univariate technology specification.
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µ P PpΛq, where PpΛq is the set of distributions on Λ. Distributions in PpΛq are
ordered in terms of first order stochastic dominance, written µ ě ν if µ first order dominates ν. (See the appendix for details.) Each firm’s technology evolves over
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time. The technology distribution history is µt “ tµτ u´8 τ “t “ pµt , µt´1 , . . .q “ pµt , µt´1 q. Call µt the ambient technology (at time t): it fully describes existing
technology at this time (Note that boldface µt denotes the current and past distributions.)
A firm, α, at time t invests i at cost rpiq to innovate on α. The technology
environment in which it operates is described by µt . A patent regime governs the firm’s access to technology and is characterized by a restrictiveness parameter,
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`, such that larger values of ` denote a greater restriction on a firm’s use of ambient technology. The exact manner in which variations in ` affect firm profitability and R&D performance is central to the paper. The pair pµt , `q
describes the IP structure facing a firm; and that along with the firm’s own technology, α, describe firm α’s knowledge environment. The firm’s technology evolves stochastically — depending on pµt , `q, the firms technology, α, and it’s by P p¨ | µt , α, i, `q.
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level of investment, i. Denote the distribution over α’s next period technology
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Throughout the discussion it is assumed that: (i) having a better technol-
ogy or investing more raises the probability of drawing a better technology, (ii) having less access to technology (through a more restrictive patent regime, `)
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lowers the probability of drawing a good technology, and (iii) better ambient technology (µt ) improves a firm’s ability to innovate. So, P pd˜ α | µt , α, i, `q
is weakly increasing in α, and i; and weakly decreasing in ` (in terms of first
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order stochastic dominance).5 Assumption (ii) captures the impact of patent restrictiveness on the firm’s ability to innovate, as the firm’s freedom to incorporate other technologies is reduced. (For example, when firms must create
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“work-arounds” to achieve a feature available in a patented technology.) Define µ1t ě µt coordinate-wise to mean that µ1t´j ě µt´j for all j ě 0. The kernel,
P pd˜ α | µt , α, i, `q, is assumed to be increasing in µt — in the sense that if µ1t
dominates µt coordinate-wise, then other things equal, a better distribution is 5 See
the appendix for formal definitions and further discussion.
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drawn conditional on µ1t than µt . Better technology in the population and better technology in the public domain improves the firm’s success in innovation. The next sections (2.2 and 2.3) describe the determinants of profit and formu-
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late the model of innovation. Following that, the firm’s optimizing problem and equilibrium behavior are considered (sections 2.4 and 2.5).
2.2
Profit and revenue
The variables, pµt , α, `q, affect a firm’s innovation distribution P , but also the in a simple single market model.
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firm’s profit π: πpµt , α, `q. To illustrate, example (2.1) derives a profit function
Example 2.1: Let firm α have cost given by pµt , α, `q, cpα1 , µt , `q ď cpα, µt , `q if α1 ľ α,
1 2 2 cpα, µt , `qq , where for any cpα, µ1t , `q ď cpα, µt , `q if µ1t ľ µt ,
and cpα, µt , `1 q ě cpα, µt , `q if `1 ě `. (See the appendix for other formu-
lations.) Firm α’s profit at price p is given by maxq pq ´ 21 cpα, µt , `qq 2 givş p p ing q “ cpα,µ with aggregate supply Qs pp, µt , `q “ cpα,µ µt pdαq. To t ,`q t ,`q ´1
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simplify, let cpα, µt , `q “ rϕpα, `qgpµt , `qs
where ϕpα, `q is a scalar quality-
efficiency index of technology (increasing in α), and g an increasing real val-
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ued function of µt reflecting the impact of ambient technology on a firm’s efficiency, and decreasing in `. Finally, suppose that demand is given by pd pQ, µt q “ dpµt qQ´β , β ą 0, where dpµt q measures the impact of ambient
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technology (such as quality). At the market clearing price profit is:
1 1 πpµt , α, `q “ γpµt , `qϕpα, `q “ rdpµt q2 gpµt , `q1´β ϕpµ ¯ t , `q´2β s 1`β ϕpα, `q, ϕpµ ¯ t , `q “ 2
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(1)
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˛
Example (2.1) is discussed in greater detail in the appendix. Later, a monotonicity property of the profit function will be used. It is convenient to introduce the condition here. (See section (3.1) for discussion.) Definition 2.1: Profit is non-decreasing in technology if πpµt , α, `q is nondecreasing in µt . 5
ż
ϕpα, `qdµt
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In example (2.1), considering µt , dpµt q is increasing µt , as is gpµt , `q1´β provided 0 ă β ă 1, while ϕpµ ¯ t , `q, the mean of the individual specific component
is increasing in µt . So, profit is nondecreasing in µt if the overall impact of the
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first two effects dominate (because of the functional form in equation (1)). Next, sections (2.3), (2.4) and (2.5) describes technology evolution, firms choices and equilibrium.
2.3
The Evolution of Technology
The investment strategies of firms in conjunction with the transition kernel,
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P , move the state of the system forward over time (from µt to µt`1 ). Firms investment strategies are represented by a joint distribution, τ , on pi, αq P I ˆΛ, written τ P MpI ˆ Λq. Consistency requires that τ have marginal µ on Λ. Let
the set of distributions on I ˆΛ consistent with µ be denoted Cpµq. Conditioning on α, τ pdi | αq, gives the distribution over investment of firm α. So, given the
current distribution on technologies, µt , if αt invests according to the strategy
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τt p¨ | αt q, then next period the aggregate distribution on technologies is given
by µt`1 .6
it ,αt
P p¨ | µt , αt , it , `qτt pdit | αt qµt pdαt q “
ż
it ,αt
P p¨ | µt , αt , it , `qτt pdit ˆ dαt q (2)
The Firm’s decision.
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2.4
ż
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µt`1 p¨q “
Let vpµt , τ t , α, `q be the present value at time t of the payoff flow to a firm, α, optimizing in each period from this point on, given the distribution up to
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the present, µt , and given a sequence of aggregate distributions τ t “ tτs u8 s“t . With discount rate δ, the firm’s optimization problem is expressed in a Bellman
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equation as:
vpµt , τ t , α, `q “ maxtπpµt , α, `q ´ rpiq ` δ i
ż
vpµt`1 , τ t`1 , α ˜ , `qP pd˜ α | µt , α, i, `qu (3)
6 This is a standard formulation. For example, see Jovanovic and Rosenthal [8], and Bergin and Bernhardt [9]). The appendix provides additional discussion.
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where µt`1 “ pµt`1 , µt q with µt`1 given by equation (2). The function v is
increasing in α: a firm with higher α can imitate the investment strategy of one
2.5
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with lower α and draw stochastically better technology.
Equilibrium.
With investment cost rpiq, if i is an optimal choice for α in equation (3) then (assuming an interior solution): ż
α ˜
vpµt`1 , τ t`1 , α ˜ , `qrP pd˜ α | µt , α, i1 , `q ´ P pd˜ α | µt , α, i, `qs “ 0
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“ 1 ‰ i Ñi i1 ´ i
´r1 piq ` δ lim 1
Assume r1 piq Ñ 8 as i Ñ 8 to ensure a finite solution. The first order condition for i is:7
´r1 piq ` δ
ż
α ˜
vpµt`1 , τ t`1 , α ˜ , `q∆i P p˜ α | µt , α, i, `q “ 0.
(4)
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The expected gain in the continuation payoff equals the additional investment cost. Assume the second order condition for an optimum is satisfied. In equilibrium, if i is chosen at α, the pair pi, αq must satisfy equation (4). Let Et be the
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set of such pairs, so that if pi, αq P Et , then i satisfies the first order condition
for α. Equilibrium requires that at each t, τt pEt q “ 1 and τt satisfies consistency. Establishing the existence of equilibrium is straightforward (Jovanovic
The Impact of Patent Restrictiveness on In-
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3
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and Rosenthal [8], Bergin and Bernhardt [9])
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vestment.
What is the impact on investment of restricting access to patented intellectual property? Here, the impact varies, depending on the quality of the firm. The discussion considers two environments where the impact of the policy change def
∆i P pX | µt , α, i, `q “ limi1 Ñi i1 1´i rP pX | µt , α, i1 , `q ´ P pX | µt , α, i, `qs for each open set X Ď Λ of P p¨ | µt , α, i, `q positive measure. 7 With
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is either greater or less on lower (relative to higher) technology firms. In the first environment, low technology firms are assumed to be more dependent than higher technology firms8 on the use of technology protected by patent: restrict-
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ing access has greater impact on weaker firms, the advantage to being good becomes greater. Provided increased patent restrictiveness doesn’t reduce the
return (success) to investment, weak firms can become better with greater research effort. Put differently, firms can “substitute” investment to compensate
for reduced access to technology. In this environment, overall investment in
R&D increases (see theorem (3.1)). This case is developed in the next section. In the second case, called the complements case, this situation is reversed
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(section (3.2)).
Remark 3.1: In general a change in patent restrictiveness may entail several conflicting effects on investment incentives — clear-cut results obtainable only in the settings of sections (3.1) and (3.2). For example, if conditions pS ´ iq and pC´iiq below are both satisfied, then strengthening patent protection puts
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pressure on weak firms to raise investment in innovation, but the gain from investment in innovation is reduced, providing conflicting incentives.
Investment and Patented Knowledge as Substitutes.
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3.1
Increasing patent restrictiveness, `, affects both profit and innovation perfor-
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mance, but the impact varies depending on a firm’s current technology. If, for example, the (negative) impact is greater on the ability of a weak technology firm to innovate, compared to a high quality firm, then the relative advantage
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to being a good firm (having a good technology) has increased, and investing in technology improvement serves as a substitute for the patented technology. This impact bias against weaker technology firms is expressed by having those
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firms experience greater impact in terms of profitability ((S-i)(a)) and innovation success ((S-i)(b)), so the relative advantage of being a better firm is greater. If, in addition, increasing ` raises the marginal product of investment then it is easier for investment to compensate for the loss of access to patented technol8 So,
if α1 ľ α, α is more dependent on patented technology, as defined in section 3.1.
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ogy (S-ii). These conditions, (S-i) and (S-ii), and payoff monotonicity imply that this compensation takes place. (S-i) Increasing patent restrictiveness, `, or worsening technology, µ has a
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greater impact on weaker firms.
(a) An increase in ` or fall in µ impacts current profits of better firms less than weaker firms:
πpµ1 , α, `1 q ´ πpµ, α, `q, is increasing in α, for `1 ě `, µ1 ď µ
(b) An increase in ` or fall in µ worsens the technology draw of weaker
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firms more. For g increasing: ş ş gp˜ αqP pd˜ α | µ1 , α, i, `1 q´ gp˜ αqP pd˜ α | µ, α, i, `q, is increasing in α, for `1 ě `, µ1 ď µ
(S-ii) Increasing patent restrictiveness, `, raises the marginal productivity of investment for each α. For g increasing: ş ş gp˜ αq∆i P pd˜ α | µ, α, i, `1 q ě α˜ gp˜ αq∆i P pd˜ α | µ, α, i, `q, α ˜
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`
for `1 ě
Condition (S-i) captures how variations in patent restrictiveness affects firms
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differentially. To motivate the condition, suppose that increasing patent restrictiveness lowers firms profits. Then, with `1 ą `, ∆π “ π 1 ´ π “ πpµ, α, `1 q ´ πpµ, α, `q is negative. Condition (S-i)(a) requires that ∆π is increasing in α:
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if α1 is a better technology than α (α1 ľ α), 0 ą πpµ, α1 , `1 q ´ πpµ, α1 , `q ą πpµ, α, `1 q ´ πpµ, α, `q. Thus, reduced access to technology (`1 ě `) has greater
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(adverse) impact on the weaker firm. Under regime `1 the relative advantage to being a better firm has increased.9 Condition (S-i)(b) concerns the impact of patent tightening on innovation performance. Greater restrictiveness has no
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impact on a firm’s use of its own technology, but it restricts access to ambient technology. Given (S-i)(b), the impact is greater on weaker firms.10 Again, the effect is to increase the relative advantage to being good.
9 Alternatively, extra patent protection may increase the value of a firm’s IP (in terms of profit), so ∆π ą 0, and if the benefit is greater to better firms, then again ∆π is increasing in α (see the appendix for further discussion). 10 Implicitly, weak technology firms make greater use of innovation in the public domain. Reduced access affects them more.
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Condition (S-ii) asserts that the marginal productivity of investment for all firms is increased when access to patented technology is reduced (` increased). A firm’s marginal research productivity (given by ∆i P ) is measured by how
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P pd˜ α | µ, α, i, `q changes due to a small change in i. With assumption (S-ii),
the more technology is publicly accessible, the less the value to creating more technology. Conversely, the less technology is publicly available (as ` increases),
the higher the marginal productivity of investment. In statistical theory, this has a natural interpretation. The less data available, the greater the benefit
from additional data (for example, the reduction of the variance in the sample
estimator declines as the sample size increases).11 A similar idea appears in
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the literature on innovation and unit cost reduction. Gottschalk and Janz [11]
and Levin and Reiss [12] model production cost as dependent on the firm’s own innovation and the pool of industry knowledge. (Cost depends on both own R&D and outside R&D). There, the lower is the pool of industry available R&D, the greater the firm’s marginal reduction of unit cost from increasing it’s R&D investment. Conversely, the greater is the outside pool of R&D, the lower
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the marginal impact of the firm increasing it’s R&D investment to reduce it’s unit cost. Here, (S-ii) plays an analogous role: increasing ` reduces access to
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outside the pool of technology and raises the marginal product of the firm’s investment in terms of technology improvement. With monotonicity of profit in technology, conditions (S-i) and (S-ii) are shown to imply that increasing
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patent restrictiveness leads to increased investment. Theorem 3.1: Suppose that profit increases with technology improvement and assumptions (S-i) and (S-ii) are satisfied. Then increasing patent restrictiveness
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improves the aggregate distribution of technologies in successive periods. As noted already, under (S-i) and (S-ii), increasing ` incentivizes firms to raise
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investment. And this increases the quality of the aggregate distribution. Monotonicity of profit in µt ensures the increased investment incentive is not reversed by a payoff decline as the aggregate distribution improves.12 Further motivation for this result and theorem (3.2) are given in section (3.3) where positive
11 See Bikhchandani and Mamer [10] for discussion of the marginal valuation of information, measured with a loss-function. 12 Without this assumption it would still be reasonable to expect that even if the resulting
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or negative covariation between i and ` is viewed from the perspective of superor sub-modularity. Note that the impact on welfare is ambiguous. Raising ` increases investment which is welfare improving (because of positive externalities
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in investment), but the greater restrictiveness has the usual negative welfare effects by restricting usage.
3.2
Investment and Patented Knowledge as Complements.
A contrasting view of increasing patent restrictiveness is that the impact is great-
est on high technology firms.13 Suppose that is the case, and in addition, that
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increasing patent restrictiveness reduces the marginal product of investment.14
Together, these effects work to dis-incentivize investment in innovation: increasing patent restrictiveness reduces the value of being a good firm and lowers the productivity of investment in improving one’s technology. To express these conditions in the model, suppose instead that better firms are more dependent on patented knowledge to generate current profit (π) and innovate (P ), so that such
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knowledge is a complement to the quality of a firms’ technology.15 Suppose also that increasing patent restrictiveness removes from use knowledge that would otherwise raise the marginal product of investment. Conditions (C-i) and (C-ii)
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formalize these properties.
(C-i) Increasing patent restrictiveness, `, or worsening technology, µt , has a
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greater impact on better firms. (a) An increase in `, or fall in µ lowers profits of better firms more than
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weaker firms: πpµ1 , α, `1 q ´ πpµ, α, `q, is decreasing in α, for `1 ě `, µ1 ď µ
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improvement in the technology distribution dis-incentivizes investment by lowering profit, it would dampen but not fully offset the initial incentive to increase investment due to the ` increase. 13 For example, because better firms make greater use (than weak firms) of intellectual property created by others, so that greater limitation on access to that intellectual property has a bigger impact. 14 Suggesting that increased access to patented raises the marginal product of investment and that investment is complemented by patented technology. 15 Alternatively, regarding profit, suppose that increasing ` raises profit via extra protection for each firm’s innovation, but the extra restrictiveness benefits weak firms more, possibly because more peripheral technology held by weak firms becomes patent protected.
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(b) An increase in `, or fall in µ worsens the technology draw of better firms more. For g increasing: ş ş gp˜ αqP pd˜ α | µ1 , α, i, `1 q´ gp˜ αqP pd˜ α | µ, α, i, `q, is decreasing in α, for `1 ě
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`, µ1 ď µ
(C-ii) Increasing patent restrictiveness lowers the marginal productivity of investment for each α. For g increasing: ş ş gp˜ αq∆i P pd˜ α | µ, α, i, `1 q ď α˜ gp˜ αq∆i P pd˜ α | µ, α, i, `q, α ˜
`
for `1 ě
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Assumption (C-i)(a) asserts that when increasing restrictiveness lowers prof-
itability, the impact is greater on good firms.16 Assumption (C-i)(b) expresses a similar effect (greater negative impact on better firms), but in terms of the impact on innovation of increased patent restrictiveness. Finally, (C-ii) says that increasing patent restrictiveness lowers the marginal productivity of investment in generating innovation. Under these circumstances, with profit monotonicity,
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greater restrictiveness lowers investment.
Theorem 3.2: Suppose that profit increases with technology improvement and
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assumptions (C-i) and (C-ii) are satisfied. Then increasing patent restrictiveness worsens the aggregate distributions in successive periods.
Some motivating discussion.
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3.3
The previous sections give conditions under which variations in investment are
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positively or negatively associated with changes in the restrictiveness of patent policy. Changes in patent restrictiveness affect both profitability and the impact of investment on R&D which in turn alters optimal investment decisions.
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The combination of such effects generates the investment response to increased restrictiveness. Under the substitutes or the complements conditions, the impact on investment is unambiguous (either positive or negative covariation of restrictiveness and investment). 16 Or, if increased restrictiveness raises a firms profitability, the gain is relatively less for a good firm.
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To motivate those conditions, recall firm α’s optimization problem given by equation (3):
i
ż
( vpµt`1 , τ t`1 , α ˜ , `qP pd˜ α | µt , α, i, `q (5)
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vpµt , τ t , α, `q “ max πpµt , α, `q ´ rpiq ` δ
Simplifying the discussion, assume pµt , µt`1 , τ t`1 q as fixed, or alternatively assume that neither the profit function or transition kernel depend on the ag-
gregate distribution. In this case, write v¯pα, i, `q for the term inside t¨ ¨ ¨ u, so
firm α solves maxi t¯ v pα, i, `qu. The solution i, varies with ` and this co-variation of investment and restrictiveness of patent policy (positive covariation in the
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substitutes case; negative in the complements case) captures the investment response to variation in restrictiveness. This may be viewed from the perspective
of super or sub-modularity. Given α, the function v¯pα, i, `q is supermodular if v B B¯ B` t Bi u
ě 0 (and submodular if
B B¯ v B` t Bi u
ď 0). With supermodularity, increasing
` has α’s best response be to raise i. Under what circumstances will this be so? Essentially, the conditions on the profit and transition kernel in (S-i), (S-ii)
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lead to a supermodular payoff function v¯, and a positive association between investment and patent restrictiveness (and the conditions (C-i), (C-ii) to a sub-
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modular function).17 Further motivation in the appendix clarifies the specific mechanism and connection to the assumptions in greater detail.
Efficiency and Welfare
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This section notes some welfare implications of the model. First, equilibrium is
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inefficient: at any level of patent restrictiveness, investment is below the socially optimal level. Second, in the complements case increasing ` lowers welfare; in
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the substitutes case, the conclusion is ambiguous. Finally, for a general model of total social welfare, the optimal value of ` in a social planner problem is ` “ 0. Turning to overall welfare (consumer and producer), increased invest-
ment improves the aggregate distribution of technologies over time, so provided improved technology raises consumer welfare, the overall effect is unambigu-
17 The additional complication that must be addressed is the knock-on impact from the resulting aggregate investment change back to individual decisions.
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ously positive.18 When investment is chosen to maximize overall welfare for a given value of `, the optimal value of ` is 0. This is discussed next. Let TSpµt , `q be a measure of consumer and producer welfare (total surplus) at time t, which
TSpµ1t , `1 q ´ TSpµt , `q ě 0,
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depends on the distribution of characteristics and the patent policy (in examşQ ˜ µq ´ ps pQ, ˜ µ, `qsdQ). ˜ Assume that: ple 2.1, TSpµ, `q “ maxQ 0 rpd pQ, µ1t ě µt , `1 ď `
(6)
so that improving technologies or reducing patent protection on existing tech-
nologies raises current welfare. Maximizing the present value of total surplus,
V pµ, `q “
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less the investment costs gives the program:
max tTSpµ, `q ´
τ PCpµq
ż
rpiqdτ ` δV pµ1 , `qu
(7)
ş where µ1 “ pµ1 , µq, with µ1 determined from µ1 p¨q “ P p¨ | α, µ, i, `qτ pdi ˆ dαq.
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Lemma 4.1: Social welfare, V pµ, `q, is decreasing in `.
˛
So, if the social planner maximizes welfare by choice of investment (with `
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exogenous), welfare decreases in `. According to theorems (3.1) and (3.2), if investment and patented technology are substitutes, increasing ` raises investment; and if complements, increasing ` reduces investment. How does welfare
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in equilibrium compare with the socially optimal level V pµ, `q? Here, in equiş librium producer surplus at time t is PSpµt , `q “ πpµt , α, `qµt pdαq. Total surplus, TSpµt , `q, at time t is the sum of producer and consumer surplus de-
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termined by the equilibrium. In equilibrium, from period t, let µet`j be the resulting distribution at time t ` j and µt`j “ pµet`j , µet`j´1 , . . . , µet`1 , µt q. The
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welfare generated with equilibrium investment is then (from time t), VE pµt , `q “ ş ř8 j j“0 δ rTSpµt`j , `q ´ α rpit`j qµt`j pdαqs.
By definition, VE pµt , `q ď V pµt , `q. From lemma (4.1), V pµt , `q is decreasing
in `. Considering the complements case, the impact of increasing ` is to worsen
18 Note that the social welfare optimization problem must respect the same intellectual property rights as appear in the individual firm problem: it addresses the externality issues, subject to access to technology being restricted according to the patent strength, `.
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the negative externality and reduce investment (which is already below the socially optimal level). So in the complements case, welfare decreases. In the substitutes case there are two effects at work: the direct effect of increasing welfare improving. Summarizing these observations:
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` worsens the negative externality, but the resulting increase in investment is
Theorem 4.1: Let VE pµ, `q denote equilibrium total surplus, and let V pµ, `q
be surplus under the social planner as defined in equation (7). Then V pµ, `q ě VE pµ, `q and V pµ, `q is declining in `. In the complements case, VE pµ, `q declines in `; in the substitutes case, VE pµ, `q may not be monotonic in `.
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Thus, increasing ` unambiguously worsens welfare in the complements case. In the substitutes case the impact is ambiguous as increasing investment and greater restrictiveness have opposite effects on welfare.
Conclusion
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A common view of patent incentives is that the ownership right to exploit discovery motivates investment in R&D: the patent is a prize or reward (of monopoly
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rights) compensating for investment and effort. From a policy perspective, this views each patent in isolation. Here, innovation is viewed as a flow with R&D building on an existing pool of intellectual property, and where access and ability
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to use that pool provides an important incentive. Patent policy affects access to that pool and how firms leverage it directly for profit and as a means to support their R&D. This raises policy questions. For example, how does patent policy
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feed through to incentives? If tightening patent policy encourages investment, does it do so because the innovation reward is greater or because firms are forced
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to greater dependency on own innovation and hence need to improve their own technology? At a more detailed level, the paper highlights the asymmetric incentives that
the patent system creates for different firms to invest. If, for example, tighter patent policy lowers firms profits, but the impact is greater on weaker firms, then weaker firms have a relatively greater incentive to improve. However, the
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channels through which these effects work are complex and may conflict: tighter patent policy may increase the incentive to improve but lower the productivity of investment in R&D. Weaker patent protection may reduce the direct incentive
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to invest in R&D, but makes available a larger portion of exisiting technology. What effects discussed here are likely to be the most important in deciding if a more restrictive patent policy encourages investment by raising the relative reward gap between a firm and others with better technology?
At the level of generality of the model developed here, these questions are dif-
ficult to investigate but suggest a direction for research with a more specialized
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model where the key functions and parameters are more tightly formulated.
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References [1] Nordhaus, W. D., The Optimal Life of a Patent, Cowles Foundation Dis-
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cussion Paper No. 241. [2] W. D. Nordhaus, The Optimum Life of a Patent: Reply, American Economic Review 62 (358) (1972) 428–431.
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Journal of Economics 44 (1992) 52–63.
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[8] Jovanovic, B. and Rosenthal, R.W., Anonymous sequential games, Journal of Mathematical Economics (1988) 77–87.
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[9] Bergin, J. and Bernhardt, D., Anonymous sequential games: existence and characterization of equilibria, Economic Theory 5 (1995) 461–489.
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[10] Sushil Bikhchandani and John W. Mamer, Decreasing Marginal Value of Information Under Symmetric Loss, Decision Analysis 10 (358) (2013) 245–
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256.
[11] Gottschalk, S. and Janz, N., Innovation Dynamics and Endogenous Market Structure, Dew discussion paper 01-39, Centre for European Economic Research (2001).
[12] R. C. Levin, P. C. Reiss, Cost-Reducing and Demand-Creating R&D with Spillovers, The Rand Journal of Economics 19 (1998) 538–556. 36
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[13] Torres, R., Stochastic Dominance, Northwestern Discussion paper.
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