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Paper to be presented at the DRUID Summer Conference on "Industrial Dynamics of the New and Old Economy - who is embracing whom?"
Copenhagen/Elsinore 6-8 June 2002
Theme A, B, E Theme A: Technical Change, Corporate Dynamics and Innovation, Theme B: Production and Use of
Knowledge in the Old & New Economy, Theme E: New Competition Policies and Intellectual Property Rights)
ON SUBSTITUTION OF INTELLECTUAL PROPERTY AND FREE DISCLOSURE: AN EX-ANTE ANALYSIS OF R&D STRATEGIES IN
SOFTWARE TECHNOLOGIES
Elad Harison Robin Cowan
MERIT, University of Maastricht
P.O. Box 616, 6200 MD Maastricht, The Netherlands Tel.: +31-43-3883883; Fax: +31-43-3884905
Email: [email protected]; [email protected]
May 20th, 2002
Abstract
Major firms have joined the Open Source movement and choose to apply its development methodology in their projects. Our model examines the links between open-ness and innovation in software platforms by analyzing how disclosure affects the technical quality of software and the profits of myopic and far-sighted firms. Our model analyzes the degree of disclosure, under various pricing strategies of the firm, that should be implemented to obtain maximal profits. Further, we reveal how social welfare of users, in terms of technical quality of the software that they implement, corresponds to profit-maximizing decisions of the firm. As the firm impels towards maximizing its profits in the short and in the long run, higher profits and technical quality of the software may be achieved at the cost of lower degree of open-ness. Policy makers may tolerate this effect on innovation by providing incentives to Open Source developers and users or by sponsoring free-software consortia.
Keywords: Intellectual Property; Software; Open Source; Disclosure; Technical Quality.
JEL Classification: L15, L86, O34.
On Substitution of Intellectual Property and Free Disclosure: An
Ex-Ante Analysis of R&D Strategies in Software Technologies∗
Elad Harison† Robin Cowan†
†MERIT, University of Maastricht, P.O. Box 6166200 MD Maastricht, The Netherlands
Paper for the DRUID Summer Conference, June 2002
(Preliminary Version - do not cite without authors’ permission)
May 20, 2002
Abstract
Major firms have joined the Open Source movement and choose to apply its develop-ment methodology in their projects. Our model examines the links between open-ness andinnovation in software platforms by analyzing how disclosure affects the technical quality ofsoftware and the profits of myopic and far-sighted firms. Our model analyzes the degree ofdisclosure, under various pricing strategies of the firm, that should be implemented to obtainmaximal profits. Further, we reveal how social welfare of users, in terms of technical qualityof the software that they implement, corresponds to profit-maximizing decisions of the firm.As the firm impels towards maximizing its profits in the short and in the long run, higherprofits and technical quality of the software may be achieved at the cost of lower degree ofopen-ness. Policy makers may tolerate this effect on innovation by providing incentives toOpen Source developers and users or by sponsoring free-software consortia.
JEL Classification: L15, L86, O34.
Keywords: Intellectual Property; Software; Open Source; Disclosure; Technical Quality.
∗Email: [email protected]; [email protected].: 00-31-43-3883883, Fax: 00-31-43-3884905
1 Introduction
Since the beginning of the 1990s, we witness a significant increase in development of Open
Source systems, publicly offered with a free-use and distribution license (e.g. Linux, Apache
and Sendmail). Part of the emerging phenomenon is explained by the rapid growth of the
Internet as a communication network for software users and developers, and yet, had Open Source
been only a tentative approach for software development, it would probably have benefited a
limited community of users and programmers and would have remained in the fringe of the
industry, and consequently, those applications would have been advanced only by a sparse group
of contributors. However, in many Open Source projects this does not seem to be the case.
Major firms join the Open Source movement and choose to apply its development methodology
in their projects. In return, firms have to disclose their core asset, namely the source code,
for free use, modification and re-sale by users and distributors and to remove any intellectual
property claims from it.1 Other firms that cannot compete with market leaders, particularly
small and medium enterprises but also “followers”, apply Open Source to improve their position
in the market and to extend the implementation of their technologies.2
Firm’s decision to embrace Open Source involves the expectation that by disclosing contents
of software technology to the public domain, complementary activities offered to users ,e.g.
implementation and technical support, can be commercially exploited and will expand through
a rapid diffusion of the proposed technology. As the use of the software expands, so do its
”production externalities”: knowledge spillovers that foster technological advance, when skilled
users add new features to the product, and increase with the level of open-ness of the source
code. When a higher level of open-ness is applied, the technical quality and the number of
opportunities for developing new features expand.3
1Recently (November 2001), IBM released its Eclipse platform, previously proprietary software developedin-house at the expense of forty million dollars, as an Open Source project (Industrial Computing Magazine,November 2001).
2Red Hat Linux is a prevalent example for a successful business model fully based on Open Source applications.The company distributes Open Source applications, which can be downloaded for free from the Internet, butprovides its customers full guarantee and technical support. Red Hat acquires the source code at no cost, testsand improves the software, and then sells it in the market. Although Red Hat Linux may be installed and usedfor free (both are permissible by Linux licensing terms), most of its customers prefer to buy an original copy ofthe software, as an “insurance premium”, and enjoy the firm’s guarantee (Young, 1999).
3Few comparative surveys examined the main variables of performance and stability of Open Source programsvs. those of proprietary programs. Recent benchmark tests present superior results of the Open Source Linuxon its proprietary rival, Windows 2000, in terms of functionality, stability and performance (see for instance:
2
Examining the success of Open Source projects, one should cautiously conclude about the
possibilities for other firms to profit by adoption of a similar model for their business activities.
Indeed, Open Source software is available to distributors and solution providers at no cost
and offers consumers higher degrees of flexibility in adapting technology to their needs than
proprietary programs do.4
Since the beginning the 1980s, software developers enjoy extensive legal framework of software
patenting and copyrights. The current legislation, which evolved in and shaped by Courts, was
officially coined by the US Patent and Trademark Office (USPTO) in 1996. The legislation
provides software developers with an extensive protection by IPR, mainly when compared with
the protection provided to inventors of other technologies: Algorithms and technical advances
in software may be patented, while the final product (i.e. software packages) is protected by
copyrights.5
The increasing numbers of software patents submitted to and approved by the USPTO and
the emergence of cases of patent infringements in information technologies reflect a wide adoption
of intellectual property rights as strategic means by software firms (Cowan and Harison, 2001).
Nevertheless, although software developers are able to appropriate from their programs and
inventions by applying intellectual property rights to protect them, many offer their creative
output at zero-price, even though the legal regime provides them a more suitable environment
to claim property rights on source code than ever before.
One positive effect, from a firm’s perspective, engaged in free dissemination of software and
even in software piracy is the expansion of the installed base of the program. Various works
examined the economic benefits of the firm from disseminating products without protection
when network externalities are at presence. Conner and Rumelt (1991) analyze the terms for
a monopolist decision whether to employ protection by technical means or whether to leave its
software unprotected in a static equilibrium. Shy and Thisse (1999) expand this framework
of discussion and introduce conditions for protecting software in a duopoly market. One may
Rothman and Buckman, 2001; PC Magazine, 2001; PC Magazine, 2002).4Users are able to copy parts of open source systems for implementation in other systems, modify them
according to their needs or distribute them to others at no cost.5The Examination Guidelines for Computer-Related Inventions - Final Version (USPTO, 1996) provides a
detailed, yet a controversial account which software components are patentable and which parts can be protectedonly by copyrights.
3
reasonably conclude that when software is distributed without protection, higher adoption rates
are obtained, adding to the utility of users. Firms benefit from dissemination of unprotected
software packages if the growth in demand for licensed copies and user’s propensity to pay
higher prices, as a result of increasing network effects by new and unauthorized users, exceed
the loss of profits from illegal use. This body of literature, however, studies software programs
as final goods, whereas disclosure of source code enables skilled developers to further the quality,
the functionality and the reliability of software. The success of Open Source projects does
not necessarily rely on the majority of consumers preferring a certain product on its rivals
and hence to ”lock-in” to a single market standard, but rather, Open Source application is
recognized successful if it attracts users to support the software and to produce new and improved
versions for a long period. Further, as this argument goes, software firms are able to reduce their
development costs by ”outsourcing” tasks of R&D projects to Open Source communities.6
On the supply side of programmers’ skills, various scholars suggest that involvement in Open
Source development is motivated by behavioural determinants, such as self satisfaction or ”al-
truism” of software developers disclosing their intellectual and professional output to the public
at ”no cost”. Others argue that new opportunities to “socialize” with members of online com-
munities who share common interests and background and the reputation gained in professional
circles are the main reasons for participation in Open Source projects (Lerner and Tirole, 2000;
Lakhani and von Hippel, 2000). Hence, the development of open sources is hardly affected by any
changes in the market and can be illustrated from an economic perspective by a zero-elasticity
supply curve. One drawback of firm’s decision to extend the share of Open Source features in its
software is the decrease in gains from distributing proprietary versions. Our model analyzes the
links between disclosure of software features, technological performance and firm’s profits. Fur-
ther, we reveal which strategy is the most preferred from the firm’s perspective and which policy
tools should be applied to foster innovation in markets of myopic and forward-looking firms. In
reality, however, the theoretical level of full disclosure does not exist, as part of the technical
know-how remains tacit within the domain of inventors. The scenario of complete protection is
un-realistic too, since firms disclose essential software components, such as Application Program6Software firms had long ago reduced their testing costs by introducing beta versions to potential users before
releasing the final product to the market.
4
Interfaces (API),7 to developers of complimentary applications and have to reveal their technical
specifications.8 Therefore, software firms choose to distribute their products as hybrids, in which
part of the source code remains proprietary and the other is made open. “Hybrid” versions of
software may differ one from the other as firms release some modules in a compiled format and
publish the code-lines of others. Alternatively, firms differentiate their products by customizing
licensing terms (McKelvey, 2001).
The communal cooperation for the development of advanced applications by computer ex-
perts, home users and amateurs questions the need for extensive frameworks of intellectual
property rights to protect software technologies. Moreover, as software producers hardly rely
on IPR regimes to prevent unauthorized duplications and rarely implement any technical means
for this purpose (Stolpe, 2000), the present regime seems to employ an over-protective IP doc-
trine. Recently, policy makers world-wide have commissioned efforts to strike a balance between
knowledge disclosure and the legal provisions of IPR, since innovation in software is particularly
important as each advance in the technology generates an enormous number of down-stream
inventions, i.e. new applications, interfaces and complementary products.
This paper examines the underlying links between open-ness and innovation by analyzing
how disclosure affects the technical quality of the software and how firms, strategically, are able
to maximize profits by applying optimal levels of disclosure, derived from market conditions. In
the following sections, we analyze how the dynamics of the market and the evolution of software
change with open-ness. We also discuss which economic attributes may improve or curtail firms’
profits and what strategies, with regards to source code disclosure and price, should be applied
by the firm to maximize gains. Section 2 describes a model for software R&D, in which a short-
sighted monopolistic firm chooses degree of open-ness that maximizes its single-period profits.
Section 3 analyzes mixed strategies of open-ness and pricing that maximize firm’s profits in the7Application Program Interface is a format used by a computer program to communicate with the operating
system or some other software applications. Understanding APIs is a major part in a programmer’s work. Exceptfor writing the routines that perform data processing, the rest of the programming is based on writing the codeto communicate with other computer programs (based on www.techweb.com/encyclopedia).
8If a firm chooses to protect its software by intellectual property rights and by releasing compiled versionswithout their source code, its rivals would still be able to reverse-engineer the functions, inputs and outputsof the software to reveal large part of the codified knowledge and embedded techniques. However, methodsof reverse engineering that render technical information are legally impermissible, infringing both intellectualproperty and Fair Use. Hence, we later assume that the technical know-how obtained from proprietary softwareis only marginal.
5
long run and how the aims of social planners correspond to the decision of the firm. Section
4 expands the scope of the discussion by illuminating firm’s strategy and market behaviour
in some particular scenarios. Finally, we draw conclusions on the linkage between software
disclosure and price to the technical quality of software and the profits of the firm and derive
some policy recommendations how innovation in ICT can be facilitated.
2 Intellectual Property vs. Disclosure: A Model with aMyopic Firm
Software technology is composed of technological features, various components that execute com-
putations and information processing and are involved in the operation of computer programs.
We assume that software features are integrated to a single, coherent technology and do not
overlap in their functionalities and tasks. Software features are allocated evenly on a contin-
uum [0, R], which describes the technical dimension of software technology. The upper limit of
technical performance of the program, or its technical quality, is R.
Following Nordhaus’ model of technical change (1969, Ch. 2), development of additional
features expands the level of quality and the performance of technology. Technology is fostered
by both firms and users, if new functionalities are added or if existent features are improved in
terms of stability and performance. In particular, users of software products are able to integrate
new features they have developed into existent programs, if the firm discloses the sources of the
application. In return to users’ efforts, the firm removes any intellectual property claims from
features that it made publicly available.
Assume for simplicity that no risk is involved in developing new features either by users or
by the firm; if development of a feature begins, it will be completed successfully. Hence, the
development of features taken by users fully substitutes firm’s internal R&D, if the firm chooses
to disclose its code-lines.9 Firm’s R&D expenditure for accomplishing a new feature is c if it
is developed in-house and c1 if conducted in Open Source communities. Since users carry out
major shares of the development process at no cost, c1 is significantly low in comparison to c.9Since participants are not required to high capital investments in hardware to take part in furthering the
software that they use, we are likely to observe an emergence of Open Source projects in software technologies,rather than in electronic engineering or biotechnology.
6
The firm chooses ex ante the share of features that it discloses to the public domain to
be developed by users to full-blown applications, α ∈ [0, 1]. The complementary share of the
technology, (1 − α), is developed by the firm itself. To emphasize, the degree of disclosure
determines not only the profits of the firm but also its investments in R&D, where on one
extreme lies full protection by IPR and, consequently, full ownership of the technology (α = 0),
and on the other hand, technology is developed only by public communities and hence can be
freely copied, disseminated and installed (α = 1). The firm chooses the degree of disclosure, α,
that maximizes its one-period profits.
The price of a single (proprietary) feature, Ψ(α), is set as a function of the level of disclosure
that the firm applies. Figure 1 illustrates graphically the parameters that the firm considers in
determining its strategy (in terms of price and disclosure). By evaluating its R&D expenditure
for open and proprietary features (zone A and B in the diagram) and the revenues achieved for
proprietary features (zone C), the firm aims at maximizing its one-period profits, π:
π = (1− α)Ψ(α)R− [c(1− α)R + c1αR] = (1− α)Ψ(α)R− [c− α(c− c1)] ·R (1)
A marginal change in the degree of disclosure (dα) encompasses three effects on firm’s costs and
gains: First, the revenues decrease by dα · R · Ψ(α) as the firm expands the non-remunerative
segment of the product (zone A’ in the figure). Second, the cost of Open Source development
increases by c1 · dα · R (zone B’) and, finally, the cost of in-house development decreases by
c · dα ·R (zone C’). Derive Equation 1 to measure the cumulative effect on firm’s profits:
dπ
dα= −Ψ(α) ·R + (1− α)
dΨ(α)dα
·R + (c− c1) ·R (2)
Proposition 1 : When a fixed price is applied by the firm (Ψ(α) = Ψ), profits decrease with an
increasing degree of disclosure.
Equation 2 provides an ambiguous result, as its value depends mainly on the pricing policy
of the firm (increasing or decreasing with α). However, in the common case of fixed price, we
may conclude that profits fall when more features are developed as open sources.
We turn now to find the terms for extremum values, when dπdα = 0:
Ψ(α) = (1− α)dΨ(α)
dα+ (c− c1) (3)
7
Or:dΨ(α)
Ψ(α) + (c− c1)=
dα
1− α(4)
By integrating the terms in Equation 4, we obtain a price function for minimal profits:
Ψ∗(α) = (c− c1) +Ψ0
1− α, (5)
where Ψ0 ≡ Const. (see a detailed description in Appendix A). Following the dynamics revealed
in Equation (5):
Proposition 2 : When the degree of disclosure increases, so does the price.
This result is not surprising at all. As the share of proprietary features from which the firm
generates revenues decreases with open-ness, the price rises to sustain gains as before. Yet, the
outcome is somewhat ambiguous as profits are negative at any degree of disclosure if this pricing
policy is applied. Further, it is hard to determine whether profits are maximal or minimal, as
Ψ∗(α) is a flux point (d2π∗dα2 = 0). However, for any given price, the degree of disclosure that
guarantees minimal profits is the following:
α∗ = 1− Ψ0
Ψ(α)− (c− c1)(6)
As Ψ(α) captures changes in α in its behaviour, we may derive only limited conclusions from
Equation 6 that consider a fixed price policy Ψ(α) = Ψ. Therefore, under these conditions,
the degree of disclosure rises when the price of the proprietary features rises. The opposite
result, however, disclosure rises with price, is inconclusive, as the price function may increase
or decrease with α. More complex scenarios, in which price depends on the degree of disclosure
(either increasing or decreasing with it) are discussed in Section 4 below.
3 Dynamic Model of Software Disclosure with a Forward-Looking Firm
We extend our model to include inter-temporal dynamics, and yet we maintain the basic terms
and definitions of the previous model. Define [0, R(t)] as a continuum that describes the technical
quality at period t and changes over time as technology evolves. R(t) is the upper limit for quality
and increases when new features are added by the users or by the firm. As in the previous model,
8
Figure 1: Illustration of the single period model
the firm decides ex ante what share of features, α ∈ [0, 1], is made public and developed by
communities of users. We assume that firm’s strategy in the long run remains un-changed, and
thus licensing terms chosen to maximize profits cannot be altered between periods. The price of
a single proprietary feature changes with the degree of disclosure that the firm applies. Firm’s
revenue in period t accounts for:
RV (t) = (1− α)Ψ(α)R(t) (7)
The total expenditure of the firm on R&D in period t is the following:
RD(t) = αR(t) · c + (1− α)R(t) · c1 = [c− α(c− c1)]R(t). (8)
A constant share of firm’s profits in each period, ρ ∈ (0, 1), is devoted to R&D in the following
period.10 Therefore, the total investment in R&D in period t, RD(t), is determined by the
profits that were gained in the preceding period, π(t− 1):
RD(t) ≡ ρ · π(t− 1) (9)
10To illustrate, R&D intensity in French software firms and information service providers is approximately 14%of their total sales (Abi-Saad et. al., 2001).
9
Subtract the cost of R&D from the revenues of the firm in Equation 7 to obtain the profits in
period t:
π(t) = (1− α)Ψ(α)R(t)− [c− α(c− c1)]R(t) = (1− α)Ψ(α)R(t)− ρπ(t− 1) (10)
Substitute Equation 8 into Equation 9 to obtain R(t) as a function of firm’s investments in R&D,
RD(t):
R(t) =RD(t)
c− α(c− c1)=
ρπ(t− 1)c− α(c− c1)
(11)
Substitute the term for R(t) into Equation 10 to obtain an inter-temporal link between firm’s
profits in successive periods:
π(t) = [(1− α)Ψ(α)ρc− α(c− c1)
− ρ]π(t− 1) (12)
Define NP as the total net profits of the firm in the long-run and γ as the discount factor. The
firm chooses optimal degree of disclosure, α, such that its profits in the long run are maximized:
maxα
NP =∞∑
t=0
(1− ρ)π(R(t), α, t)γt (13)
The target function, W (t), is maximized if the periodic profits are maximized too. Hence,
employing calculus of variations techniques, the optimal degree of α would maximize the net
profits in the long-run (NP ) if it maximizes the value function in every period. 11 We define the
value function of the firm in period t, W (t), by adding the profits in period t to the discounted
value of gains that an expansion of technological features brings to the firm in the following
period:
maxα
W (t) = [(1− α)Ψ(α)ρc− α(c− c1)
− ρ]π(t− 1) + γ · V (π∗(t + 1), α) (14)
Derive W (t) to find extremum values of α:
∂W (t)∂α
= ρ · π(t− 1)[−Ψ(α) + (1− α)dΨ
dα ][c− α(c− c1)] + (c− c1)(1− α)Ψ(α)[c− α(c− c1)]2
+ γ · ∂V (t + 1)∂π∗(t)
· dπ∗(t)dα
(15)
11Maximizing the Bellman Equation with respect to disclosure, α, maximizes the value function of the firm inevery period. A detailed description of the method appears in Dixit (1991, Chapter 11).
10
Applying the Envelope Theorem to solve ∂V (t+1)∂π∗(α) , we receive:
∂V (t+1)∂π∗(t) =
∂W (t + 1)∂π∗(t)
(16)
=[−Ψ(α) + (1− α)dΨ
dα ][c− α(c− c1)] + (c− c1)(1− α)Ψ(α)[c− α(c− c1)]2
(17)
Derive dπ∗(t)dα from Equation 12:
dπ∗(t)dα
= ρ · π(t− 1)[−Ψ(α) + (1− α)dΨ
dα ][c− α(c− c1)] + (c− c1)(1− α)Ψ(α)[c− α(c− c1)]2
(18)
Substitute the results from Equations 17 and 18 into Equation 15, to receive the partial derivative
of the value function:
∂W (t)∂α
= ρ · π(t− 1)[1 + γ · [ (1− α)Ψ(α)ρ
c− α(c− c1)− ρ]
]
· [−Ψ(α) + (1− α)dΨdα ][c− α(c− c1)] + (c− c1)(1− α)Ψ(α)
[c− α(c− c1)]2(19)
Equation 19 provides us with two important properties of the favourable strategies to obtain
maximal profits with regards to the disclosure of the source code. The extremum solution of the
value function and the pricing policy of proprietary features are both important to analyze which
price-disclosure conditions provide the firm with maximal or minimal profits. In particular, if
maximal profits are obtained in an intermediate degree of disclosure (0 < α < 1), then the hybrid
strategy is the most favoured by the firm. However, if W (t) obtains a minimum, we determine
by numerical analysis whether complete disclosure (α = 1) or full protection (α = 0) is the
most preferred strategy. An absolute answer whether Open Source or full protection is the most
profitable strategy does not exist. Rather, the profitability is affected, to a large extent, by the
firm’s pricing policy for proprietary components.
Proposition 3 : Profits increase with disclosure when the price of a single feature, Ψ(α), exceeds
the following function:
Ψ∗(α) =[c + c1 · α
1− α
]·Ψ0, (20)
α ∈ [0, 1] ,Ψ0 ≡ Const. Minimal, stable level of profits are obtained at equality (for a detailed
proof, see Appendix B). A similar outcome of the model is presented also in the model of
11
a myopic firm. Since the firm benefits only from proprietary features protected by intellectual
property, when their share decreases, the price for the remaining ”closed” features would increase.
Therefore, the price of a single software feature, Ψ∗(α), increases with the degree of disclosure, α,
to ”compensate” for lost revenues as a result of expanding the share of non-proprietary features.
However, the profit in the long-run increases if a minimal pricing as presented above is applied,
since users’ contributions to technology expand the continuum [0, R(t)]. Therefore, the firm
benefits recent developments added by users and commercialized: (1−α) · 4R(t). We turn now
to examine whether the common policy of fixed price and complete protection, applied by many
software firms, yields higher profits in the long run in comparison to full or partial disclosure of
the source code.
Proposition 4 : Given a fixed-price policy for proprietary features, profits decrease when disclosure
increases, i.e. ∂W (t)∂α < 0.
By substituting dΨdα in Equation 20 follows:
∂W (t)∂α = ρ · π(t− 1)
[1 + γ
((1− α)Ψ(α)ρc− α(c− c1)
− ρ
)]· [−Ψ(α) [c− α(c− c1)] + (c− c1)(1− α)Ψ(α)]
= ρ · π(t− 1)[1 + γ ·
((1− α)Ψ(α)ρc− α(c− c1)
− ρ
)]· [−Ψ(α) · c1] (21)
Since the terms ρ ·π(t−1),[1 + γ ·
((1−α)Ψ(α)ρc−α(c−c1)
− ρ)]
and Ψ(α) are strictly positive, ∂W (t)∂α < 0.
Therefore, when the firm applies a fixed price policy, very low levels of disclosure of the source
code and release of compiled versions are the most favourable strategies. Formally:
{∂W (t)∂α
< 0, ∀α ∈ [0, 1] | dΨ(α)dα
= 0} (22)
We turn to find the conditions of price and disclosure that optimize the technical quality of the
software, R(t). Measuring the technical level in period t + 1 as a function of the profits in the
preceding period, as appears in Equation 11, we receive:
R(t + 1) =ρπ(t)
c− α(c− c1)(23)
Substitute the term for π(t) from Equation 10 into Equation 23 to obtain an inter-temporal link
between R(t + 1) and R(t):
R(t + 1) = ρ ·R(t) ·[
(1− α)Ψ(α)c− α(c− c1)
− 1]
(24)
12
Deriving the terms for extremum values reveals:
Proposition 5 : The minimal quality is achieved when the price of proprietary features exceeds
the following function:
Ψ∗(α) =[c + c1 · α
1− α
]·Ψ0, (25)
Ψ0 ≡ Const. This result is identical to the condition for obtaining minimal profits in the long
run (proposition 4 ). Further, both technical quality and profits change almost similarly when the
disclosure and the price are modified (for a detailed description, see Appendix C).12 Therefore,
firm’s strategies which are geared towards maximizing profits in the long run correspond the
aims of policy makers to obtain high degrees of innovation and technical change, i.e. a rapid
increase in R(t). Deriving the terms for the extremum values of profits and technical quality
reveals that maximal or minimal values of quality and profits depend mainly on the pricing of
proprietary features by the firm. Therefore, the results of the model are strongly affected by
conditions of disclosure and price in the short and in the long run. In the following section we
present a numerical analysis of the model for various pricing strategies.
4 Illustrating the Dynamics of Prices of Proprietary Sources
The decision on the level of disclosure is largely affected by the pricing policy that the firm applies.
In the former sections of the paper, we discovered that firm’s profits are closely correlated with
an the marginal price to disclosure and hence the pricing policy encompasses major influence
on firm’s strategies and profits. The minimal price-disclosure curve for forward-looking firms
(Equation 20) is illustrated in Figure 2. For most values of α, the marginal price increases
very moderately. However, as α approaches 1 (full disclosure), the price of proprietary features
increases very steeply. Further, the minimal price of proprietary features is correlated with the
ratio (c/c1). The higher the cost of developing software within the firm in comparison to the
cost of Open Source projects, higher degree of disclosure that seems to be more favourable for
the firm. When the cost of developing Open Source features become closer to those of in-house
R&D (i.e. the ratio cc1
decreases), the price curve shifts to the left and the prices of proprietary
features increase very rapidly for smaller values of α.12The discount factor tolerates the effect of α on the marginal profits of the firm in the long run.
13
As concluded in Section 2 and 3 above, when the degree of disclosure increases, the price for
proprietary features increases too (for both myopic and far-sighted firms). This is a conflicting
situation from a social welfare perspective. On one hand, policy makers attempt to foster the
adoption of advanced technologies to increase the level of social welfare (in terms of the technical
quality of the technology in use). Higher prices of proprietary features will reduce the demand
for them and will hinder a complete adoption of the technology. On the other hand, policy
makers perceive disclosure as a positive effect on innovation and technical change, as individual
knowledge is shared with other users and firms. Further, Open Source projects reduces the
need to employ computer experts in trivial tasks that users accomplish successfully within Open
Source community and enable the firm to utilize its resources by re-allocating personnel to
advanced R&D activities. Analyzing minimal price vs. disclosure, we may conclude that the
marginal price becomes very high when the firm applies high degree of disclosure. For example,
when the ratio cc1
= 2 and the firm chooses to disclose half of its features to the public domain,
the price of proprietary feature will rise only in 10.4% in comparison to the price of the same
feature when the source code is fully protected (Ψ(α = 0)). Therefore, provision of subsidy,
s(α), for proprietary features as a percentage of their price would increase both the diffusion of
technology and knowledge spillovers. Formally:
s(α) =Ψ(α)
Ψ(α = 0)− 1 (26)
When the difference between the costs of Open Source development and in-house programming
is smaller (i.e. cc1
decreases), the price of a proprietary feature increases and so does the subsidy
s(α) for any value of disclosure. The subsidy curve shifts to the left as c1 increases towards
c, and vice versa. The analysis of the links between disclosure, price and single-period profits
in Section 2 is conclusive about a negative correlation between disclosure and profit in cases
that fixed price is applied (see also Fig. 4a). However, when the pricing policy of proprietary
features is a function of α, the result is a non-linear profit function, π. The complex behaviour
of the profit function enhances the difficulty to derive generic ”rules of thumb” to steer the
strategies of software firms, as non-linearity exists even in simple scenarios where the price Ψ(α)
is a linear function of α (Figures 4b and 4c). However, in some cases, as presented in Fig. 4b, an
14
Figure 2: Minimal price of a proprietary feature as a function of the degree of disclosure fordifferent ratios of development costs: c
c1= 2 (continuous line) and c
c1= 3.33 (broken line)
intermediate level of disclosure (i.e. a software ”hybrid”) provides the firm with maximal profits,
higher than if full protection policy or complete open-ness of the source code were applied.
15
Figure 3: The level of subsidy, s(α), as a function of the degree of disclosure for different ratiosof development costs: c
c1= 2 (continuous line) and c
c1= 3.33 (broken line)
(Fig. 4a)
(Fig. 4b)
16
(Fig. 4c)
Figure 4: Myopic firm’s one-period profits (π) in various pricing strategies of proprietary features(Ψ(α)): (a) fixed price; (b) price increases with disclosure; (c) Price increases with disclosure(different set of parameters).
5 Conclusions
IPR regimes for software technologies have evolved since the mid 1980s, aiming to resolve issues
of piracy and unauthorized use by expanding the guidelines of traditional legislation, i.e. patents
and copyrights, and by including information technologies in their scope of protection. However,
along the same period, alternative models of intellectual property use, based on the tradition
of Free or Open Source, in which a rapid diffusion of unprotected software is used as the basis
of a profit-making venture have developed. The existent body of literature explores positive
externalities in software piracy and infringements of intellectual property in computer programs.
For example, emergence of network effects generates higher utility for users and expands the
diffusion of software products among legal users and their propensity to pay for the product.
However, this faculty of thought treats computer programs in a form of final products (i.e. com-
piled software packages) and does not evaluate the role of knowledge spillovers in advancing the
technology, had the source code of computer programs made accessible to skilled users. Our
model includes “production externalities”, contributions of users to the technical quality and
functionality of the software, positively correlated with the degree of open-ness. The model ana-
lyzes the relations between software protection, its price and firm’s profits in markets of myopic
and forward-looking firms. The first part of the model presents new insights on the links be-
tween open-ness and firm’s profits. When a fixed-price policy is applied for proprietary features,
17
the correlation between disclosure and profits is negative. Firms would prefer to migrate from
in-house development to open-source methodologies if higher profitability were guaranteed. The
model supports the rationale that firms prefer to apply the ”bazaar model” of Open Source on
the traditional modes of software development only if they expect higher rewards than the gains
from distributing proprietary products. Hence, our model approves the strategic rationale be-
yond firm’s decision to disclose its main asset, the source code, in particular conditions. Further,
when the price of proprietary features does not change with the degree of open-ness, complete
protection is favourable in terms of firm’s profits and technological performance. However, price
dynamics depend on the difference between the costs of developing software as Open Source or
in-house, among other attributes of firm’s strategy. The closer those costs become, the higher
the price of proprietary features is at any degree of disclosure. These results emphasize the
complexity of the behaviour in markets of software technologies. Policies that aim at fostering
technology by modifying pricing, R&D costs and disclosure may divert the technological trajec-
tory to different directions than meant. Hence, innovation and technical change in ICT require
an implementation of diverse and implausible approach towards software open-ness, rather than
application of a general and somewhat sophistic framework. Another important lesson is asso-
ciated with the use fiscal tools to foster higher degrees of innovation and technical quality in
software products. As the firm impels towards maximizing its profits in the short and in the long
run, higher degrees of technical quality of software are achieved at the cost of lower open-ness of
the source code. However, policy makers may maintain the pace of technological development by
implementing subsidy schemes that elevate the demand of users for the non-disclosed share of the
technology. By reducing the prices of proprietary features, e.g. by subsidizing directly the price
of proprietary features, endowing firm’s R&D in return source code disclosure or by establishing
free-software consortia, technology would progress more rapidly, as skilled users would devote
skills and efforts to promote technical performance and quality of software technologies.
18
6 References
Abi-Saad P., David C., Gandon M., Weisenburger E. (2001), Recherche & Developpement enFrance: Resulutats 1999, Estimations 2000, Objectifs Socio-Economiques du BCRD2001, Paris, Ministere de l’Education Nationale.
Conner K.R., Rumelt K.P. (1991), “Software Piracy: An Analysis in Protection Strategies”,Management Science, Vol. 37, No. 2.
Cowan R., Harison E. (2001), Intellectual Property Rights in a Knowledge-Based Econ-omy, MERIT Study for the Dutch Advisory Council for Science and Technology Policy(AWT), AWT Background Study No. 21, May 2001, Maastricht.
Dixit A.K. (1991), Optimization in Economic Theory, 2nd. Edition, Oxford, Oxford Univer-sity Press.
Lakhani K., von Hippel E. (2000), “How Open Source Software Works: ”Free” User to UserAssistance”, MIT Sloan School of Management Working Paper, No. 4117, May 2000.
Lerner J., Tirole J. (2000), “The Simple Economics of Open Source”, NBER Working Paper,No. 7600, March 2000.
McKelvey M. (2001), “The Economic Dynamics of Software: Three Competing BusinessModels Exemplified Through Microsoft, Netscape and Linux”, Economics of Innovationand New Technologies, Vol. 10, pp. 199-236.
Nordhaus W.D. (1969), Invention, Growth and Welfare: A Theoretical Treatment of Tech-nological Change, Cambridge, MIT Press.
PC Magazine (2001), “Performance Tests: File Server Throughput and Response Times”,November 2001, Available in:http://www.pcmag.com/article/0,2997,s%253D25068%2526a%253D16554,00.asp (viewedMay 2002).
PC Magazine (2002), “Samba runs rings around Win2000”, April 2002, Available in:http://www.vnunet.com/News/1131114 (viewed May 2002).
Rothman J.B., Buckman J. (2001), “Which OS is Fastest for High-Performance NetworkApplications?”, Sys Admin, Vol. 10.
Shy O., Thisse J.F. (1999), “A Strategic Approach to Software Protection”, Journal of Eco-nomics and Management Strategy, Vol. 8, No. 2.
Stolpe M. (2000), “Protection Against Software Piracy: A Study of Technology Adoptionfor the Enforcement of Intellectual Property Rights”, Economics of Innovation and NewTechnology, Vol. 9, No. 1.
USPTO (1996), Examination Guidelines for Computer-Related Inventions - Final Version,US Patent and Trademark Office, Washington, D.C., February 1996.
Young (1999), “Giving It Away: How Red Hat Software Stumbled Across a New EconomicModel and Helped Improve an Industry”, in: DiBona et. al. (eds.) (1999), Open Sources:Voices from the Open Sources Revolution, Sebastopol, O’Reilly and Associates.
19
Appendix A Substitute dπdα = 0 in Equation 2 to obtain the terms for extremum points:
Ψ(α) = (1− α)dΨ(α)
dα+ (c− c1) (A1)
Arranging Equation A1, we receive:
dΨ(α)Ψ(α) + (c− c1)
=dα
1− α(A2)
Integrate both terms of Equation A2:∫
dΨ(α)Ψ(α) + (c− c1)
=∫
dα
1− α(A3)
Then, solving Equation A3:
Ψ0 − ln(1− α) = ln(Ψ(α)− (c− c1)) (A4)
Where Ψ0 ≡ Const. From Equation A4 we receive the minimal price function, as follows:
Ψ∗(α) = (c− c1) +Ψ0
1− α(A5)
20
Appendix B Minimal pricing, for which firm’s profits increase with disclosure, is obtained
from derivation of Equation 8, as appears also in Equation 19:
∂W (t)∂α
= ρ · π(t− 1)[1 + γ · [ (1− α)Ψ(α)ρ
c− α(c− c1)− ρ]
]
· [−Ψ(α) + (1− α)dΨdα ][c− α(c− c1)] + (c− c1)(1− α)Ψ(α)
[c− α(c− c1)]2(B1)
Firm’s profits are positive or equal to zero in any period: π(t − 1) ≥ 0, ∀t, α ∈ [0, 1]. Asγ, ρ, α ∈ [0, 1], the term
[1 + γ · [ (1−α)Ψ(α)ρ
c−α(c−c1)− ρ]
]is strictly positive for every value of γ, ρ, α.
Hence, it is necessary to examine only the following term to obtain the price conditions for which∂W∂α ≥ 0:
[−Ψ(α) + (1− α)dΨdα
][c− α(c− c1)] + (c− c1)(1− α)Ψ(α) ≥ 0 (B2)
The firm appropriates only from the proprietary features that it introduces. Assume that theprice for a feature does not decrease with disclosure, i.e. dΨ(α)
dα > 0. Re-arranging B2, we receive:
Ψ(α) · c1 ≤ (1− α)dΨdα
[c− α(c− c1)] (B3)
Hence:dΨ
Ψ(α)≥ c1 · dα
(1− α)[c− α(c− c1)](B4)
Integrating both sides of Equation B4 by α and by Ψ:∫
dΨΨ(α)
≥∫
c1 · dα
(1− α)[c− α(c− c1)](B5)
we receive:ln Ψ(α) ≥ − ln(α− 1) + ln(−c + αc− αc1) + Ψ0 (B6)
or:
lnΨ(α) ≥ ln[(c + c1 · α
1− α)Ψ0
](B7)
The necessary condition for ∂W∂α > 0 is therefore:
Ψ∗(α) ≥[c + c1 · α
1− α
]·Ψ0 (B8)
And the minimal price Ψ∗(α) is positive and increases with α, for any value of α ∈ [0, 1].
21
Appendix C The intertemporal link between R(t) and R(t + 1) is the following:
R(t + 1) = ρ ·R(t) ·[
(1− α)Ψ(α)c− α(c− c1)
− 1]
(C1)
Derive R(t + 1) by α:
∂R(t + 1)∂α
= ρR(t)
[[−Ψ(α) + (1− α)dΨdα
][c− α (c− c1)] + (c− c1) (1− α)Ψ(α)[c− α (c− c1)]
](C2)
Hence, the condition for quality to grow with disclosure is as following:[−Ψ(α) + (1− α)
dΨdα
][c− α (c− c1)] + (c− c1) (1− α)Ψ(α) > 0 (C3)
Simplifying Equation C3, we receive:
Ψ(α) <1− α
c1· [c− α (c− c1)] · dΨ
dα(C4)
Arranging and integrating both sides of Equation C4:∫
dΨΨ(α)
>
∫c1 · dα
(1− α) [c− α (c− c1)](C5)
and solving both sides of the equation:
ln Ψ(α) > − ln(α− 1) + ln (−c + α (c− c1)) + Ψ0 (C6)
or:
Ψ∗(α) >
(c +
αc1
1− α
)·Ψ0 (C7)
22
