The Core of economies with collective goods and a social division of labour

Abstract

This paper considers the Core of a competitive market economy with private commodities as well as (non-Samuelsonian) collective goods that are provided through an endogenous social division of labour. Our approach is founded on the hypothesis that every agent is a "consumerproducer"-producing private commodities as well as consuming collective and private goods. We develop the σ -Core concept, assuming that collective goods are scalable with community size.We show that the σ -Core can be founded on deviations of coalitions of arbitrary size, extending the seminal insights of Vind and Schmeidler for pure exchange economies. Our analysis also shows that self-organisation in a social division of labour can be incorporated into the Edgeworthian barter process directly. This is formulated as an equivalence of the σ -Core and a structured σ -Core concept based on blocking coalitions that use internal divisions of labour. Furthermore, Grodal's theorem is extended, allowing applications of metrics that express productive similarities between agents making up blocking coalitions.Finally, we consider the equivalence of the σ -Core and the set of cost share equilibrium allocations.

Fairness and formation rules of coalitions

“…6 The covering  is exogenous because for our analysis the reasons that induce a certain composition of the society are irrelevant. It is not excluded that  is obtained by a metric on the space of agents' characteristics, as in Grodal (1972) and in Basile et al (2021) among others, so that for instance each set C i contains agents with similar tastes; or by a metric on the space of agents as in Cato ( 2010) and interpret C i as the set of neighbors in the spatial sense. 7 In Donnini and Pesce (2021a) it is proved that, under A ( 3), if  is a connected covering of T, -strict fairness characterizes equal-income competitive allocations, that is,…”

“…The covering $${\rm{ {\mathcal R} }}$$ is exogenous because for our analysis the reasons that induce a certain composition of the society are irrelevant. It is not excluded that $${\rm{ {\mathcal R} }}$$ is obtained by a metric on the space of agents' characteristics, as in Grodal (1972) and in Basile et al (2021) among others, so that for instance each set $${C}_{i}$$ contains agents with similar tastes; or by a metric on the space of agents as in Cato (2010) and interpret $${C}_{i}$$ as the set of neighbors in the spatial sense.…”

“…Several papers, extending the seminal results of Schmeidler (1972), Grodal (1972), and Vind (1972) to different frameworks and for different equilibrium concepts, belong to this study branch. For example, Khan (1974) considers the core of a finite economy, Hervés‐Beloso et al (2000) and Evren and Hüsseinov (2008) study economies with infinite‐dimensional commodity space, Hervés‐Beloso et al (2005b) and Hervés‐Beloso et al (2014) examine economies with asymmetric information, Hervés‐Beloso et al (2005a) and Bhowmik and Cao (2012) combine asymmetric information and infinite‐dimensional commodity space, Gilles (2019) considers production economies, and Basile et al (2021) allow also the presence of collective goods. Shimomura (2022) and Hervés‐Estévez and Moreno‐García (2018) study, instead, how the restriction on the formation of coalitions affects the bargaining set defined as a weakening of the core.…”

Contributing with private bundles to public goods

“…The problem of collective goods provision has also been analyzed within a general equilibrium model, using the cooperative solution of the core (seeBasile et al 2021, and the references therein).…”