Existence and nature of CvdN equilibrium

CvdN equilibrium extends ratio equilibrium to local public good economies. A key and unique feature of CvdN equilibrium is that jurisdictions are fully endogenized, where the equilibrating factor is agents’ agreement on public good levels and the sharing of public good production costs. We show equilibrium existence and sorting behavior for a large class of public good economies. We furthermore elucidate how key aspects of the economy influence the nature of CvdN equilibrium, including the role of consumption preferences, jurisdictional preferences, and properties of the public good production function. These factors make possible different equilibrium jurisdiction structures, including the grand coalition, only singletons, or intermediate-sized jurisdictions, as well as jurisdictions with homogeneous or heterogeneous membership. Usefully, because it fully endogenizes jurisdiction formation, CvdN equilibrium offers a unified approach to economies with local public goods and those with global public goods, and it facilitates investigation into the underlying factors of an economy that lead to public goods being provided locally or globally. Our model can provide microfoundations for multiple concepts from the literature, including homophily, segregation, sorting, and small-group effectiveness.