Abstract
The present study analyses the effects of two-sided cross-ownership structures in a Cournot duopoly with firm-specific monopolistic unions. Since such mutual cross-participations imply a lower degree of competition, the conventional wisdom is that consumer surplus and social welfare, despite the increase in industry profits, are harmed. By contrast, when the labour market is unionised, we show the counterintuitive result that both consumer surplus and social welfare increase with the share of mutual cross-participation. Interestingly, this occurs not only when unions are wage-aggressive but even if they are fairly “risk-averse”. Therefore, a rather paradoxical conclusion—which may have anti-trust policy implications—is that the interlocking cross-ownership ensuring the highest profit (i.e. the “most” collusive mutual cross-participation) may be socially preferred when there are unions in oligopoly industries. Finally, it is shown that, even though details change, the results also hold qualitatively under differentiated products, price competition and triopoly.
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Notes
As Booth (1995, p. 95) observes: “It appears to be an empirical regularity that imperfections in the labor market are correlated with imperfections in the product market”.
Various effects of cross-ownership have been analysed by, among others, Farrell and Shapiro 1990; Macho-Stadler and Verdier 1991; Reitman 1994; Dickescheid 2001; Barcena-Ruiz and Olaizola 2007; Barcena-Ruiz and Campo 2012; Fanti 2013, but none of them, even in the simplified frame of one-sided cross-ownership, have dealt with the relationship between social welfare, unions and “more collusion” between firms.
As noted by Lommerud et al. (2005, 723) “whereas international merger is a highly prevalent phenomenon among firms, we hardly ever observe a formal cooperation between trade unions across borders. One main reason is probably that capital is highly mobile between countries, whereas labour is generally not”. The issue of how centralisation and coordination of wage bargaining affect employment and social welfare for countries with integrated product markets was examined early on by Corneo (1995).
As regards the first case, Renault acquired, in 1990, a 45 % stake in Volvo Trucks, a 25 % stake in Volvo Car, and an 8.2 % stake in Volvo A.B., Volvo’s holding company, while Volvo acquired 20 % of Renault S.A. and 45 % of Renault’s truck-making operations (see ”New Head is Selected For Renault,” N.Y Times, May 25, 1992, p. 35, as reported by Gilo and Spiegel 2003, 3). Subsequently, Renault in 1999 initially acquired a 36.8 % stake in Nissan, while Nissan in turn took a 15 % non-voting stake in Renault. As regards the second case, in the early 1990s, Japanese Nippon Steel and Korean Pohang Iron, two of the world’s largest steelmakers, held 0.5 % ownership stakes in each other. They increased these stakes to 1 % in the late 1990s and then planned to increase them to 3 %.
For instance: (1) in Japan (only focusing on the automobile sector in 1993) Toyota (resp. Daihatsu) holds shares in Daihatsu (resp. Toyota) in percentage of about 16.5 % (resp. 0.21 %), Toyota (resp. Hino) holds shares in Hino (resp. Toyota), in percentage of about 11.8 % (resp. 0.2 %), Hino (resp. Daihatsu) holds shares in Daihatsu (resp. Hino) in percentage of about 0.15 % (resp. 0.13 %), Nissan (resp. Fuji) holds shares in Fuji (resp. Nissan) in percentage of about 4.35 % (resp. 0.49 %) and Suzuki (resp. Isuzu) holds shares in Isuzu (resp. Suzuki) in percentage of about 1.7 % (resp. 1.32 %) (Alley, 1997); (2) in Italy ownership links between Italian listed companies belonging to groups which are both participating in other listed groups and participated by other listed groups in 1990 involved large companies representing a market value in percentage of total stock market capitalisation about 4.3 % and in percentage of involved companies’ capitalisation about 10.9 % (Bank of Italy 2008; 3) in the US (only focusing on the computer industry for 1994-95) cross-ownership relations are shown by those institutions that own about 77 percent of Intel and 71 percent of Compaq and at the same time have holdings in at least one of the other five computer industry companies listed (i.e. Apple, Compaq, IBM, Intel, Microsoft, Motorola) (Hansen and Lott 1996).
For example, firm i’s union, while pushing for a wage increase above that of firm j’s union, takes account of the fact that the associated increase in its firm’s unit cost may significantly reduce its output, and thus the number of union members employed in the firm.
En passant we note that since cross-ownership may involve numerous (at least two) owners of each firm, then when there are several heterogeneous firm owners and several goods the objective of profit maximisation may be amply justified only under the hypothesis that the ownership of the firm is very concentrated in a small fraction of consumers. In such a case owners (or their managers) maximise profits because “for any owner the loss as a consumer due to the increase in price is more than compensated by the increase in profit income” (Mas-Colell 1984, 121). By contrast, “suppose that every consumer has an equal claim on profits. Would the manager of the firm be instructed to maximize profits? Obviously not” (Mas-Colell 1984, 121). This line of reasoning may suggest that on the grounds of efficiency “a spread ownership of firms may be preferable to a concentrated one” (Mas-Colell 1984, 121). However, since a spread ownership implies that firm’s decisions affect every owner very little, another consequence would be an increased separation between managers and owners.
Of course very strong risk-aversion amounts to saying that unions fix a wage close to the “competitive” (or “reserve”) one and thus the conventional welfare result necessarily continues to hold.
The possibility that unions might moderate their wage demands was first shown by Dowrick (1989) and this may be a driving force for other unconventional effects. For instance, wage moderation is the channel through which an incumbent’s profits may be enhanced by the entry of new firms, as described in Naylor and Soegaard (2014).
As regards the anti-trust policy concerns raised by cross-ownership see, for instance, (O’Brian and Salop 2000).
It is usual to assume \(h\le 0.5\), because it is implicitly supposed that the owner of the majority of the shares “manages” the firm’s choices. However, in principle, it would be possible even to postulate that the majority shareholder “delegates” such choices to the minority shareholder if this were more convenient for both shareholders. This case is left for further research.
Note that shareholder A chooses \(q_{1}\), while shareholder B chooses \(q_{2}\). This implies that each shareholder (firm) internalises the fact that both firms are competing on quantities and that when the interlocking cross-ownership share is 50 %, profit maximisation obtains the monopolistic output (equally shared between firms).
The assumption of exogenously given mutual shares allows us to deal with the complexity which would be generated by potentially asymmetric endogenous shares. However, although the latter case is algebraically intractable, some considerations are in order. Since this model is symmetric it seems natural to conjecture the occurrence at equilibrium of symmetric shares, although any asymmetric combination of shares summing to one—i.e. generating highest total profits—is always achievable for opportune side-payments for acquiring shares. This difficult but intriguing investigation is left for future work. However, preliminary results show that if the choice of the share of cross-ownership is endogenous it may occur that—given sufficiently strong unions and a sufficiently high initial share of participation in the rival firm—each shareholder could prefer an even free-of-charge transfer of their own majority shares (i.e. cash flow rights without control) to the rival shareholder. This is because the positive effect of the larger collusion induced by such a transfer on the profits of the remaining participating shares outweighs the profit loss due to the free-of-charge transfer of shares. Needless to say, in the absence of unions any free transfer of shares would be damaging for any shareholder.
The assumption (chiefly for simplicity) of a monopoly union is very usual in the unionised oligopoly literature, e.g. Lommerud et al. (2005) who note that “As pointed out by, e.g. Dowrick (1989), this can be viewed as a limiting case of the wage-bargaining union, where the union has all the bargaining strength” (p. 723).
As noted by Zhao (2001, 190) for justifying the widespread use of this formulation in the trade unions literature “The advantages of the Stone–Geary function are tractability and flexibility”.
Note that wages are always non-negative in the assumed interval \(h\in (0, 0.5)\). Also note that when the mutual cross-ownership share is \(h=0.5\) since wages are zero as in the non-unionised case, then profits are maximised and equal to the benchmark (non-unionised) case. Therefore it is evident that mutual cross-shareholdings may also be conceived as a “device” to reduce the union’s rent.
We observe that the literature considers in the definition of social welfare the union’s rent rather than the union’s utility function. For instance, in the words of Zhao (2001, 194) “Because union members are also final good consumers... we use union rents instead of union utility in the welfare function. This is a standard treatment in the literature, see Brander and Spencer (1988) and Mezzetti and Dinopoulos (1991).” Note that Eq. 16 measures the union’s rent (recalling that \(w^{\circ }=0\)) when the union’s utility function is given by Eq. (10).
Needless to say, the derivative dQ/(dh) is more manageable and thus economically interpretable than the derivative dSW/(dh). Moreover, the functions Q(h) and SW(h) have the same behaviour and also quantitatively the thresholds shown in the main text are the same for both functions.
It is easy to see that \(\;\frac{\partial ^2Q}{( {\partial h})^2}>\)0 and thus the function Q(h) is U-shaped.
Note that the paper’s results are not specific to the assumption of monopoly unions and may also be extended to the wage bargaining case. To see this informally, first note that conventional results are restored when the union’s wage-interest tends to zero and thus the monopolistic union’s wage tends to be equal to the competitive wage. In the case of union-firm bargaining the competitive wage is also paid when firms have full bargaining power, while the monopolistic union’s wage is also paid when unions have full bargaining power. Then, also in the case of wage bargaining, the unconventional results of this paper tend to hold with sufficiently high union power as well as union wage-interest.
Note that from a policy point of view the same level of social welfare may be achieved in principle either by allowing cross-ownership or by regulating union behaviour. For instance, in the usual case of the union’s neutral preferences (i.e. \(\theta =1)\), the same level of welfare may be achieved either by allowing the fully collusive cross-ownership structure (i.e. \(h=0.5)\) or by acting to reduce the wage-orientation of unions up to \(\theta =0.67\). However, whether the authorities should regulate unions instead of allowing cross-ownership is an interesting issue which lies beyond the scope of the present paper.
For economy of space we provide only an outline of these extensions, which are obviously tractable with the same procedures more extensively detailed above in the Cournot case and are available on request.
For instance, in the standard case in which unions maximise their rent (i.e. \(\theta =1)\), a mutual cross-shareholding of about 12.5 % maximises social welfare.
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Fanti, L. Interlocking cross-ownership in a unionised duopoly: when social welfare benefits from “more collusion”. J Econ 119, 47–63 (2016). https://doi.org/10.1007/s00712-016-0485-5
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DOI: https://doi.org/10.1007/s00712-016-0485-5