Discussion Paper No.282
Economic Growth and Information Disclosure through Two
IPR Protections: Patent and Trade Secret

Keishun Suzuki

13 Aug, 2013

TOHOKU ECONOMICS RESEARCH GROUPGRADUATE SCHOOL OF ECONOMICS AND
MANAGEMENT TOHOKU UNIVERSITY

27-1 KAWAUCHI, AOBA-KU, SENDAI,
980-8576 JAPANEconomic Growth and Information Disclosure through Two IPR
Protections: Patent and Trade Secret∗Keishun Suzuki†
13 Aug, 2013

Abstract
This paper analyzes the growth eﬀect of strengthening patent protection to which trade
secret is introduced as another protection method. In the model, innovators protect theirinventions comprising many fractional parts by patent and trade secret. While trade secrets
conceal the technological information in the short run, patents partially disclose the information to competitors. When the patent protection is strong, competitors can hardly use thetechnological information freely and it helps successful innovators earn higher proﬁts. On
the other hand, less disclosed information deteriorates the other ﬁrm’s R&D productivity.
The result shows that strengthening patent protection increases the growth rate when theleakage risk of trade secrets is high. However, when the risk is low, stronger patent protection
hinders growth.

JEL Classiﬁcation: O31, O34, L16
Keywords: Innovation, Patent, Trade Secret, Imitation, Disclosure Requirement in Patent
Application.
∗
I would like to thank Ryo Horii, Akiomi Kitagawa, Koki Oikawa, Yunfang Hu, the numerous people whocommented on earlier versions of the paper in the 2012 Japan Economic Association Spring Meeting at Hokkaido
University, and the all participants of the 2013 Asian Meeting of Econometric Society in Singapore. Of course,
all remaining errors are my own.
†
3rd grade of the doctoral course, Graduate School of Economic and Management, Tohoku University, 271 Kawauchi Aoba-ku, Sendai, Japan Email: b1ed1009@student.econ.tohoku.ac.jp. Tel: +81-22-795-6265. Fax:
+81-22-795-6270.

1

1

Introduction

In the traditional view, strong intellectual property rights (IPRs) protection enhances economic
growth because it secures innovator’s proﬁts and provides inventors with incentives to innovate.
Although there is a trade-oﬀ between monopolistic distortion and economic growth (e.g., Nordhaus 1969), static distortion has been regarded as a necessary evil for dynamic gain. In the
recent decades, enhancing IPR protection has been promoted largely by the OECD countries,
especially after 1994, when the TRIPS Agreement was implemented.1
However, empirical studies do not necessarily show a positive relationship between economic
growth and the strength of IPR protection.2 For example, Falvey et al. (2006) showed thatthe eﬀect of IPR on growth is positive in low- and high-income countries but not positive in
middle-income countries. Chen and Puttitanun (2005) estimated the eﬀect of IPR on GDP
per capita in developing countries and showed a U-shaped relationship between them. Similarly,
Horii and Iwaisako (2007) also pointed to the ambiguous relationship between the level of patent
protection and the average per capita growth rate. In addition, some empirical studies show thatstronger IPRs have a non-monotonic eﬀect on R&D. For example, Allred and Park (2007) ﬁnd
a U-shaped relationship between ﬁrm-level R&D and the strength of patent rights in developed
countries.
A patent holder can transmit private information to competitors even before the patent expires.3 While the patent system is meant to protect the properties, during the patent prosecution
process, applicants for a patent must disclose some technological information to the public in

1
Park (2008) created an index that represents the level of patent protection. The index is composed of ﬁvescores, some of which are duration of protection, patentable coverage, and enforcement mechanisms. Using thisindex, he showed that the strength of patent protection has increased over time globally.
2
At this point, we may need to pay attention to time lag as one reason. Generally speaking, R&D projects
take time to complete, especially for commercialization; therefore, the growth eﬀect may not appear immediately
after the policy change.
3
For example, the detail of the technological information of numerous patent applications can be accessed
freely on the Internet. The amount of access to the website of the Japan Patent Oﬃce (JPO) from China is verylarge, and experts note that the website is used for imitative activities in China.

2

return to receive protection. When the patent system requires a high degree of disclosure in theapplication, the disclosed information gives competitors clues that help them catch up and eveninnovate further. This disclosure actually causes some ﬁrms to avoid patenting their innovation.
Cohen et al. (2002) reported that 46% of Japanese ﬁrms report “over disclosure” as the mostimportant reason for not applying for a patent. In this paper, I deﬁned the level of disclosure
requirement in patent application as the strength of patent protection.
Trade secrets have an advantage over patents in that they do not disclose any information
to competitors unless the secrets are leaked. In a questionnaire by Cohen et al. (2002), most
U.S. ﬁrms respond that trade secrets are more eﬀective than patents for appropriating beneﬁt
from innovation.4 In addition, Cohen et al. (2000, p. 7) state that“Diﬀerent mechanisms may
even be employed at the same time for a given innovation when an innovation is composed of
separately protectable components or features.” Thus, to study IPR policies more realistically,
we need to focus on the role of trade secrets as an alternative protection.
The model considers an economy in which innovators develop a good that contains many
fractional parts. A successful innovator decides how many parts of the good are to be protectedby patent, and the rest are maintained as trade secrets. Patents ensure a stable proﬁt in the longrun, but the period proﬁt is relatively low because the patents disclose technological information
to competitors. On the other hand, by keeping the information a secret, the patent holder canearn high period proﬁt in the short run. However, if the secret leaks out to competitors, proﬁts
will drastically decrease because the innovation has not been patented. Some studies in industrialorganization address the decision of whether to patent.5 However, in DGE modeling, there arefew studies in which two IPR protections and the patenting behavior are explicitly introduced.
4

Especially in the process innovation, both U.S. and Japanese ﬁrms depend on trade secrets rather than otherprotection methods.
5
Anton and Yao (2004) established a model in which an innovator discretely decides whether to protect his
innovation by patent or as a trade secret, as well as what aspects of the invention are the innovator wishes todisclose. Similarly, Ottoz and Cugno (2008) constructed a model in which an innovator can protect the innovation
by a patent-secret mix. These studies focus on how innovation size and strength of protection change a ﬁrm’s
protection strategy, and do not include an analysis of how such a change aﬀects the economy.

3This paper investigates the growth eﬀect of disclosure necessary for patent protection. In
the model, disclosed information becomes the common knowledge and other ﬁrms can use it
for the partial imitation and further innovation. Lowering disclosure requirement decreases theamount of the common knowledge, which has two opposite eﬀects on economic growth. First,
the reduction of the common knowledge increases proﬁt because the productivity of competitive
fringes becomes low. This proﬁt increase naturally stimulates the incentives for innovation.
However, because potential innovators cannot access much of the information, it increases their
R&D costs and discourages innovation in the long run. When the leakage risk is suﬃciently
low, the former positive eﬀect dominates the latter negative eﬀect. As a result, lowering thedisclosure requirement may accelerate economic growth. Interestingly, in the case of middle
leakage risk, the relationship between the required disclosure level in the patent application andeconomic growth exhibits a U-shaped curve.
Although most studies have concentrated on analyzing the optimal patent policy, they have
not yet reached a consensus on the optimal strength of IPR protection. In the context ofindustrial organization, Gilbert and Shapiro (1990) conclude that a patent system with inﬁnite
length and narrow breadth is desirable. On the other hand, Klemperer (1990) shows that apatent design with either very long or very short length is optimal. In DGE modeling, thepioneering work by Judd (1985) demonstrates that the optimal length of patent protection is
inﬁnite. However, Horowitz and Lai (1996) and Iwaisako and Futagami (2007) deem ﬁnite length
to be optimal.
In addition, there are few studies in which trade secret is explicitly introduced. Some studies
do not specify the protection method by treating the probability that costless imitation occurs
as a level of IPR protection. In such a context, Horii and Iwaisako (2007) obtained an inverted
U-shaped relationship between IPR protection level and growth rate. This speciﬁcation is feasible for simpliﬁcation and contributes to an analysis of the abstract eﬀects of IPR protection.

4However, the result of such studies may be too generic to be employed as an actual IPR policy.
The main diﬀerence between the current study and the aforementioned literature is that I
explicitly consider both IPR protection and endogenous “mixed protection” in the model. By
studying this realistic situation, we can obtain a new implication of IPR protection and the roleof information disclosure.
The rest of the paper is structured as follows. Section 2 brieﬂy introduces the role of patents
and trade secrets in the model. Section 3 develops an endogenous growth model that incorporates
two IPR protections. We obtain the growth eﬀect of two IPR protections numerically in section
4. Finally, section 5 concludes the paper.

2

Basic Setup of Patent and Trade SecretFirst, this section brieﬂy shows the role of two IPR protections by calculating the ﬁrm’s proﬁt.
Suppose that there is only one good that comprises many fractional parts, and the good is
produced by a monopolist. Let µ ∈ [0, 1] denote the percentage of “patented parts” in the good.
Then, 1 − µ indicates the portion of “secret parts.” Although µ is exogenous here, we will derive
it endogenously in the next section. For simplicity, I assume that the patent protection goesforever unless the ﬁrm pays the patent maintenance fee.
Patents are an imperfect form of protection because the ﬁrms must disclose the technologicalinformation of the innovation when they apply for the patent. Furthermore, this process enables
imitators to access the information about the product’s composition or the production method.
I simply assume that a fraction of δ ∈ [0, 1] in the patented parts becomes common knowledge
and that other ﬁrms can use the information without infringing the patent. We can regard δ as
the requirement level of the patent disclosure in the patent application or the level of opennessof the patent system. Therefore, a large δ indicates weak protection.
Similarly, the trade secret approach does not oﬀer perfect protection because the secret leaks

5

Protected parts Protected1−δProtected parts Disclosed
leakageby patentparts byby patent

trade secretδ

trade secret

Disclosed parts

Disclosed partsby patent

by patentµparts by1−µFigure 1: The transition of protected parts of the innovation. The protected parts in each stage arerepresented by the shaded area. The left panel depicts the stage before the trade secrets are leaked out(stage-1), and the right panel shows the stage after leakage (stage-2).

out with a probability of ℓ. The ﬁrms can keep the trade secret as private information at ﬁrst,
but once the leakage occurs, all the secret parts of the good are disclosed. For convenience, wecall the situation before (after) the leakage “stage-1 (stage-2).”
Fig 1 shows how the two ways of protection individually classify the innovation into protectedparts and disclosed parts for each stage. The innovation is divided into patented parts µ (leftside) and secret parts 1 − µ (right side). In stage-1, the secret parts are perfectly protected,
but the patented parts are partially protected due to the information disclosure by patentapplication. Thereby, the patented parts are bisected into protected parts and disclosed parts,
as shown in the left panel of Fig 1. As a result, the protected parts of the innovation in stage-1
are all secret parts and partial patented parts. In stage-2, all the secret parts are disclosed andthe protected parts are only the partial patented area, as depicted in the right panel of Fig 1.
I deﬁne dn (µ) as the percentage of unprotected parts of the good in stage n = 1, 2. FromFig 1, dn (µ) is evaluated as follows.
d1 (µ) = δµ,(1)d2 (µ) = 1 − (1 − δ)µ.

(2)

The monopolist has a technological advantage against the imitators according to the amountof protected information. He can produce one good by employing one worker. On the other6

hand, imitators can produce χn ≤ 1 units of the same good with one unit of labor.6 I assume
that χn depends on dn and specify χn as following the function of µ.
χn (µ) = λ−1 + (1 − λ−1 )dn (µ), n = 1, 2.

(3)

λ−1 is the minimum value of χn , which is attained when no information is disclosed (dn = 0).
We can check χ1 (µ) = 1 when dn (µ) = 1 and χ1 (µ) = λ−1 when dn (µ) = 0 hold.7 Because
imitators can use additional information (1 − µ) after the leakage, the amount of information
disclosure in both stages may be diﬀerent (d1 ≤ d2 ). For this reason, χ1 (µ) ≤ χ2 (µ) holds,
which implies the advantage in stage-1 is larger than 1 in stage-2 when µ < 1.
In the market, the monopolist and the imitators are engaged in Bertrand competition andthe monopolist employs the limit-pricing strategy. The unit production cost of the imitator instage-n is χn−1 w, and the unit cost of monopolists is w. Therefore, the monopolist can exclude
the imitators from the market with a price p = χ−1n w.
To derive the proﬁt of the monopolist, I assume that the demand function is an inverse of
the price, x(t) = 1/p(t), and the total consumer expenditure equals 1.8 Then, the monopolist’s
proﬁt isπn = p · x − w · x= 1−w·χnw= (1 − λ−1 )(1 − dn ).
Finally, we can calculate πn in each stage as follows:()
π1 (µ) = 1 − λ−1 (1 − δµ) and

(4)

(
)
π2 (µ) = 1 − λ−1 (1 − δ)µ.

(5)6

We can also interpret χn as the cost disadvantage for imitators. When χn is very small, imitators must input
a large number of workers for production. In contrast, imitators can perfectly copy in the case of χn = 1.
7
The case of δ = 0 and µ = 1 corresponds to Grossman and Helpman’s model in which the technologicaladvantage of the monopolist is λ−1 .
8In the full model, I will show that the assumption is endogenously obtained in the equilibrium. Here, we takethe results in advance.

7

Figure 2: Patented fraction and the proﬁt in each stage.
Fig 2 shows the proﬁt curve for each stage. πn is the linear function of µ and satisﬁes π1 (1) =π0 (1) and π2 (0) = 0. The upper downward-sloping straight line represents the proﬁt for stage-1
and the lower upward-sloping straight line is the proﬁt for stage-2.
Here, there is a trade-oﬀ between π1 and π2 . To see this brieﬂy, consider the case thatthe innovator protects a small fraction of the innovation by patent (µL ). Then, he can earna relatively high proﬁt before leakage (π1L ) because most of the technological information isconcealed from other ﬁrms. However, after the leakage occurs, he obtains a low proﬁt (π2L )because the patented parts that still remain are relatively small. Next, we consider the casewhere the innovator patents a large fraction of the innovation (µH ). Because the technologicalinformation about the patented parts is partially disclosed to other ﬁrms, he earns a relatively
small proﬁt in stage-1 (π1H ). After the leakage, however, the reduction size of the proﬁt isrelatively small because the innovator does not overly depend on maintaining the trade secret.
Therefore, he can still earn a relatively high proﬁt in stage-2 (π2H ).

8

3The Rest of the Model

The model is an extension of Grossman and Helpman (1991), which is a quality-ladder model.
There is a continuum of the sector indexed by j ∈ [0, 1] and a monopolist in each sector.
The monopolist can earn proﬁt until a potential ﬁrm succeeds in an innovation in that sector.
Because the quality of a new product is higher than the previous one, the incumbent is replacedby the new innovator. For a more detailed description of the model, see Grossman and Helpman(1991).

3.1

Households

The economy consists of L identical households and there is no population growth. Each household serves a unit of labor inelastically and gains a wage w in every period. They maximize
intertemporal utility over an inﬁnite horizon as follows:
∫ ∞
Ut =

e−ρ(τ −t) ln C(τ )dτ,(6)twhere ρ is the subjective discount rate, and C(τ ) is an index of consumption at time τ . The
instantaneous utility is given by∫ θlnln C(τ ) =
0

( m̃
i
∑

)

∫ 1

λm (i)xmt (i) di +
θ

m=0


ln 

m̃j
∑


λm (j)xmt (j) dj,

(7)

m=0

where xmt (i) is the consumption of the good whose quality is m in industry i at time t, and θ
is the number of the industries from whom the monopolist has shielded the trade secret (thesituation in stage-1). For convenience, we call such industries “sector-1.” Then, 1 − θ is thenumber of the industries to whom the monopolist’s trade secret has been disclosed; we call theseindustries “sector-2.”
The quality of each good is represented as an integer m power of λ > 1, which means thatthe quality of the new good is λ times as high as the previous one. In industry i, there are m̃i

9types of goods, and the quality of the latest good is λm̃i . In the equilibrium, households buy
only the good of the highest quality in each sector because of limit-pricing.
Under the logarithmic utility function, households equally spend their budget across theindustries. Therefore, the demand of a good in the industry i is xm̃i (t) = E/pm̃i (t), where E isexpenditure and pm̃i is the price of the good whose quality is m̃i .
In this setting, the ideal price index associated with the consumption index C is[∫ θln

P = exp

(p

0

m̃i
λm̃i

∫ 1

)
di +

ln

(p

θ

m̃j
λm̃j

)

]
dj .

(8)

Given the aggregate price index, households spend to maximize their intertemporal utility.
From the result of the maximization, household’s optimal time path of spending is representedby Ė/E = r − ρ. By using aggregate expenditure as the numéraire according to Grossman andHelpman (1991), we get E = 1 and r = ρ.

3.2

Firms

The time schedule in an industry is as follows. At ﬁrst, a successful innovator chooses optimal
mixed protection between patent and trade secret. Then, he produces goods and earns proﬁt
in stage-1 until innovation occurs in the industry with a probability of z1 . In addition, thesecret parts of the innovation leak out with a constant probability ℓ in stage-1. After that, theincumbent moves to stage-2 and his proﬁt decreases due to the information disclosure of thesecret parts. Furthermore, once another ﬁrm succeeds in its R&D with an innovation rate z2 , itreplaces the incumbent and emerges as the new incumbent.
I assume that the patent cost is a maintenance fee for simplicity and that the incumbents
must pay c(µ) = γµ2 /2 in every period, where γ > 0.9 To analyze the role of trade secret, I
9While the speciﬁcation of convex patent cost enables us to obtain an interior solution, most fees (e.g., ﬁlingfees) may be proportional to the number of patents. However, the patent cost in the model includes not only
application cost but also other costs. For example, to be granted a patent of an invention of which it is diﬃcult todetermine the non-obvious aspects (e.g., Program code), innovators need to pay additional costs for the patentissuing. Suppose a good comprises many parts and each part has a peculiar diﬃculty in being granted the patent.
At ﬁrst, innovators will apply ﬁrst for patents of the easiest parts, but eventually they will be required to pay
additional costs to ﬁle subsequent patents.

10assume that γ is not so small and therefore the optimal µ is less than 1 in the equilibrium. Theirperiod payoﬀ is the proﬁt obtained in section 2 minus the patent cost. An incumbent decides µ
for maximizing the value of innovation V1 , deﬁned as a total expected payoﬀ after the innovation
occurs. First, we calculate V2 , which is the expected sum of the payoﬀ after the trade secretleakage.
∫ ∞V2 =e−(r+z2 )s [π2 (µ) − c(µ)] ds.

t=

π2 (µ) − c(µ).
r + z2(9)Then, from a no-arbitrage condition, V1 is derived as follows:
rV1 = π1 (µ∗ ) − c(µ∗ ) + ℓ (V2 − V1 ) − z1 V1⇔ V1 =π1 (µ∗ ) − c(µ∗ ) + ℓ [π2 (µ∗ ) − c(µ∗ )] /(r + z2 ).
r + ℓ + z1

(10)Each incumbent chooses his µ to maximize V1 with a given z. From the ﬁrst-order condition,
we obtain an optimal µ as follows:

)
(
)( ℓ


 γ −1 1 − λ−1 r+ℓ+z−δwhen z2 < ℓ/δ − r − ℓ2µ∗ (z2 ) = 0 when z2 ≥ ℓ/δ − r − ℓ.

3.3

(11)

R&D sector

In the economy, all innovations stem from the R&D activities by potential ﬁrms.10 The preceding
R&D cost is covered by issuing equities whose value is equal to V1 .
The blueprints are invented according to the Poisson process so that the success probability
in any time interval dt is zn dt = [LR Θn /An (µ)]dt, where LR is the number of researchers,
Θn /An (µ) indicates the R&D productivity, Θ1 = θ, and Θ2 = 1−θ. I assume that R&D becomes

10
This is called “allow eﬀect” or “replacement eﬀect.” All incumbents in sector-1 have no incentive to innovateby paying some cost because they cannot increase their proﬁt through the new innovation. The monopolists
in sector-2 can raise their proﬁt by successful innovation, although the incentive to innovate is lower than the
incentive of the potential ﬁrms because they have zero-proﬁt now and because the R&D technology is a constantreturn here. Therefore, all researchers are employed in the potential ﬁrms.

11

more eﬃcient when the number of targeted sectors Θn is higher.11 In addition, in this model,
potential ﬁrms can obtain some clues for further innovation from the disclosed information. I
specify An (µ), which indicates R&D ineﬃciency, as the following decreasing function of dn .
An (µ) = Ā − dn ,(12)where Ā is a positive parameter.

3.4

Free Entry

A successful innovator earns expected payoﬀ V1 . On the other hand, the innovator must pay
R&D cost wAn (µ)/Θn for innovation in sector-n. Therefore, free entry into R&D in each sector
requires that
A1 (µ)≥ V1 , equality holds whenever z1 > 0.
θA2 (µ)w≥ V1 , equality holds whenever z2 > 0.
1−θ
w

3.5

(13)
(14)

Labor Market

In the economy, the labor supply L is allocated between production and R&D; therefore, thelabor market clearing condition is

L=θ

3.6

χ1 (µ)
χ2 (µ)+ (1 − θ)+ A1 (µ) · z1 + A2 (µ) · z2 .
w
w

(15)

Equilibrium

At ﬁrst, we derive the condition that the fractions of sector-1 and sector-2 are constant overtime. A monopolist in sector-1 moves into sector-2 with a constant probability ℓ. On the other
hand, a ﬁrm in sector-2 is replaced by a new incumbent in sector-1 with a probability z2 . Then,

11

This spillover can be interpreted as follows. Each industry potentially has a diﬀerent R&D diﬃculty andpotential ﬁrms may ﬁnd it easy to discover a suitable industry in which to innovate when the number of the“target” is large.

12

the instantaneous change of θ is presented as θ̇ = (1 − θ)z2 − ℓθ. Therefore, in the steady state,
the following equation holds:θ=z2.
z2 + ℓ(16)

There are two types of equilibrium in the model.12 The ﬁrst case is that all R&D concentrate
in sector-2, z1 = 0 and z2 > 0. Recall that A1 ≥ A2 necessarily holds. If the initial numberof sector-2 is suﬃciently large, potential ﬁrms target only the industries in sector-2 because the
R&D productivity is high. Although larger z2 decreases the (1 − θ), the equilibrium of this casebecomes stable when ℓ is suﬃciently large. In this case, next equation holds in the equilibrium:
A1
A2
>
.
θ
1−θ

(17)

The second case is that innovation simultaneously occurs in two sectors, z1 > 0 and z2 > 0.
In this case, the R&D productivity across the sector is the same, and innovators are indiﬀerent
with regard to the sector. Therefore, the next equation holds:
A2
A1
=
.
θ
1−θ

(18)

Once the long-run equilibrium is determined, we can calculate the growth rate of the consumption index C as below:g ∗ = [θz1 + (1 − θ)z2 ] ln λ.

4

(19)

Simulation

This section examines the growth eﬀect of the disclosure requirement of the patent system. To
discuss the eﬀect, I numerically calculate the relationship between δ and the growth rate underdiﬀerent ℓ.

The model does not have third case in which z1 > 0 and z2 = 0 are satisﬁed. In this case, A1 /θ < A2 /(1 − θ)initially holds. However, some industries in sector-1 continuously move to sector-2 due to information leakage,and θ gradually decreases until A1 /θ = A2 /(1 − θ) holds.
1213Figure 3: Growth rate and the openness of the patent system (δ). The upper curve “L” corresponds to the case of ℓ = 0.35. The middle curve “M” is the case of ℓ = 0.45. The lower
curve “H” is the case of ℓ = 0.8. These graphs indicate that the growth eﬀect is ambiguous anddepends on the leakage probability.

4.1

First case: z1 = 0 and z2 > 0

The simulation uses the following parameters: L = 4, λ = 1.2, ρ = 0.03, Ā = 2, and γ = 1/4.
For a sample of the leakage probability, the simulation uses ℓ = 0.35, ℓ = 0.45, ℓ = 0.8.
Fig 3 shows three diﬀerent patterns of the growth eﬀect. In Case L (ℓ = 0.35), weak patent
protection (higher δ) enhances growth. In contrast, in Case H (ℓ = 0.8), larger δ has a negative
impact on growth in an opposite direction. In Case M (ℓ = 0.45), the relationship exhibits
U-shape and the growth eﬀect depends on the initial δ.

Interpretation
The inﬂuence on g due to the weakening patent policy (δ ↑) can be decomposed into the eﬀects
on (1 − θ) and z2 . However, as shown in Panel (a) of Fig 4, the relationship between innovation
rate z2 and δ determines the growth eﬀect shown in Fig 3. Therefore, to interpret the result, weonly have to focus on the impact of δ on z2 .

14

Figure 4: Other variables and the openness of the patent system (δ).

Figure 5: Firm value and the openness of the patent system (δ).

15

Suppose that the government adapts a stronger patent policy (δ ↓). This policy has two
opposite eﬀects on the incentive of innovators. First, strong patent protection increases the ﬁrm
value (V1 ), as shown in Fig 5. When δ is low, competitive fringes have only little information of
the inventions and then the cost advantage of the monopolists becomes high. Panel (f) of Fig 4
indicates that small δ necessarily decreases the productivity of competitive fringes in sector-2.
Then, monopolists earn high proﬁt because they can charge a high price. This eﬀect on V1
will stimulate the incentive of innovation. However, the second eﬀect has a negative impact oninnovation. When potential ﬁrms obtain only little information, the R&D ineﬃciency goes up
as depicted in Panel (c) of Fig 4. As a result, the entire impact on innovation is determinedby these opposite eﬀects. For convenience, I call these “cost advantage eﬀect” and “R&D
ineﬃciency eﬀect”, respectively.
In Case H, the lowering disclosure in patent system (δ ↓) has a positive eﬀect on the growthrate. In this case, the cost advantage eﬀect is relatively strong and dominates the R&D ineﬃciency eﬀect. When ℓ is high, incumbents protect many parts of the invention by patent because
trade secret is a relatively weak protection strategy. Then, the incumbent can conceal a great
deal of information involved with the invention when the government decreases the disclosure
requirement. This means the ﬁrm value is drastically increased by lowering δ, as shown in Fig
5.
In Case L, as illustrated in Fig 4, the lowering disclosure in patent system (δ ↓) has anegative eﬀect on the innovation rate. In this case, conversely, Panels (e) and (f) of Fig 4 showthat small δ does not increase the monopolist’s cost advantage a great deal. When ℓ is relatively
low, innovators protect many parts of the inventions by trade secret. Therefore, the additionalamount of the protected parts by strengthening patent protection (δ ↓) is limited. Fig 6 brieﬂy
illustrates this mechanism.
In Case M, the policy has an ambiguous impact on the innovation rate. We can consider the16

Figure 6: Protected area and unprotected area in stage-1. Initial patented parts are regions
A, B, and C, and secret parts are regions D, E, and F. Suppose that the government increases
the strength of patent protection (δ → δ ′ ). Then, a new monopolist increases the fraction ofpatented parts (µ → µ′ ). In this case, the additional amount of protected parts is representedby (B − E). Clearly, the amount is relatively high when the initial µ is large.
result by using the same interpretation. In this case, the cost advantage eﬀect oﬀsets the R&D
ineﬃciency eﬀect.
As a result, the size of the impact of strengthening patent protection on ﬁrm value depends
on the ﬁrm’s protection strategy and the optimal protection strategy is aﬀected by the leakage
rate.

4.2

Second case: z1 > 0 and z2 > 0

In this case, unlike the ﬁrst case, innovation occurs in sector-1 and θ = A1 /(A1 + A2 ) holds. By
using this equation and (16), we can obtain z2 in the steady state. After that, from (1)-(5) and(10)-(15), we can also solve z1 in the steady state.
The simulation of this case uses the following parameters: L = 4, λ = 1.2, ρ = 0.03, Ā = 2,
and γ = 1/10. As discussed above, when ℓ is suﬃciently small the equilibrium of this case canbe attained. Therefore, the numerical analysis uses ℓ = 0.02, ℓ = 0.05, and ℓ = 0.18.
The growth eﬀect is shown in Fig.7. A lower δ primarily decreases the growth rate and the17Figure 7: Growth rate and the openness of the patent system (δ). The upper curve “LL”
corresponds to the case of ℓ = 0.02. The middle curve “LM” is the case of ℓ = 0.05. The lower
curve “LH” is the case of ℓ = 0.18.
result is similar to the Case L in the ﬁrst case. For the same reason in ﬁrst case, strong patent
protection discourages the innovation in sector-2. As represented in Fig 8, the curve which shows
the relationship between z2 and δ is upward-sloping in three cases. This negative impact on z2
directly aﬀect the growth rate in this case.
However, the eﬀect of lowering δ on z1 is ambiguous. Especially, Panel (b) and (c) of Fig
8 show a weak U-shape relationship between them. What causes the diﬀerence of the eﬀect
on innovation rate between sector-1 and sector-2? To consider this, let us look at Panels (c)and (d) of Fig 9. In sector-2, the R&D ineﬃciency drastically increases by lowering δ. On theother hand, the size of the negative impact of the R&D productivity in sector-1 is relatively
small, as shown in the Panel (c). Recall that the additional amount of protected information
becomes small when ℓ is suﬃciently low as discussed in Fig 6. Although lowering the disclosure
requirement of a patent certainly increases the protected parts per patented part, it also induces
innovators to increase the fraction of patent protection. Because the latter eﬀect works to oﬀset
the former, the R&D ineﬃciency eﬀect is mitigated. As a result, the negative impact on the18

growth rate is also mitigated by the increase of z1 .
In addition, Panels (b) and (c) of Fig 8 also show that the sector in which innovative activity
mainly concentrates is diﬀerent between Case LM and Case LH. In Case LM, many potential
ﬁrms engage in R&D in sector-1. When ℓ is suﬃciently small, the number of sector-1 is relatively
large, which stimulates innovation in sector-1. Conversely, in Case LH, the number of sector-1
is relatively small, which lowers R&D productivity in sector-1; therefore, z2 > z1 holds.

5

Conclusion

I extended the quality-ladder model of endogenous growth by considering two IPR protections
and a choice problem between them. This model deﬁned the strength of patent protection as
the level of disclosure requirements in patent applications. The results showed that the growtheﬀect of strengthening patent protection may discourage the growth rate.
When the disclosure level of the patent is small, it reduces the common knowledge becausemonopolists can conceal a great deal of information involved with the invention through thepatent process. This concealment increases the cost advantage against competitive fringes andenables monopolists to obtain higher proﬁt. As a result, it stimulates the incentive to innovate by increasing ﬁrm value. However, when innovators cannot use disclosed information for
R&D due to the strong protection, R&D activity becomes ineﬃcient. Therefore, lower common
knowledge negatively aﬀects the R&D productivity, and this eﬀect discourages innovation. In
particular, the latter negative eﬀect is strong when the leakage probability is suﬃciently small,and the growth eﬀect of the policy becomes negative. In other words, when trade secret is arelatively strong protection strategy for innovators, strengthening patent protection is harmfulfor economic growth. When the leakage probability is suﬃciently large and monopolists mainly
protect their inventions by patent, strong patent protection conversely enhances the growth because the former positive eﬀect is relatively strong. The results indicated that policy makers

19Figure 8: Innovation rates (z1 and z2 ) and the openness of the patent system (δ). The upper
curve “LL” corresponds to the case of ℓ = 0.02. The middle curve “LM” is the case of ℓ = 0.05.
The lower curve “LH” is the case of ℓ = 0.18.

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Figure 9: Other variables and the openness of the patent system (δ).

21

have to pay attention to the relative importance of patent protection for actual ﬁrms. In addition, the relationship between growth rate and patent strength are represented by a U-shaped
curve under a middle leakage probability. This result has been empirically demonstrated (e.g.,
Chen and Puttitanun (2005)). In this case, policy maker should consider the current amount of
disclosure required for patent protection.
In this paper, the leakage probability is regarded as an exogenous parameter. As an extension, we can consider the case where the probability is endogenously determined. For example,
it does not seem very unlikely that the probability depends on the amount of trade secrets. If aﬁrm has many trade secrets, it may be diﬃcult for a ﬁrm to secure them all. Otherwise, using
the leakage mechanism as a means to spy or reverse engineer an innovation can be one way toendogenize the leakage probability. However, regardless of the extension we consider, the model
presented in this paper may serve as a starting point for the introduction of two IPR protections
in a DGE model.

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