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Private Provision of a Complementary Public Good∗ Private Provision of a Complementary Public Good∗ Richard Schmidtke † University of Munich Preliminary Version Abstract For several years, an increasing number of firms are investing in Open Source Software (OSS). While improvements in such a non- excludable public good are not appropriable, companies can benefit indirectly in a complementary proprietary segment. We study this incentive for investment in OSS. In particular we ask how (1) market entry and (2) public investments in the public good affects the firms’ behaviour and profits. Surprisingly, we find that there exist cases where incumbents benefit from market entry. Moreover, we show the counter-intuitive result that public spending does not necessarily lead to a decreasing voluntary private contribution. JEL-classification numbers: C72, L13, L86 Keywords: Open Source Software, Private Provision of Public Goods, Cournot- Nash Equilibrium, Complements, Market Entry ∗I would like to thank Monika Schnitzer, Karolina Leib, Thomas M¨uller, Sougata Poddar and Patrick Waelbroeck and participants at the EDGE Jamboree in Marseille, at the International Industrial Organiza- tion Conference in Chicago, at the Society for Economic Research on Copyright Issues Annual Conference in Torino, at the Kiel-Munich Workshop 2005 in Kloster Seeon at the E.A.R.I.E. in Berlin and at the Annual Meeting of the Verein fuer Socialpolitik in Dresden for helpful comments and suggestions. †Department of Economics, University of Munich, Akademiestr. 1/III, 80799 Munich, Germany, Tel.: +49-89-2180 3232, Fax.: +49-89-2180 2767, e-mail: [email protected] 1 1 Introduction For several years, an increasing number of firms like IBM and Hewlett-Packard or Suse and Red Hat have begun to invest in Open Source Software. Open Source Software, such as Linux, is typically under the General Public License (GPL) and therefore any improvement must be provided for free. Hence, an Open Source Software can be seen as a non-excludable public good meaning that firms are not able to sell the Open Source Software or their improvements. This issue raises the question why companies do contribute to such a public good. Lerner and Tirole (2000) argue that firms expect to benefit from their expertise in some market segment of which the demand is boosted by the introduction of a complementary Open Source Software. Although the companies cannot capture directly the value of an open source program’s improvement, they can profit in- directly through selling more complementary proprietary goods at a potentially higher price. Notice, that this incentive to contribute to a non-excludable public good arises not only in the case of Open Source Software. In fact, if e.g. a firm’s advertising increases not only the demand for the firm’s own good but also the demand for its competitors’ products (Friedman (1983) calls it cooperative advertising) or if a firm’s lobby-activity has a positive effect on the whole industry, the analysis remains the same. In this paper we study the incentive of investment in such a non-excludable public good. In particular we address the following two questions: (1) What is the effect of a higher public good investment by the government on the firms’ production decisions and their profits? (2) How does market entry and therefore fiercer competition affect the incentive to contribute to the public good and how does it influence the incumbents’ profits? We contribute to answering the questions (1) and (2) by analyzing a model with Cournot-Competition where the firms can produce a private and a public good, but can sell only the private good. For the consumers, the private and public goods are complements. An increase in the available quantity of the public good increases their willingness to pay for the private good. 2 The first question is especially interesting because of the ongoing discussion if and how the government should support Open Source Software.1 One might fear that an increase in the government’s contribution to the public good decreases firms’ voluntary spending like it is known from the public good literature (e.g Bergstrom et al. (1985)). Interestingly, we will show that this does not have to be the case and that it is even possible that the firms’ investments increase if the government increases its contribution to the public good. Thus it is not obvious whether the government’s and the firms’ public good investments are strategic complements or substitutes to each other. The second question is shortly addressed by Lerner and Tirole (2000). They argue that the usual free-rider problem should appear because the firms are not able to capture all the benefits of their investments. Therefore, one might think that with an increasing number of firms the free-rider problem gets worse and so the firms’ contribution to the public good decrease. As a consequence the firms’ profits and the social surplus might decrease. We show in this paper that the market entry of an additional firm has a positive externality (through the entrant’s contribution to the public good) and a negative externality (through the entrant’s production of the private good) on the incum- bents. We find that for certain cost and demand functions each firm reduces its output as a consequence of market entry and suffers a decrease in profits. In this case incumbents dislike market entry. Surprisingly, for certain cost and demand constellations, it is also possible that with market entry every firm expands its output and is able to increase its profit. However, a social planer unambiguously prefers market entry. This article is related to the public good literature that is concerned with the private provision of a non-excludable public good. In standard models of public good provision,2 households can buy or produce the private and the public good and they receive a certain utility directly from the existence of these goods. In our model, firms do not benefit directly form the production of a public good. 1See e.g. Hahn (2002), Evans and Reddy (2002) or Schmidt and Schnitzer (2002). 2See e.g. Bergstrom et al. (1986) for a general approach and e.g Bitzer and Schr¨oder (2002) or Johnson (2002) for an application to Open Source Software. 3 They produce the public good because of the complementarity to the private good. This leads to a new effect: The incentive of the firms to contribute to the public good depends on the market environment and therefore on the number of com- petitors. In the normal setup the marginal utility of the public good is determined through the utility function and is exogenously given. In our setup it is endoge- nous and depends on the ability to use the additional unit of the public good to earn money in the proprietary sector. This, however, depends on the degree of competition in this sector. A second strand of literature our paper is related to is the literature of Multi- market Oligopoly. Bulow, Geanakoplos and Klemperer (1985) analyze the effects of a change in one market environment. In their model different markets are re- lated through the cost function. In our model the markets are not related through the production technology but through the demand function. Bulow, Geanakoplos and Klemperer (1985) address this issue but do not formalize it. They mention that firms must take care off cross-effects in making marginal revenue calculations and consider the strategic effects of their actions in one market on competitors’ actions in a second. In our model we formalize this issue and extend it to the interesting case of a non-excludable public good which is in contrast to the model of Bulow et al. (1985) where only private goods are considered. Becker and Murphy (1993) analyze a model in which advertisement and a adver- tised good enters the utility function of the households. Advertisement has the property that it raises the willingness to pay for the advertised good and is from the economic viewpoint complementary to the advertised good. Nevertheless, in their setup a firm’s advertisement is only complementary to its own private good. In our model it is also complementary to the competitors’ private goods. In some sense, the paper most closely related to ours is Friedman (1983). He uses a dynamic setup and treats advertising like capital in the sense that a firm can build up a ”goodwill stock” through advertising comparable to a capital stock. Due to his modelling an increasing number of active firms leads to a steady-state in which conventional competitive effects dominate and prices converge to marginal costs. However, we look at a static game to concentrate explicitly on the externalities between the firms and the goods and come up with different results. We will proceed as follows. The next section sets up the general model. In 4 Section 3 we look at the properties of the market equilibrium. After this we analyze in Section 4 the general production adjustment process and the reaction of the profits due to an exogenous change in the production of the private and the public good. In Section 5 we apply this analysis to determine the effects of a government intervention and the effects of market entry. The final section concludes. 2 The Model Consumers Consider individuals who consume two goods: A private good and a non- excludable public good. Let X describe the available quantity of the private good, e.g. computer hardware, and Y the available quantity of the non-excludable public good, e.g. Open Source Software.3 These two types of goods are complements for the consumers. The consumers have to pay a price p for every unit of the private good they want to consume.
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