Complete Markets with Bankruptcy Risk and Pecuniary Default Penalties

For an infinite horizon economy with complete contingent markets and bankruptcy risk, like the one studied by Araujo and Sandroni (1999) and Araujo, da Silva and Faro (2016), we show that an equilibrium may fail to exist even if agents' beliefs are homogeneous. In order to discourage agents from making promises that they know in advance they will not be able to keep, default penalties must be harsh enough. The minimum level of penalty compatible with equilibrium depends on the agents' distribution of beliefs and utility functions. When beliefs are asymptotically homogeneous, it is possible to find a uniform lower bound for the severity of the penalty. When beliefs are asymptotically singular, it is still possible to find default penalties compatible with equilibrium but they must be stochastic and unbounded in the long run. We also show how these positive results depend crucially on the interpretation of default penalties. In particular, if we consider explicit economic punishments, similar to those in Kehoe and Levine (1993), then an equilibrium never exists, even if agents' beliefs are homogeneous.