R&D, free entry, and social inefficiency

Abstract

We employ a three-stage game model with cost-reducing research and development (R&D) that is subject to spillovers to consider the problem of excess entry under free-entry equilibrium relative to the social optimum. Firms choose to enter or exit a market in the first stage, choose R&D in the second stage and output in the final stage. Results show that there is socially inefficient or excessive entry in equilibrium. However, we uniquely demonstrate that research spillovers hold the key to whether established results regarding socially inefficient entry hold. Specifically, excessive entry occurs as long as research spillovers are relatively small, but this is not necessarily the case with large spillovers. Some policy implications are discussed.

Keywords:

• R&D
• entry
• social inefficiency
• oligopoly

JEL Classification :

• L13
• O33
• D43

Acknowledgements

We would like to thank the editor, Dr Cristiano Antonelli, and two referees for helpful comments and suggestions. Goel thanks Z.E.W., Germany for hospitality during a research stay. The usual disclaimer applies.

Notes

See Berry and Waldfogel (1999) for an application (see also Seade 1980).

Even without R&D, related research has had to resort to specific functional forms to obtain sharper results (see, e.g. Mankiw and Whinston 1986). However, we provide the reader with insights into related general forms in various places.

Perry (1984) also assumes that the average cost function is decreasing in the quantity of output and fixed costs are needed when firms enter the industry, but Ito et al. (1988) assume that although the average cost function is decreasing, there are no fixed costs. Tandon (1984) assumes that an average cost function is constant and there are no fixed costs (see also Goel 1999).

Goel and Haruna (2007) consider a general form of research costs to analyze the behavior of labor-managed firms.

The case of ρ=1 corresponding to an RJV is considered by Kamien, Muller, and Zang (1992).

Our consideration of research spillovers implicitly assumes that a firm's ability to benefit from other's research is independent of the firm's own R&D. Similar treatment of research spillovers has been employed elsewhere in the literature, most notably by d'Asprement and Jacquemin (1988) in their seminal work comparing cooperative and non-cooperative duopoly in the presence of spillovers (see also Atallah 2002). However, this may not always be true as a firm's absorptive capacity might be determined by its own research (Cohen and Levinthal 1990).

 We can take the cost functions with multiplicative incorporation of R&D results such as , and The reader can easily confirm that, given such cost functions, the solutions in the R&D stage will be quite complicated or lead to a corner one (or no solution). As a result, the multiplicative case generally incurs such problems and, furthermore, is less tractable and intuitive than the additive case.

Suzumura and Kiyono (1987) assume that firms possess quasi-Cournot conjectures (see also Novshek 1980).

See, for example, Amir and Wooders (1998) and Henriques (1990) for the stability of equilibrium in the R&D stage.

As demonstrated by d'Aspremont and Jacquemin (1988), whether the level of R&D is positive is dependent on the R&D spillover rates.

In general, the level of output also depends on R&D spillover rates (see, e.g. d'Aspremont and Jacquemin 1988).

Perry (1984) and Mankiw and Whinston (1986) consider a free-entry equilibrium by using an integer number of firms.

Mankiw and Whinston (1986) make some assumptions to ensure that profits per firm are a decreasing function of the number of firms, and Suzumura and Kiyono (1987) show that they are its decreasing function.

On the contrary, Mankiw and Whinston (1986) assume that profits of each incumbent are reduced as the number of incumbent firms increases. The theoretical result that the presence of R&D spillovers crucially affects the behavior of firms and trade policy is demonstrated by d'Aspremont and Jacquemin (1988) and Goel and Haruna (forthcoming).

The function is rewritten as

Now, given is non-positive, and is negative; while, given is positive, and is non-positive.

We know from the characteristic of the functions that .

Mankiw and Whinston (1986) assume that each firm's output is a decreasing function of the number of firms in the industry.

Tandon (1984) does not compare the number of firms in the two instances. Haruna (2010, 97) obtains similar results in the absence of R&D spillovers.

The effects of R&D spillovers on costs and profits of firms have been estimated by many scholars including, Jaffe (1986), Bernstein (1989), Bernstein and Nadiri (1989), and Suzuki (1993). In contrast, estimation of the magnitude of the R&D spillover rate is rather difficult and thus less common. Jaffe (1986, 994) estimates that the spillover rate may be 0.03 and could be as high as 0.3.

Mankiw and Whinston (1986) assume that an increase in the number of firms leads to a reduction in output, while Suzumura and Kiyono (1987) show that increased number of firms decreases their outputs.

Although Tandon (1984) compares R&D expenditure, output, and welfare under a free-entry equilibrium and the first-best social optimum, he does not obtain a result concerning the comparison of the numbers of firms under the two cases. From some numerical calculations he concludes that ‘I have shown here that free entry to the R&D game would lead to excess entry, in the sense that an industry with fewer firms would be socially preferable’ (Tandon 1984, 402).