Industry profits and competition under bilateral oligopoly
Introduction
It is a cornerstone result of the standard Cournot model of oligopoly that industry profits will decrease as the number of firms competing in the product market increases. The nature of this relationship influences, inter alia, the incentives of firms both to merge and to deter entry by new firms: it is a fundamental determinant of market structure. In this paper, we show that under bilateral oligopoly, when downstream firms’ costs are not exogenous but are determined through (Nash) bargaining with upstream agents, the relationship between industry profits and the number of competing firms depends on the relative bargaining power of the downstream and upstream agents. If the former have sufficient bargaining power, then there is a range over which industry profits increase with the number of firms competing in the product market.
As far as we are aware, this is a new result. Dowrick (1989) considers a bilateral oligopoly—in which unions act as the upstream agent—and shows how the bargained wage varies with the number of firms, but does not focus on the relationship between profits and the number of firms. Horn and Wolinsky (1988) examine a differentiated oligopoly with upstream agents (unions) and downstream firms, but assume a duopolistic market.1
The rest of this paper is organized as follows. In Section 2, we outline the basic model and in Section 3 we draw out the implications of the model for the relationship between industry profits and the number of Cournot competitors. Section 4 concludes.
Section snippets
The model
We follow Horn and Wolinsky (1988) in supposing that the upstream agents are firm-specific trade unions bargaining with firms over the wage rate. We analyze a non-cooperative two-stage game in which n identical firms produce an identical good. In the first stage (the labor market game), each firm independently bargains over its wage with a local labor union: bargaining is decentralized. The outcome of the labor market game is described by the solution to the n union-firm pairs’ sub-game perfect
Industry profits and competition
We now investigate how industry profits vary with the number of firms in the market. Differentiating Eq. (14) with respect to n, we obtainwhich is positive—implying that industry profits are non-decreasing in the number of firms—if the following condition is satisfied:Initially, consider condition Eq. (16) for the special case that β=1. In this case, the condition is satisfied for −1≤n≤3. It follows that for this monopoly union case industry
Conclusions
We have shown that in a unionized bilateral oligopoly with decentralized bargaining, industry profits are initially increasing in the number of firms, n, in the product market if unions have sufficient bargaining power, β. The standard oligopoly result is turned round because an increase in n causes a profit-enhancing fall in bargained wages and this dominates the standard profit-reducing effect of an increase in n if β is sufficiently large and if n itself is sufficiently small. As we have
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