The Effect of Competition from Open Source Software on the Quality of Proprietary Software in The Presence of Network Externalities

Purpose: A growing number of open source software emerges in many segments of the software market. In addition, software products usually exhibit network externalities. The purpose of this paper is to study the impact of open source software on the quality strategies of proprietary software vendors when the market presents positive network externalities. Design/methodology/approach: To analyze how open source software affects the quality of proprietary software, this paper constructs two vertical differentiation models: the basic model considers proprietary software monopolizing the market, and the extended model considers proprietary software competing with open source substitute. Findings: This paper mainly finds that the presence of open source software does not necessarily lead to the improvement of proprietary software quality. The network externalities and the compatibility between open source and proprietary software can change the impact of open source software on the quality of proprietary software and affect the quality strategies of proprietary software vendors under certain conditions. Originality/value: The main contribution of this paper is to examine the effect of open source software on the quality strategies for proprietary software vendors in software markets with network externalities.


Introduction
The rapid development of open source software (OSS) is one of the most important events in the software industry. Open source software gives developers the freedom to run it for any purpose, to share its source codes, to identify and correct errors, and to redistribute its source codes (O'Reilly's, 1999;Wheeler, 2007). It has gradually become a great threat to proprietary software in many markets. For examples, Linux, as an open source operating system, occupies more than thirty percent market share in the server operating system market, and Microsoft's Windows, as a proprietary operating system, holds about fifty percent market share; over three-fifths of websites adopt Apache (an open source software) in the web server market, but only around three-tenths use Microsoft's Internet Information (a proprietary software) (Lin, 2008).
Some scholars study the competition between proprietary software and its open source alternatives. Dalle and Jullien (2002)

examine the technological competition between
proprietary and open source software by an interaction theory model; Meng and Lee (2005) investigate the compatibility between open source software and its proprietary substitute; Lin (2008) analyzes the impact of users' expertise on the market in which proprietary software competes with open source software; Pradniwat (2008) and Gramstad (2014)  software's quality. Compared with traditional physical goods, one of the most notable characteristics is that software products usually exhibit positive network externalities, which refer to the increase of user utility when more users employ the same or compatible products (Katz & Shapiro, 1985;Shy, 2001). The positive network externalities effect of software may promote a software product enjoying a commanding market share (Cheng et al., 2011) Two theoretical models are established by extending the vertical differentiation setting of Mussa and Rosen (1978). Their model assumes that the preference heterogeneity of consumers is one dimensional, and studies the monopoly quality choice. This paper mainly

The Basic Model
Consider a software market which exhibits positive network externalities. Potential software users are indexed by their level of the technical skills, which is measured by . Assume that the software users with higher level of technical ability have lower , but those with lower level of technical ability have higher . A user's willingness to pay for the software usability is higher when his/her level of technical skills is lower (Choudhary & Zhou, 2007). The total number of potential users is normalized to 1 and users are uniformly distributed over the interval appear in the basic model. The utility for the potential user at   [0,1] when he/she adopts proprietary software is defined as: ( 1) In (1), vp and fp are the usability and functional quality of proprietary software respectively; pp is the price for proprietary software; adp presents the utility user deriving from the network externalities, in which a (a > 0) is the intensity of network externalities and dp is the installed base of proprietary software (Katz & Shapiro, 1985;Xing, 2014b). Note that: (i) the software quality is assumed to only depend on its usability (includes the ease of installation and user interface, the level of technical support, etc) and functional quality (includes feature set, reliability, security, etc) (Choudhary & Zhou, 2007); (ii) this study only considers a direct network externalities effect (Shy, 2001).
The profit function of proprietary vendor is given by: ( 2) In (2), rfp 2 denotes the cost of improving functional quality, where r is a positive parameter.
The proprietary vendor decides the functional quality (fp ) and price (pp) for its software. Note that the usability of proprietary software (vp) is assumed to be exogenous. The timing of choosing quality and pricing is as follows. In the first stage, the proprietary vendor determines the functional quality of software. In the second stage, it sets software price. According to the market coverage, the following two cases are considered.

Case I: Proprietary Software Monopolizes in a Fully Covered Market
If the market is fully covered, all potential users adopt the proprietary software. In this case, the installed base equals 1 (i.e., dp = 1). The proprietary vendor chooses its price according to the equality: fp + a -pp = 0. Thus, the optimal price for proprietary software is: Then the profit function of proprietary vendor on fp is given by: Solving the first order condition of profit function gives the optimal functional quality: -864-Journal of Industrial Engineering and Management -http://dx.doi.org/10. 3926/jiem.1362 Obviously, the second order condition is met when r > 0. In this case, the optimal functional quality of proprietary software does not depend on the network externalities.

Case II: Proprietary Software Monopolizes in a Partially Covered Market
If the market is partially covered, some potential users with high level of technical skills do not adopt the proprietary software. In this case, the marginal user type ( ) who is indifferent between adopting and not adopting proprietary software is given by: Solving this equation yields: Since the installed base meets: dp = 1 -, the demand function of proprietary software is: (7) Thus, the profit function of proprietary vendor is: According to the first order condition, the optimal price of proprietary software is: The second order condition requires: vp > a. The profit function of proprietary vendor on fp is given by: The first order condition of (10) with respect to fp gives the optimal functional quality of proprietary software: The second order condition requires: -865-Journal of Industrial Engineering and Management -http://dx.doi.org/10. 3926/jiem.1362 Obviously, the optimal functional quality of proprietary software increases as the intensity of network externalities increases when the proprietary vendor partially monopolizes the market.
However, it does not depend on the network externalities when the proprietary vendor monopolizes the whole market.

Case III: Proprietary Software Competes with Open Source Software
This section considers the case that open source software also presents in the market. Open source software is from a not-for-profit community. In this case, proprietary software competes with its open source substitute. The utilities for the potential user at   [0,1] when he/she adopts open source and proprietary software are respectively defined as: (13)   (14) In (13) and (14) According to (16), (17) and (18) In the second stage, software providers set price. Since the price of open source software is equal to zero (i.e., po = 0), only the optimal price for proprietary software needs to solve. The first order condition of (22) with respect to pp yields: The second order condition requires: vpo -2a(1 -k) > 0. Plugging (23) into (22) In the first stage, the proprietary vendor chooses its software quality. The first order condition of (24) with respect to fp is: Proof. according to (26), and .
The above proposition gives a comparison of proprietary software's optimal functional quality under two specific compatible degrees (k = 0 and k = 1). It shows that the optimal functional quality of proprietary software when two types of software are fully compatible may be higher or lower than when they are fully incompatible. -869-

Comparison
This section compares the optimal results under the case of proprietary software monopolizing and that under the case of it facing the competition of open source software.

Comparison of fp # and fp *
Comparing the optimal functional quality of proprietary software under case I and that under case III, the following result is find.
The above proposition shows that, proprietary software's optimal functional quality when it monopolizes the whole market is higher than when it competes with open source software. The reason is that, proprietary vendor can obtain more profit when monopolizing the whole market than when facing competition from open source software, thus it has more money to improve its software quality under case I than under case III. That is, the presence of open source software may lead to the functional quality of proprietary software increase or decrease. This is different from some existing research results (Raghunathan et al., 2005;Lanzi, 2009). In contrast to a proprietary software monopolizing case, Raghunathan et al. (2005) find that the quality of proprietary software will decrease and while Lanzi (2009) (Raghunathan et al., 2005;Choudhary & Zhou, 2007;Xing, 2012).

Conclusions
Through modifying the vertical differentiation model, this