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.