The degeneration of workers' cooperatives under endogenous membership in mixed oligopoly

Delbono, Flavio; Reggiani, Carlo Working Paper The degeneration of workers' cooperatives under endogenous membership in mixed oligopoly Quaderni - Working Paper DSE, No. 1194 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Delbono, Flavio; Reggiani, Carlo (2024) : The degeneration of workers' cooperatives under endogenous membership in mixed oligopoly, Quaderni - Working Paper DSE, No. 1194, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/7658 This Version is available at: https://hdl.handle.net/10419/300149 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ ISSN 2282-6483 The Degeneration of Workers’ Cooperatives under Endogenous Membership in Mixed Oligopoly Flavio Delbono Carlo Reggiani Quaderni - Working Paper DSE N° 1194 The Degeneration of Workers’ Cooperatives under Endogenous Membership in Mixed Oligopoly ∗ Flavio Delbono†Carlo Reggiani‡ March 2023 Abstract We propose a new model of mixed oligopoly where a workers’ cooperative firms competes with a number of profit maximising companies. Building upon a large empirical evidence, we innovate as compared to the traditional literature on the objective function of the cooperative; moreover, its membership is treated as endogenous in the Cournot-Nash equilibrium. We show which factors may be responsible of the degeneration of the workers’ cooperative firms, which occurs when the number of members shrinks with respect to the overall employees. JEL Classification: L21, L25, P13. Keywords: cooperatives, mixed oligopoly, degeneration. ∗ We thank Gianni De Fraja and John Pencavel for insightful comments and suggestions. The usual disclaimer applies. † Department of Economics, University of Bologna, Italy. Email: fla[email protected]. Corresponding author. ‡ Department of Economics, University of Manchester, United Kingdom. Email: [email protected]. 1 Non-technical summary In this paper, we have propose a new model to describe the behavior of a workers’ cooperative that competes with a number of profit maximising companies. The main novelties lie in a evidence-backed formulation of the cooperative objective function and in the endogeneity of membership. Building upon a large empirical evidence, we embed its strategic choices within an oligopolistic industry populated also by a number of profit seeking companies. The analysis of the equilibrium of our model reveals that membership matters in driving the properties of the equilibrium itself. Moreover, a careful scrutiny of the membership rate allows one to envisage which factors may be responsible for a fall in the proportion of non-member workers. We interpret a reduction of the membership ratio as a neat example of ”degeneration”. We show which factors may be responsible of the degeneration of the workers’ cooperative firms, which occurs when the number of members shrinks with respect to the overall employees. Beyond these new theoretical findings, we also recommend caution when interpreting data on cooperative firms and workers’ cooperatives in particular. We indeed provided evidence that the actual weight of the cooperative presence (understood as the ultimate decision maker) in an economic system is greater than the one obtained by simply counting the official direct weight. This is because the transformation of workers’ cooperatives into stock companies controlled by cooperatives should be considered as well to obtain a more accurate picture of the overall cooperative magnitude. The degeneration issue, if any, could then be quantified within such a more complete frame. 2 1 Introduction According to a recent report of the International Cooperative Alliance (see Euricse (2020)), at least a billion people are members of cooperatives. In Europe - where Italy, France and Spain rank top - cooperatives account directly for almost 5 million employees. 1 Cooperatives are firms open to a large number of citizens for they usually require a modest entry fee to become member. They are run democratically by members (one head-one vote) who are the ultimate residual claimants of net revenue. Among the various types of cooperatives (see Ammirato, 2018 and Zamagni, 2015 for useful taxonomies), we focus here on workers’ cooperatives (henceforth, WCFs) often named labor-managed firms in the past. In such companies the ultimate control is held by workers because they own the firm. To prevent misunderstandings, a WCF does not necessarily meet Sertel (1982) definition of workers’ firm, where “all workers are members and all member are workers”. In fact, we are interested in analyzing the membership ratio, i.e., the ratio between the number of working members and the number of workers. Such a ratio is obviously equal to one in a workers’ firm. The founding members are labor suppliers who advance the necessary equity. This feature restricts the birth of WCFs to sectors with relatively low capital/labor ratios and low risk (as documented, for instance, by Podivinsky and Stewart, 2007 in the British manufacturing sectors). Then, unsurprisingly, WCFs are mainly operating in comparatively small manufacturing business, and they are frequently active in services as transportation, catering, facility management, tourism, entertainment. It is a matter of fact that WCFs are significantly less common than capitalmanaged firms and “no one argues that successful capitalist firms tend to degenerate into WCFs” (Dow, 2018, p.107). 2 Conversely, a group of scholars 3 have claimed that WCFs seem to lean towards the capitalist ones (the so-called degeneration). In the next pages we will deal precisely with such an issue, although one may 1 These figures make it somehow surprising the substantial disappearance of cooperatives from economics textbooks. See Hill (2000) and Kalmi (2007) for thoughtful accounts and explanations of such a tendency. 2 As a model of enterprise alternative to the capitalist one, WCFs have received much attention in the literature since John Stuart Mill. He seemed exceedingly optimistic about the success of the cooperative form. In his Principles of Political Economy, published in 1848, four years after the birth of the first (users’) cooperative (Rochdale, 1844), he claimed that worker-run organizations would eventually crowd capitalist enterprises out of the market because of their greater efficiency and other benefits for the working owners. 3See Dow, 2018, ch. 7, for an excellent discussion of the relevant literature. 3 prefer to refer to it as “transformation” of WCFs. The choice would not be a merely stylistic one to avoid the intrinsically pejorative flavor of the term “degeneration”, but it would also be driven by the multiplicity of experiences that can be collected when looking at the evolution of WCFs in the last decades. We will notice indeed that the actual cooperative magnitude would be significantly underestimated if summarized only through the number and performance of companies registered as cooperatives. The rich Italian experience, for instance, provides a more accurate evidence of the direct and indirect weight of cooperatives (including WCFs) within the economy in terms of employment as well as GDP. In the second part of the paper we will switch to theory. We propose a new model of mixed oligopoly where a workers’ cooperative firm competes with a number of profit maximizing companies. Building upon a large empirical evidence, we innovate as compared to the traditional literature on the objective function of the cooperative; moreover, its membership is treated as endogenous in the CournotNash equilibrium. We investigate the optimal choice of the membership within a new model of WCF’s behavior and we shall show which factors may explain its convergence towards a capitalist business organization. We will interpret a reduction of the membership ratio as an instance of WCF degeneration, because as the proportion of members decreases the cooperative tends to look like the capitalist ones. To the best of our knowledge, we are first in treating the membership within a WCF as endogenous in a model of oligopoly.4 Among the main findings, we show that the membership ratio plays a crucial role. First, if not all workers are also members, then the two types of firms behave identically. If, instead, the membership ratio is unitary, the equilibrium is asymmetric and, in general, WCF’s choices differ from their profit maximising counterparts. The latter outcome is typical under the traditional objective function that has been used by most of the theoretical literature since Ward (1958). Second, we investigate which factors are responsible for the degeneration of WCF. For instance, we show that an increase in market size, which is usually correlated to the dimension of the companies, leads to a fall in the membership ratio. The rest of the paper is organized as follows. Section 2 briefly reviews the related literature within a broader perspective about the academic research on WCFs since the late ’50s of the last century. In section 3 we clarify how the transformation process of WCFs should be properly addressed on the basis of some available evidence. In section 4 we propose a model allowing us to investigate the choice of 4 Dow (2018, ch. 9) investigates the choice of membership under the assumptions of perfect competition in the product market and an objective function ` a la Ward (1958). 4 the membership ratio within an oligopolistic market structure. Section 5 provides a full characterization of the equilibrium of our mixed market. Section 6 concludes. 2 Related literature The overall literature on WCFs is now vast: see, for instance, the classic survey by Bonin et al. (1993) and the more recent contributions by Jones (2018), Dow (2018), Mirabel (2021) and Mygind and Poulsen (2021). Two phases can be roughly identified. The first one, since the pioneering contribution by Ward (1958), was mainly concerned with the analysis of the so-called market socialism, a marketbased economy different from the conventional capitalist ones because of the presence of companies own and/or run by workers. Since Ward’s article, most of the early theoretical literature modeled the WCF as maximizing the net income per worker (see Domar, 1966 and Vanek, 1970, among the most influential essays). More precisely, the short-run WCF’s maximand is assumed to be revenue, net of fixed cost, per member. Under price-taking behavior, if all identical workers (the only variable input) are members, this is equivalent to maximize the difference between revenue and all costs (named profit in a capitalist company) per member. Besides not finding significant empirical support, such approach entails a disturbing negative response of output (and then labor demand) to output price increases: this is known in the literature as the perverse effect. An interesting formulation avoiding backward-bending supply curve of the WCF is in Kahana and Nitzan (1989). Under price-taking behavior and a unitary membership ratio, a WCF chooses the levels of inputs and output to maximize the income per worker/member subject to an employment constraint or, alternatively, the level of employment subject to a profit per worker/member constraint. By duality arguments, one proves the equivalence between two approaches which aim at capturing the concern for employment that should shape the decisions of firms owned and run by workers-members according to a democratic governance. This concern has been often detected in empirical research (further reviewed below). The theoretical literature made little progress until the early ‘90s when, retaining the same objective function as in Ward (1958), the behavior of a WCF has been studied within models of mixed oligopoly, i.e., concentrated markets hosting firms pursuing different goals (De Fraja and Delbono, 1990). However, while these models remove the extreme assumption of price-taking behavior in the product market, they retain Ward (1958)’s formulation about the WCF objective function 5 (see, e.g., Delbono and Rossini, 1992 and Delbono et al., 2023 for the relevant references). Likely also because of the stalemate in modeling WCF’s behavior, the last thirty years have witnessed a massive increase in empirical studies. Starting from a group of seminal papers investigating the plywood industry in the US Pacific Northwest, Craig and Pencavel (1992, 1993) and Craig et al. (1995) drew the conclusion that a WCF tends to adjust earnings more than employment when reacting to changes in market condition. The same conclusion is reached by Burd ´ ın and Dean (2009, 2012) regarding the Uruguayan economy. Both sets of papers share the finding that employment seems to occupy a more prominent role than earnings in the objective function of WCFs . This empirical evidence has been confirmed, inter alia, in a group of studies on Italian WCFs, e.g., Delbono and Reggiani (2013), Euricse (2013), Navarra (2016), and Caselli et al. (2022). As for the so-called degeneration problem, several scholars have argued that - under imperfect (or no) membership markets - members of successful WCFs would find it preferable to hire employees and to pay them the market wage when departing members have to be replaced. 5 The evidence collected in several countries is far from being conclusive and also shows that some institutional mechanisms may restrain the actual feasibility of the “degeneration”. For instance, in France, also non-members are eligible for participating in the distribution of dividends; fiscal incentives, as in Italy, may discourage WCFs from shrinking the membership ratio or the conversion into a capital-managed company.6 Moreover, it is worth noticing that sometimes the transformation goes the other way around, when unsuccessful capitalist companies sometimes “degenerate” into WCFs. This is the case of workers buy-out by means of which employees in a capitalcontrolled firm take over the company to prevent its bankruptcy. For instance, between 2011 and 2021, the Italian cooperative fund CFI (https://www.cfi.it/workersbuyout.php) has supported 88 such acquisitions of firms which account for a total turnover of 365 million euro and employ 2,286 persons. A similar conversion has been observed in France: between 1997 and 2001, about 7% of WCF’s entry in French industries resulted from rescues of capital-controlled companies (P ´ erotin, 2006). Furthermore, “a related process may involve the formation of non-cooperative 5 Sertel (1991) shows that under imperfect competition in the product market, the equilibrium is not altered by replacing a profit maximiser by a Ward (1958)-like WCF if (i) there is a market for cooperative memberships and (ii) the membership ratio is unitary. Under conditions (i) and (ii), Mikami (2018) finds that a WCF is as efficient and viable as a capitalist firm. 6 See Dean (2019) for an empirical study on the presence of degeneration in Uruguayan WCFs. 6 subsidiaries by worker cooperatives or outsourcing of some activities to conventional firms” (Dow, 2018, p.108). This aspect seems important in general and in Italy in particular; hence, we briefly turn our attention to this additional evidence. 3 The cooperative magnitude To assess the overall cooperative magnitude, we need a set of data which transcend the number of cooperatives, their diffusion, sizes and direct impact on the economy (e.g., employment, GDP). A preliminary question, indeed, deals with the cooperative control over firms: a control which often extends outside the boundaries of cooperative firms. In other words, while stock companies can hardly take cooperatives over, given the dissemination of (normally untradable) property rights, cooperatives can acquire control over stock companies as this often occurs. For instance, Unipol-Sai, one of the leading companies in the Italian insurance market, is a firm listed on the national stock market, but it is controlled throughout an agreement among a group of cooperative companies. To pursue the goal of summarizing the overall cooperative control over firms, we need to rely upon the category of business group, defined by Eurostat as: “an association of enterprises bound together by legal and/or financial links. (...) It constitutes an economic entity which is empowered to make choices, particularly concerning the unit it comprises” (European Regulation 696/93). Of course, we are interested in business groups controlled by WCFs. To begin with, we focus on the Italian experience as it ranks top worldwide for the macroeconomic impact of cooperatives (7% of total employment and about 4% of the GDP of the private sector, according to Istat). In 2015 in Italy 29,414 cooperatives out of 59,027 active cooperatives were of the workers’ type and were responsible of about 45% and 42% of overall cooperative added value and employment, respectively. Moreover, as carefully reported in Borzaga et al. (2019), 812 business groups were controlled by a cooperative firm and 1971 is the number of controlled non-cooperative enterprises. If we consider WCFs, they are 389 out of 812. We may conclude that, considering subsidiaries and cooperative groups, the overall macroeconomic impact of Italian cooperatives (the cooperative magnitude) goes up to 4.4% of GDP and 7.4 % of employment of the private sector. Most of this uplift can be attributed to the control of non-cooperative companies by WCFs, as they account for about a half of the business groups led in 2015 by cooperative companies. 7 Comparative statics. We now perform a comparative statics analysis on the equilibrium value of the membership ratio for the case of r < r , i.e., m∗<1 . To do so, we differentiate m∗ with respect to the parameters of our model (treating n as a continuous variable). By simple inspection of the equilibrium membership ratio (13) , the derivative with respect to r and τ is clearly positive. In both cases, profits are unaffected, but the increase in the value of assets dominates the additional cost of extra members. On the contrary, an increase in c only worsens the overall payoff and, as a reaction, membership is reduced. If the maximum size of the market, a , increases, instead, the model predicts a degeneration of the WCF as the membership ratio decreases. Formally, this happens because LM does not vary, whereas LW increases: hence, m∗ shrinks. Intuitively, current members face a trade-off. Indeed, the profits to be distributed are higher if the demand increases. However, on the one hand, the current members would not like to share them with more members; on the other hand, more members would strengthen the financial position of the firm. The first effect dominates the second. If the market size is correlated with firm size, our result rationalizes some evidence about the membership ratio. Indeed, this seems decreasing in the size of the WCF. For a sample of WCFs adhering to Legacoop, such a ratio is currently around 60% for small and medium firms, but it falls to about 36% in large WCFs. 10 The effects of changes in the marginal cost of labor, ω , and in the number of capitalist firms, n , have the same intuitive explanation. In either case, as a response to the fall in profits, the WCF increases its membership to expand the value of its assets. As long as Γ<Γ , the WCF is active and its value does not impact the equilibrium membership. Similarly, also the value of the weight of profits ϕ does not affect the equilibrium membership ratio. The next proposition summarizes the previous results about degeneration: Proposition 3 (Degeneration).The membership ratio m∗is decreasing in aand c. 10 These percentages are reported in a private communication (e-mail, November 14th, 2023) by Francesco Linguiti, of the Research Area of Legacoop (Rome, Italy). His estimates come from the analysis of a sample of 146 Italian WCFs, accounting for 12,722 workers and 6,223 working members, where the average membership ratio is around 49%. 14 6 Concluding remarks In this paper, we have proposed a new model to describe the behavior of a workers’ cooperative. The main novelties lie in a evidence-backed formulation of the cooperative objective function and in the endogeneity of membership. We embed its strategic choices within an oligopolistic industry populated also by a number of profit seeking companies. The analysis of the Cournot-Nash equilibrium of our model reveals that membership matters in driving the properties of the equilibrium itself. Moreover, a careful scrutiny of the membership rate allows one to envisage which factors may be responsible for a fall in the proportion of non-member workers. We interpret a reduction of the membership ratio as a neat example of ”degeneration”. Beyond these new theoretical findings, we also recommend caution when interpreting data on cooperative firms and workers’ cooperatives in particular. We indeed provided evidence that the actual weight of the cooperative presence (understood as the ultimate decision maker) in an economic system is greater than the one obtained by simply counting the official direct weight. This is because the transformation of workers’ cooperatives into stock companies controlled by cooperatives should be considered as well to obtain a more accurate picture of the overall cooperative magnitude. The degeneration issue, if any, could then be quantified within such a more complete frame. Our approach can be extended in many direction; we sketch three of them. First, the static nature of the model could be relaxed in order to study the dynamics of the membership and the role of undistributed profits on its evolution. 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