By using various indicators, empirical evidence for the manufacturing sector strongly suggests that there is a positive relationship between the size and diversification of firms. Moreover, there is evidence on an important role of firm-specific characteristics for both diversification patterns and firm size. For instance, Davies et al. (2001) conclude that “many empirical studies confirm positive statistical associations between diversification, firm size, R&D and advertising” (p. 1317) and argue that “diversification is driven [...] by a desire to exploit a specific asset” (p. 1334).
This paper presents an oligopoly model of asymmetric multiproduct firms in order to examine the apparent link between firm size, diversification and specific characteristics of firms. The set up may be described as follows. Potential firms decide whether or not to enter at some fixed cost. They are endowed with some possibly different (and immutable) marginal cost and product quality. These characteristics are of public good nature from the perspective of a firm, i.e., apply to any good within a firm’s product line. After entering the economy, firms choose the number of products offered to the market (stage 1), and then enter product market competition (stage 2).
The main contribution of the paper is twofold. First, it derives basic properties of profit functions of multiproduct firms for the widely-used linear-demand model with differentiated goods under Cournot competition, for a given configuration of product ranges (stage 2 equilibrium). Second, using these properties, the analysis shows that, typically, firms with more favorable quality-cost margins have both larger size (measured by total sales) and larger product ranges, consistent with the empirical evidence outlined above.
Moreover, the analysis seeks to identify determinants of average industry diver-sification, in addition to those of the size-diversification relationship. For instance, Gorecki (1975, p. 134) suggests that “specific assets of a technological nature formed the basis of much [industry] diversification” in the UK, whereas Baldwin et al. (2000) find no evidence of a role of technological characteristics for average diversification in Canada.The present analysis supports the findings of Gorecki (1975) by showing that, for a given number of symmetric firms, an increase in quality-cost margins raises product ranges. In contrast, higher substitutability of products reduces diversification of product lines.
The mechanisms which give rise to a positive size-diversification relationship suggest more generality beyond the Cournot model. For this reason, and in order to capture the notion that products offered by a firm are closer substitutes for each other than for products sold by other firms (unlike in the linear-demand model), Bertrand competition in the nested multinomial logit model is examined (e.g. Anderson and de Palma, 1992; Anderson, de Palma and Thisse, 1992). Restricting the analysis to duopoly for tractability reasons, it is shown that also in the nested multinomial logit model a larger firm has a more diversified product line.
There is a considerable literature on the determinants of corporate diversification. Besides the emphasis of empirical researchers on the role of technological characteristics, at least three further sources of diversification are frequently mentioned in the literature. First, there is the “agency view”, according to which “a manager might direct a firm’s diversification in a way that increases the firm’s demand for his or her particular skills” (Montgomery, 1994, p. 166). Second, it has been suggested that diversification contributes to risk management of firms. Third, diversification may be a mean to extend the boundaries of a firm in the presence of internal coordination problems. Whereas the first two of these views do not seem to imply a particular size-diversification relationship, the latter is potentially interesting in this respect as internal coordination problems naturally arise in large firms. To the best of my knowledge, however, the theoretical literature has not yet focussed on the relationship between product diversification and firm size.
The remainder of the paper is organized as follows. Section 2 presents the linear demand model with Cournot competition and asymmetric multiproduct firms. Section 3 analyzes the equilibrium for this model in the light of the empirical regularities outlined above. Section 4 examines the size-diversification relationship in alternative multiproduct models. The last section concludes.
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