R&D and Output Behavior of Duopolistic Firms with Conjectural Variations in R&D

• Author: Shoji Haruna; Katsunari Ohashi
• Pages: 287-300

We thank Professor Naoto Jinji, and seminar and symposium participants at Waseda, Osaka City, and Tokyo Universities for their helpful suggestions and comments.

Shoji Haruna. Professor, Ph.D. Department of Economics, Okayama University, Japan (e-mail: haruna_shoji@yahoo.co.jp).

Page 287

Introduction

Innovation plays an indispensable role in firm activities such as production, sales, new product development, and rivalry. Now innovation conducted by a firm is classified into two types: One type is process innovation, which aims to reduce the production costs by improving the production and/or sales process; and the other is product innovation, which aims to enhance the quality of a product and develop new products. d’Aspremont and Jacquemin (1988) focus on oligopolistic firms that conduct research and development (R&D) aiming at process innovation, and investigate their R&D and output behavior when spillovers on the fruits of R&D activities exist. It is shown that with high spillover rates, the R&D investment of each firm increases when the firms cooperate at both stages, in comparison with those under R&D cooperation and output competition and under R&D and output competition, while, with low spillover rates, they obtain a different result from the above.

By introducing product differentiation and using the more general model, Kamien et al. (1992) extend the analysis of d’Aspremont and Jacquemin (1988), and consider the effects of the establishment of an R&D research joint venture (RJV) under both R&D competition and R&D cartelization, demonstrating that its establishment increases the R&D under R&D cartelization in comparison with the one under R&D competition. It is also shown that RJV cartelization leads to the maximum welfare (social surplus) within the four cases of R&D competition, R&D cartelization, RJV competition, and RJV cartelization. The influence of strategic R&D and collusion on the market performance has been investigated by many researchers (e.g., Simpson and Vonortas (1994)) in addition to the work.¹ The role of R&D investment as the strategic (business stealing) method is widely considered in trade theory and trade policy as well.

Gollop and Roberts (1979), Iwata (1974), and Suzuki et al. (1993) demonstrate by empirical analysis that oligopolistic firms in several industries possess conjectural variations inPage 288 quantities. Their results explicitly differ from the traditional Cournot assumption. This causes us to easily predict that real firms employ conjectural variasions when choosing the levels of R&D.

Ohashi and Haruna (2009) shed light on output and R&D behavior of oligopolistic firms under various competition in the second stage by incorporating conjectural variations in quantities. Their approach using conjectural variations in R&D can make it possible for us to grasp such behavior under various rivalry conditions in an output market apart from Cournot competition, Bertrand competition, and Collusion.²,³

They show that the R&D and output behavior of firms is explicitly affected by the degree of quantity competition (which is measured by such conjectural variations): That is, given large (small) R&D spillovers, positive conjectural variations lead to larger (smaller) R&D investment than no conjectural ones. This extends the analyses of d’Aspremont and Jacquemin (1988), and Kamien et al. (1992).

However, no papers address R&D and quantity behavior of firms with conjectural variations in R&D who predict their rivals’ reactions to their decision on R&D, when making their decisions. Firms in the automobile, liquid crystal panel and semiconductor industries almost certainly make a decision on R&D investment, anticipating their rivals’ reactions on its decision. In these industries conjectural variations in R&D are recently taking an important role more and more to well manage firms. Therefore, the conventional idea that they determine their R&D strategy, ignoring their rivals’ response like the Cournot assumption, is right irrelevant. Then we incorporate conjectural variations in R&D into our analysis. By this our analysis could generalize and reconsider traditional analyses such as, for example, d’Aspremont and Jacquemin (1988), and Kamien et al. (1992), and throws a new real light on the investigation of the R&D and output behavior of oligopolistic firms.

We obtain the following results from the analysis. Whether conjectural variations in R&D are positive or negative has a great impact on the decisions of firms as well as the rates of spillovers. Specifically, the firms make a greater (less) investment in R&D in the presence of positive (negative) conjectural variations than in zero conjectural variations. Like this, the level of market performance is reversed by whether the conjectural variations are positive or negative. This implies that the assumption of zero conjectural variations will lead to misinterpretation on firm behavior and market performance. The validity of d’Aspremont and Jacquemin’s result (1988) is also confirmed in an extended model.

The remainder of the paper is organized as follows: In Section 2 we provide a duopolistic two-stage game model with conjectural variations in R&D; and in Section 3 we take twoPage 289 scenarios, depending on whether or not such conjectural variations exist, and then examine how the conjectural variations influence R&D and output of firms with R&D spillovers. In Section 4 we compare prices, profits of firms, and welfare. Moreover, to promote comprehension of the relationship of profits with the degrees of spillovers and competition we provide an illustration by the use of an example of numerical computation. The introduction of CVs in R&D provides the relationship between R&D and continuous changes, not discrete changes, in R&D rivalry. The final section concludes the paper

R&D and Output Behavior of Duopolistic Firms with Conjectural Variations in R&D

1. The Model

We elucidate R&D and output behavior of oligopolistic firms with conjectural variations (CVs) in R&D and reexamine some of previous results on firm R&D strategy. Following the two-stage game model of d’Aspremont and Jacquemin (1988), we employ a duopoly model in which two firms simultaneously choose the levels of R&D at the first stage and then outputs at the second stage.⁴ In the second stage they are always involved in Cournot quantity competition.

The market’s linear inverse demand function takes the form of

p = a−b(q_i + q_j), a > 0 and b > 0, i, j = 1, 2, i ≠ j, (1)

where q_i and p denote the output of firm i and output price, respectively. Both firms produce a homogeneous good.

When the firms invest in R&D to make an innovation in the process of manufacturing and/or sales, the cost function of firm i is given by c_i = c−x_i− ρx j, i ≠ j, where c is marginal costs, x_i and x j are cost reductions acquired by firms i and j as a result of their R&D investments, respectively, and ρ (∈ [0,1]) is a spillover rate.⁵ The presence of spillovers implies that firms cannot make the fruits of their R&D investments appropriable perfectly except for ρ = 0.⁶ Put it differently, some fruits of each firm obtained by its own R&D activities flow out to other firms in the same industry without payment, so firm i’s R&D lowers not only its own production costs but also those of its rival. Particularly, ρ = 1 means that all of firms perfectly share information on all results obtained by their R&D activities each other. When they establish a research joint venture (RJV), the information on the results is perfectly shared among them. In order to reduce its production costs by x_i firm i has to spend vx_i²/2, v > 0, as R&D costs, where v stands for the efficiency...