Summary
We develop a model of R&D competition between an incumbent and a potential entrant with network externalities and durable goods. We show that the threat of entry eliminates the commitment problem that an incumbent may face in its R&D decision due to the goods durability. Moreover, a potential entrant over-invests in R&D and an established incumbent might exhibit higher, equal or lower R&D investments in comparison with the social optimum. In our model, the incumbent’s commitment problem and the efficiency of its R&D level is determined by the extent of the network externalities.
Introduction
An industry exhibits network externalities when the benefit that consumers enjoy from purchasing one or several of its goods depends on the number of other consumers that use the same and/or compatible products. For the firms in those sectors (e.g. software, telecommunications, consumer electronics, etc.), the presence of network externalities implies that the attractiveness of their products is a function of their quality-adjusted prices and the potential benefit attached to their expected network sizes (i.e. installed bases).
Those products (i.e. network goods) tend to be characterized by two features closely related. Durability and rapid technological progress. 2 Durability implies that network goods tend to ”wear out” not as a result of physical deterioration, but as a consequence of technical obsolescence; a feature due to technological progress. For example, a given software (or mobile phone, or video game, etc.) can be functional for a long time. However, the utility derived by its use tend to be dissipated due to new (and actually very frequent) developments that are more closely related to consumers needs and tastes.
This paper considers a stylized network industry where these two features, durability and technological progress, are analyzed together. In particular, we propose a model of R&D competition between an incumbent and a potential entrant and consider the implications of the durability of network goods. Our main objective is to isolate the role of network externalities and analyze the social efficiency of the R&D incentives of the firms in this industry.
We depart from the current literature by considering, simultaneously, an oligopolistic setup, endogenous R&D processes and durable goods. Therefore, this paper is not only closely related to the literature on durable goods and to the literature on technological progress in network industries, but represents a first step in bridge them together.
The economic literature has highlighted the role that durability plays in the evolution of a market dominated by a monopolist. In particular, the conventional problem for the monopolist is that, having sold a durable good, there is an incentive to reduce price later to bring into the market those consumers that would not pay the initial high price. However, consumers realize that the monopolist has such an incentive to reduce price once they have purchased and those that value the good less highly will withhold their purchase until price falls. For this reason the monopolist is unable to extract as much money from the market as would be possible with a pre-commitment of ”no future price reductions”. The fact that in the absence of commitment the monopolist may act against his own profitability implies a ”time-inconsistency” problem (i.e. choices that maximize current profitability might not maximize overall profitability).
This notion was first discussed by Coase (1972) and has been labelled as the ”Coase Conjecture”. 3 Since its formulation, the Coase Conjecture has been theoretically devel-oped in several papers that consider the robustness of the basic observation. 4
The essential problem is that the monopolist’s actions in the future provide competi-tion for the company in the present market. 5 If the monopolist is able to lease the good, distort technology or implement buy back procedures then more profit can be extracted from the market since these strategies restrict the aftermarket. 6 Failing this the monopo-list has an incentive to reduce durability or make the good obsolete after a period of time. 7 The existing analysis of durability in the presence of network externalities has intended,as the main literature on durability, to verify the validity of the Coase Conjecture. 8 However, the implications of durability are much broader than the pricing commitment
problem considered in the analysis of the Coase Conjecture. In particular, the result that a monopolist in the absence of commitment may affect its own overall profitability applies in several contexts. In fact, as pointed out by Waldman (2003), any present and future action that affects the future (relative) value of the monopolist’s used goods might be subject to the ”time-inconsistency” described above. One leading case of such actions is a firm’s R&D expenditures which, by definition, affect the (relative) value of used (or previously sold) goods. 9
In the presence of network externalities, the similar analysis of introduction of new durable goods has been analyzed. 10 However, this literature is focused on a monopolistic setup and considers the production of new technologies as exogenous. Hence, and to the best of our knowledge, there is no analysis that consider explicitly the process of endogenous R&D processes in the presence of network externalities and durable goods.
The paper presented by Ellison and Fudenberg (2000) is the closest to ours and is ac-tually our departure point. In that paper, the authors consider a monopoly that operates in a two-period framework and produces durable network goods. In the first period the monopoly produces a good with a given low quality and, subsequently, has the choice of introducing an improved version in the second period. Network externalities play a role because the improvement of the old good implies backward compatibility. That is, consumers of the new good enjoy network benefits from the entire population, while con-sumers of the old good only enjoy network benefits from consumers of the same good. 11 In their model, there is an inflow of new consumers in the second period and, with consumer homogeneity, the paper shows that the monopolist has the incentive to introduce the improved good, even though the monopolist’s overall profits (and social surplus) is reduced. That is, in the absence of commitment the monopolist’s choice that maximizes current (second period) profits does not maximize overall profitability.
We present a model that extends that of Ellison and Fudenberg (2000) by introducing and endogenous R&D process in the production of the new technology, and consider the role of a potential entrant. We show results not present in the Ellison and Fudenberg (2000) analysis. In particular, we consider a two-period framework with an incumbent, a potential entrant and an inflow of new consumers. Consumers are homogeneous and participate in a market with durable network goods.
In the first period, there is a first group of consumers that buy a network good from the established incumbent. Before the second period starts, a potential entrant appears in the market and, jointly with the incumbent, decides on an investment level that will allow him to compete in the second period. This R&D process is stochastic. By investing a certain amount, both firm determine the probability that in the second period they are able to produce a new product that is quality-improved relative to the existing good produced by the incumbent. Conditional on the success or failure of the innovation process, both firms compete in price in the second period when a new group of consumers arrive.
We analyze the incentives to innovate for both firms, we compare it to the social opti-mum and investigate the role of the network externalities. With our simplified approach, we are able to isolate the impact of network externalities and reach three main results. 12 First, the threat of entry reverses the commitment problem that a monopolist (without such threat) may face in its R&D decision given good durability. This result is not present in the current literature and follows from the role that R&D incentives play in deterring entry. In our case, the monopolist’s commitment problem arises only due to the presence of network externalities.
Second, the levels of R&D determined by market outcome might differ from the so-cially optimal levels. In particular, a potential entrant always over-invests (as an entry strategy) and an established incumbent might exhibit higher, lower or equal R&D levels in comparison with the social optimum. This result suggests that successful entry takes place too often in comparison with the social optimum.
And third, the extent of network externalities is the crucial parameter in the efficiency of the incumbent R&D level. In fact, it is only the presence of network externalities that permits, potentially, to the established incumbent to provide an efficient level of innovation. Without network externalities (or very low network effects), it is shown that the incumbent firm always under-invests in R&D efforts. This result sheds some light on the debate whether a dominant incumbent in a network industry provides sufficient innovation to the society.
The paper is organized as follows. The next section presents the model. Section 3 presents the analysis of its equilibrium. Section 4 computes the social optimum and compares it with the results of the market outcome. Finally, section 5 concludes and discusses some areas of further research.
Those products (i.e. network goods) tend to be characterized by two features closely related. Durability and rapid technological progress. 2 Durability implies that network goods tend to ”wear out” not as a result of physical deterioration, but as a consequence of technical obsolescence; a feature due to technological progress. For example, a given software (or mobile phone, or video game, etc.) can be functional for a long time. However, the utility derived by its use tend to be dissipated due to new (and actually very frequent) developments that are more closely related to consumers needs and tastes.
This paper considers a stylized network industry where these two features, durability and technological progress, are analyzed together. In particular, we propose a model of R&D competition between an incumbent and a potential entrant and consider the implications of the durability of network goods. Our main objective is to isolate the role of network externalities and analyze the social efficiency of the R&D incentives of the firms in this industry.
We depart from the current literature by considering, simultaneously, an oligopolistic setup, endogenous R&D processes and durable goods. Therefore, this paper is not only closely related to the literature on durable goods and to the literature on technological progress in network industries, but represents a first step in bridge them together.
The economic literature has highlighted the role that durability plays in the evolution of a market dominated by a monopolist. In particular, the conventional problem for the monopolist is that, having sold a durable good, there is an incentive to reduce price later to bring into the market those consumers that would not pay the initial high price. However, consumers realize that the monopolist has such an incentive to reduce price once they have purchased and those that value the good less highly will withhold their purchase until price falls. For this reason the monopolist is unable to extract as much money from the market as would be possible with a pre-commitment of ”no future price reductions”. The fact that in the absence of commitment the monopolist may act against his own profitability implies a ”time-inconsistency” problem (i.e. choices that maximize current profitability might not maximize overall profitability).
This notion was first discussed by Coase (1972) and has been labelled as the ”Coase Conjecture”. 3 Since its formulation, the Coase Conjecture has been theoretically devel-oped in several papers that consider the robustness of the basic observation. 4
The essential problem is that the monopolist’s actions in the future provide competi-tion for the company in the present market. 5 If the monopolist is able to lease the good, distort technology or implement buy back procedures then more profit can be extracted from the market since these strategies restrict the aftermarket. 6 Failing this the monopo-list has an incentive to reduce durability or make the good obsolete after a period of time. 7 The existing analysis of durability in the presence of network externalities has intended,as the main literature on durability, to verify the validity of the Coase Conjecture. 8 However, the implications of durability are much broader than the pricing commitment
problem considered in the analysis of the Coase Conjecture. In particular, the result that a monopolist in the absence of commitment may affect its own overall profitability applies in several contexts. In fact, as pointed out by Waldman (2003), any present and future action that affects the future (relative) value of the monopolist’s used goods might be subject to the ”time-inconsistency” described above. One leading case of such actions is a firm’s R&D expenditures which, by definition, affect the (relative) value of used (or previously sold) goods. 9
In the presence of network externalities, the similar analysis of introduction of new durable goods has been analyzed. 10 However, this literature is focused on a monopolistic setup and considers the production of new technologies as exogenous. Hence, and to the best of our knowledge, there is no analysis that consider explicitly the process of endogenous R&D processes in the presence of network externalities and durable goods.
The paper presented by Ellison and Fudenberg (2000) is the closest to ours and is ac-tually our departure point. In that paper, the authors consider a monopoly that operates in a two-period framework and produces durable network goods. In the first period the monopoly produces a good with a given low quality and, subsequently, has the choice of introducing an improved version in the second period. Network externalities play a role because the improvement of the old good implies backward compatibility. That is, consumers of the new good enjoy network benefits from the entire population, while con-sumers of the old good only enjoy network benefits from consumers of the same good. 11 In their model, there is an inflow of new consumers in the second period and, with consumer homogeneity, the paper shows that the monopolist has the incentive to introduce the improved good, even though the monopolist’s overall profits (and social surplus) is reduced. That is, in the absence of commitment the monopolist’s choice that maximizes current (second period) profits does not maximize overall profitability.
We present a model that extends that of Ellison and Fudenberg (2000) by introducing and endogenous R&D process in the production of the new technology, and consider the role of a potential entrant. We show results not present in the Ellison and Fudenberg (2000) analysis. In particular, we consider a two-period framework with an incumbent, a potential entrant and an inflow of new consumers. Consumers are homogeneous and participate in a market with durable network goods.
In the first period, there is a first group of consumers that buy a network good from the established incumbent. Before the second period starts, a potential entrant appears in the market and, jointly with the incumbent, decides on an investment level that will allow him to compete in the second period. This R&D process is stochastic. By investing a certain amount, both firm determine the probability that in the second period they are able to produce a new product that is quality-improved relative to the existing good produced by the incumbent. Conditional on the success or failure of the innovation process, both firms compete in price in the second period when a new group of consumers arrive.
We analyze the incentives to innovate for both firms, we compare it to the social opti-mum and investigate the role of the network externalities. With our simplified approach, we are able to isolate the impact of network externalities and reach three main results. 12 First, the threat of entry reverses the commitment problem that a monopolist (without such threat) may face in its R&D decision given good durability. This result is not present in the current literature and follows from the role that R&D incentives play in deterring entry. In our case, the monopolist’s commitment problem arises only due to the presence of network externalities.
Second, the levels of R&D determined by market outcome might differ from the so-cially optimal levels. In particular, a potential entrant always over-invests (as an entry strategy) and an established incumbent might exhibit higher, lower or equal R&D levels in comparison with the social optimum. This result suggests that successful entry takes place too often in comparison with the social optimum.
And third, the extent of network externalities is the crucial parameter in the efficiency of the incumbent R&D level. In fact, it is only the presence of network externalities that permits, potentially, to the established incumbent to provide an efficient level of innovation. Without network externalities (or very low network effects), it is shown that the incumbent firm always under-invests in R&D efforts. This result sheds some light on the debate whether a dominant incumbent in a network industry provides sufficient innovation to the society.
The paper is organized as follows. The next section presents the model. Section 3 presents the analysis of its equilibrium. Section 4 computes the social optimum and compares it with the results of the market outcome. Finally, section 5 concludes and discusses some areas of further research.
The Model
We consider a model of a network industry with durable goods based on that of Ellison and Fudenberg (2000). 13 There are two periods denoted by t = 1 and t = 2 with a group of homogeneous consumers arriving in each period. In period 1 there is a monopolist incumbent that is challenged in period 2 by a potential entrant. In period 2, firms compete in prices with quality differentiated products. Quality is determined through endogenous and stochastic R&D processes carried out in period 1.
Supply Side and R&D Process
In period 1, an incumbent monopolist, I, produces a durable network good with quality level q1 (i.e. stand-alone value). The good lasts two periods after which it vanishes. We consider the case of product innovations where, subject to R&D expenditures, the incumbent might be able to produce a network good of better quality to be introduced in period 2. In our model, this process of innovation is carried out at the end of period 1. In addition, we assume that the outcome of the R&D process is stochastic with two possible outcomes, success or failure. This outcome is realized at the beginning of period 2.
In period 1, an incumbent monopolist, I, produces a durable network good with quality level q1 (i.e. stand-alone value). The good lasts two periods after which it vanishes. We consider the case of product innovations where, subject to R&D expenditures, the incumbent might be able to produce a network good of better quality to be introduced in period 2. In our model, this process of innovation is carried out at the end of period 1. In addition, we assume that the outcome of the R&D process is stochastic with two possible outcomes, success or failure. This outcome is realized at the beginning of period 2.
Demand Side and Expectation Formation Process
The demand side represents the core of the model. In each period there is a group of Nt homogeneous consumers arriving in the market and, for convenience, we normalize N1 + N2 = 1. Consumers exhibit a per-period unitary demand for a network good and buy as soon as they reach the market. This implies that the N1 consumers make a purchase decisions in period 1 and in period 2. Given durability, this is not a trivial implication.
To see this, note that the price charged to the N1 consumers in period 1 tries to extract period 1 and 2 surpluses (i.e. the good is durable). However, period 2 surplus is affected by the outcome of the R&D processes, the prices of the two firms in period 2 and the N1 and N2 consumers’ choices. Therefore, the willingness to pay of the N1 consumers in period 1 depends on their beliefs on how the firms are going to behave in period 2. This gives rise to the commitment problem discussed in the introduction.
The demand side represents the core of the model. In each period there is a group of Nt homogeneous consumers arriving in the market and, for convenience, we normalize N1 + N2 = 1. Consumers exhibit a per-period unitary demand for a network good and buy as soon as they reach the market. This implies that the N1 consumers make a purchase decisions in period 1 and in period 2. Given durability, this is not a trivial implication.
To see this, note that the price charged to the N1 consumers in period 1 tries to extract period 1 and 2 surpluses (i.e. the good is durable). However, period 2 surplus is affected by the outcome of the R&D processes, the prices of the two firms in period 2 and the N1 and N2 consumers’ choices. Therefore, the willingness to pay of the N1 consumers in period 1 depends on their beliefs on how the firms are going to behave in period 2. This gives rise to the commitment problem discussed in the introduction.
Conclusions
We presented a model of R&D competition between an incumbent and a potential entrant in market with durable goods and network externalities. In particular, we analyzed the market outcome and the social efficiency of the incentive to innovate in the presence of uncertain innovation processes. The robustness of the presented results with respect to the assumed functional forms is the objective of current work.
We found three main results. First, the threat of entry reverses the commitment problem that a monopolist (without such threat) may face in its R&D decision given the durability of the network goods. This result is not present in the current literature on R&D and follows from the role that R&D incentives play in deterring entry. In our case, the monopolist’s commitment problem arises only due to the presence of network externalities.
We presented a model of R&D competition between an incumbent and a potential entrant in market with durable goods and network externalities. In particular, we analyzed the market outcome and the social efficiency of the incentive to innovate in the presence of uncertain innovation processes. The robustness of the presented results with respect to the assumed functional forms is the objective of current work.
We found three main results. First, the threat of entry reverses the commitment problem that a monopolist (without such threat) may face in its R&D decision given the durability of the network goods. This result is not present in the current literature on R&D and follows from the role that R&D incentives play in deterring entry. In our case, the monopolist’s commitment problem arises only due to the presence of network externalities.
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