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

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.