Coalitional instability of the distributive Lindahl equilibrium

Bergstrom [3] has showed that the Lindahlian approach to the analysis of public goods may also be used to analyze a model of wide-spread externalities in which agents have preferences defined on allocations rather than on individual commodity bundles. He has provided versions of the first and second welfare theorem for a distributive Lindahl equilibrium and also presented sufficient conditions for its existence. However, we shall show that, in contrast to Foley's [4] result on the core stability of a Lindahl equilibrium, a distributive Lindahl equilibrium need not satisfy coalitional stability. We will provide a robust example in which the unique, distributive Lindahl equilibrium does not belong to the alpha-core defined either as in Scarf [11] or as in Yannelis [12].