Existence and Non-Triviality of Equilibria in Economies with Default and Government

Abstract

This paper attempts  to accommodate the government into  Dubey, Geanakoplos and Shubik (2005) framework  in an explicit way, and proves that a non-trivial equilibrium  exists. By non-trivial equilibrium, we mean an equilibrium where there exists trading in the financial markets and some private borrower defaults.   The government,  characterised by its spending and tax  plans\footnote{Both are assumed to be exogenous like in Gale (1990).},  enters our economic model  by trading   financial assets  in order to balance  its budget. Proof of existence  is made by considering a generalised  game \`a la Debreu (1952)\footnote{Already well  known  in the GEI literature.}, and its  non-triviality  is obtained by using  the   non-differentiable optimisation theory.