Impact of labour unions on the merger incentive of firms

Abstract

This paper analyses the impact of labour unions on the merger incentives of firms. We find that a horizontal merger takes place if there is some synergy effect. However, a vertical merger takes place only if the synergy effect is bigger than a certain size.

Keywords:

• Merger (horizontal, vertical)
• union
• Shapley value

Acknowledgements

The author is grateful to Suchan Chae and an anonymous referee for helpful comments and valuable suggestions

Notes

Although Horn & Wolinsky (1988a) analyse the merger incentives of firms and unions in one model, they do it independently, that is, they do not consider the interaction of merger decisions of firms and unions.

Let N denote the set of players and for a coalition C( C ⊆ N), v( C) denote the worth of C. Then, Shapley value of player i is ϕ _i ( v) = [∑ _C⊆N−i | C | !( | N | − | C | − 1) !/ | N | ! ]( v( C ∪ {i} ) − v( C) ) (see Shapley, 1953).

In our model, ‘revenue’ means the revenue of a firm when there is no strike in the firm. Thus, it is natural to assume that the FIRM's revenue is the same whether the unions merge or not.

The importance of worker substitutability for merger incentives of unions is well analysed in Horn & Wolinsky (1988b).

In the terminology of Horn & Wolinsky (1988b), workers of Union 1and Union 2 are complements when the relation between Firm 1 and Firm 2 is vertical.

We assume that Union 1 and Union 2 cannot merge unless Firm 1 and Firm 2 merge. By (N, m), we mean that at the first stage the firms do not merge and at the second stage the unions would merge if the firms merged at the first stage.

A is negative if α₁ + α₂ > R ₁ + R ₂. Then, R > R ₁ + R ₂ because R ≥ α₁ + α₂ by the presumption of (ii). Thus, when α₁ + α₂ > R ₁ + R ₂ so that A < 0, there is a strictly positive synergy effect in a merger and the merger takes place.