Flexible versus dedicated technology adoption in the presence of a public firm.

• Author: Gil-Molto, Maria Jose

1. Introduction

   In the recent past, many firms all over the world have substituted their traditional production processes with more flexible systems. Some of these flexible technologies allow for greater capacity (process flexibility), which can increase the ability of firms to adapt to fluctuations in demand (Boyer and Moreaux 1997; Boyer, Jacques, and Moreaux 2002). In other cases, the advantage of a flexible manufacturing system (FMS) over dedicated equipment (DE) is that the former allows a firm to supply several products and consequently to participate in different markets (in other words, to become a multiproduct or multimarket firm (1)) without having to invest in separated manufacturing processes. This is called product flexibility and is the main focus of our paper. Apart from benefits, flexible technologies also report higher set-up costs, mainly in the form of development or adjustment costs (Jaikumar 1986).

   The study of the adoption of FMS by private firms was first introduced by Roller and Tombak (1990) and Kim, Roller, and Tombak (1992) in the context of oligopolistic competition. Their findings indicate that the adoption of flexible technologies requires a sufficiently low adoption cost, sufficiently high product differentiation, and large enough markets, while consumers benefit from the use of FMS due to the increase in competition. (2) In addition, Roller and Tombak (1993) validate these results with an empirical study. Dixon (1994) evaluates the welfare effects of using FMS when the marginal cost of production is increasing in the number of goods produced and when the markets are unrelated. As a result, adopting FMS might lead to welfare losses due to the inefficiency in production. On the other hand, Eaton and Schmitt (1994) point out that the adoption of FMS may correspond to preemptive strategies, leading to higher levels of concentration, in the context of horizontal product differentiation.

   To the best of our knowledge, the issue of technology choice as exemplified by the adoption of FMS versus DE technologies has not been studied in the context of a mixed market where private (profit-maximizing) firms coexist with public (not-for-profit) ones. Such mixed markets are quite prevalent in transition economies, but not exclusively so; telecommunications, health services, and the postal sector in many countries are organized as mixed markets. Although many public firms have been privatized in recent years, it is worth pointing out that the behavior of these recently privatized firms remains subject to public regulation.

   Our analysis is motivated by a large number of industries in which multiproduct and single-product firms coexist and the presence of public (or newly privatized but still regulated) firms is common. This is the case for industries such as energy supply, transport, telecommunications, or health care. First, consider the case of telecommunications. Traditionally, the provision of internet access, telephone, and TV services required the use of different technologies and separate production processes for each one of them. At present, however, cable technology can be used by firms to provide these three different services using the same production process, thereby enabling firms to be present in all three markets and to exploit economies of scope. In this sense, cable technology can be considered an example of FMS. (3) Interestingly, the matter raised public concerns when the technology first appeared and was made available to firms. In the UK, regulators have encouraged cable companies to provide telephone services, but have not allowed the former public operator, British Telecom, to enter the television business (Waverman and Sirel 1997). Similarly, Spanish Telefonica was not permitted to compete with cable operators for a certain period of time (Cantos-Sanchez, Monet, and Sempere 2003).

   Another example draws from the health care sector. There is evidence of economies of scope (Ozcan, Luk, and Haksever 1992), which can be related to the use of FMS. There are several empirical studies stressing that public hospitals provide a wider range of services than private hospitals (Shortell et al. 1986; Shortell et al. 1987; Schlesinger et al. 1997). Moreover, public hospitals tend to provide more innovative services without competition, whereas private hospitals are more likely to add these services when there is competition (Schlesinger 1998). This body of observations suggests that both the public or private character of firms and the degree of competition among them seem to be key factors influencing the adoption of FMS (thus, the multiproduct/multimarket character of firms).

   Our main contribution is to introduce the analysis of the choice of production flexibility in the context of a mixed duopoly. Our model consists of two output competing firms (one of them being public) and two markets. Following Roller and Tombak (1990) and Kim, Roller, and Tombak (1992), we assume that there is a degree of product substitutability across markets. Using a flexible technology allows firms to be present in both markets, whereas using a dedicated technology constrains firms to be present in only one of them. We aim at characterizing the market conditions (i.e., market size and substitutability) and technology cost conditions that would lead in equilibrium to the adoption of FMS as opposed to DE. For comparison purposes, we also undertake this characterization for the case of a private duopoly. We find that a configuration where both firms adopt flexible technologies requires less-demanding technology cost conditions in the mixed duopoly than in the private duopoly. A similar result occurs when both firms use a dedicated technology for very low or very high substitutability.

   A natural question to address in this context relates to the potential benefits of privatizing the public firm when a flexible technology becomes available. This issue, which has been ignored so far by the literature on mixed oligopoly, is relevant from the practical and policy-making point of view. This is especially so in the light of recent liberalization trends across the world, in many cases in industries where, as exemplified before, multiproduct firms (may) coexist with single-product firms. In the absence of the issue of flexible technology adoption, the literature on mixed oligopoly has shown that privatizing a public firm would be worthy from the social welfare point of view if the public firm is less efficient than the private firm and the marginal cost of production is linear, if there is freedom of entry, or if, with economies of scale, the number of private firms is large enough (de Fraja and Delbono 1989, 1990; Estrin and de Meza 1995; Anderson, de Palma, and Thisse 1997). However, if firms' outputs are subsidized, the effects of privatization are not so positive, with welfare unaffected if firms move simultaneously (White 1996; Pal and White 1998; Poyago-Theotoky 2001, among others) or even reduced if the public leader becomes a private leader postprivatization (Fjell and Heywood 2004). In our paper, in order to isolate the issue of the strategic adoption of flexible technologies, we will abstain from introducing public subsidies. Interestingly, our results indicate that privatization is socially beneficial only when both firms in the mixed duopoly adopt FMS and products are sufficiently differentiated. As we argue later, this corresponds with market and technology conditions that grant high profitability from investing in FMS.

   The plan of the paper is as follows: First, we introduce the model (section 2) and then characterize the different equilibria (section 3). Next, we consider social welfare and the question of privatization (section 4). Finally, we summarize our main findings (section 5).

2. The Model

   We introduce the study of the mixed duopoly within the framework of Roller and Tombak (1990) and Kim, Roller, and Tombak (1992). Although we keep the main features of these two contributions, we also allow for decreasing returns to scale. This assumption is widely spread in the literature on mixed oligopoly and is useful in order to avoid the case of natural monopolies, which, considering the scope of our paper, is uninteresting.

   Consider a duopoly competing in output and facing the choice between adopting an FMS or a DE. The use of FMS allows participation in two existing markets, A and B. The use of the DE constrains firms to be active only in one of the markets. In the case of the mixed duopoly, one of the two firms, denoted by the subscript 2, is public (not-for-profit) and acts as a social welfare maximizer. (4) Assuming that the public firm is a social welfare maximizer is in line with the majority of the literature on mixed oligopoly. (5)

   The system of inverse demand functions is given by

   [p.sup.A] = a - [Q.sup.A] [gamma][Q.sup.B]

   and

   [p.sup.B] = a - [Q.sup.B] [gamma][Q.sup.A]

   where [p.sup.A] and [p.sup.B] are the prices for products A and B, respectively, [Q.sup.A] and [Q.sup.B] are the total quantities in market A and market B, respectively, and a > 0 measures market potential. The parameter [gamma], measures the substitutability of products A and B, [lambda] [member of] [0, 1); the higher [gamma], the fiercer the competition between firms across markets.

   The profit of each firm is given by

   [[pi].sub.i,j] = [P.sup.A][Q.sup.A.sub.i,j] + [P.sup.B] [Q.sup.B.sub.i,j] - [C.sub.i]([Q.sup.A.sub.i,j] + [Q.sup.B.sub.i,j]) - [F.sub.k],

   where i denotes the firm (i = 1 or 2) and j denotes the state of the industry according to the technologies used by the two firms. In particular,

   j = 1 if both firms are using FMS;

   j = 2 if firm 1 is using DE and firm 2 is using FMS;

   j = 3 if firm 1 is using FMS and firm 2 is using DE;

   j = 4 if both firms are using DE.

   [Q.sup.A.sub.i,j] and [Q.sup.B.sub.i,j] are the quantities chosen by firm i in state j for markets A and B, respectively. Without loss of generality...