Complete markets with bankruptcy risk and pecuniary default punishments

For an infinite horizon economy with complete contingent markets, bankruptcy risk and default penalties (given by linear loss in utils), Araujo and Sandroni (Econometrica 67(3): 663–672, 1999) and Araujo et al. (J Econ Theory 165:242–256, 2016) show that if agents’ posteriors of their average probabilistic beliefs do not converge in the long run, then a competitive equilibrium without bankruptcy does not exist. The first contribution of this paper is to show that even if all agents have homogenous beliefs, existence of an equilibrium is guaranteed only under stringent conditions on default penalty rates. In order to discourage agents from making promises that they know in advance they will not be able to honor, default penalty rates must be large enough. Are the “real-life” default penalties sufficiently harsh? Since utility penalties are difficult to measure in practise, we propose to address this question by replacing the “reduced-form” linear loss in utils by pecuniary punishments in the line of Kehoe and Levine (Rev Econ Stud 60:865–888, 1993). We show that, independently of the severity of the pecuniary punishment, an equilibrium without bankruptcy never exists.