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

Abstract

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 “consumer–producer”—producing private commodities as well as consuming collective and private goods. We develop the $$\sigma$$ σ -Core concept, assuming that collective goods are scalable with community size. We show that the $$\sigma$$ 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 $$\sigma$$ σ -Core and a structured $$\sigma$$ 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 $$\sigma$$ σ -Core and the set of cost share equilibrium allocations.