Existence of Equilibria for Shared Goods

A shared good is an impure public good in which personalized consumptions are produced by groups using a sharing technology. Rivalry in consumption is captured by the shape of this technology. Private goods and pure public goods are special cases in which there is complete rivalry and no rivalry, respectively. A competitive shared goods equilibrium is defined in which there are markets for all goods, there are personalized prices for the consumption of shared goods, and both firms and groups are profit maximizers. When all shared goods are private (resp. public), this equilibrium is a Walrasian (resp. Lindahl) equilibrium. Sufficient conditions for the existence of a competitive shared goods equilibrium are identified. An alternative equilibrium concept in which groups behave cooperatively towards their beneficiaries is also considered and an equilibrium existence theorem for it is established.