Existence of financial equilibria with endogenous short selling restrictions and real assets Michele Gori Dipartimento di Matematica per le Decisioni, Universit`a degli Studi di Firenze via delle Pandette 9, 50127 Firenze e-mail: michele.gori@unifi.it Marina Pireddu Department of Economics, European University Institute via della Piazzuola 43, 50133 Firenze e-mail: Marina.Pireddu@EUI.eu Antonio Villanacci Dipartimento di Matematica per le Decisioni, Universit`a degli Studi di Firenze via delle Pandette 9, 50127 Firenze e-mail: antonio.villanacci@unifi.it August 24, 2012 Abstract We consider a model with real assets and restricted participation described by household specific price dependent short selling constraints. We show existence of equilibria for all elements in an explicitly characterized large subset of the set of economies. Keywords: General equilibrium; Restricted participation; Financial markets; Real assets. JEL classification: D50, D52, D53. 1 Introduction We analyze a general financial equilibrium model with real assets and restricted participation. Assets are said to be real if they promise to deliver bundles of commodities. Participation is said to be restricted if each asset demand has to belong to a household specific set. For a recent, brief survey of the literature on restricted participation see Carosi et al. (2009). The standard main reference on financial equilibrium with real assets is still Duffie and Shafer (1985). As it is well known, in the case of incomplete markets with real assets, equilibria may not exist since changes in prices may change the rank of the return matrix causing a discontinuity in the demand function. On the other hand, using a description of the financial structure in terms of Grassmannian manifolds, Duffie and Shafer (1985) show existence for every utility function vector, and every endowment and yield vector in an open and full measure set. There are only few papers which combine real assets and restricted participation in a sufficiently general manner and most of them deal with the context of default and collateral. Radner (1972) proves existence of equilibria for a modification of the general equilibrium model with incomplete financial markets, in which there is an exogenous upper bound on the short sale of assets. Geanakoplos (1997) provides an existence result for a model with default and durable goods in which the requirement that security sales 1