The Optimal Price of Default

With assets taken to be pools, rational expectations on their delivery rates are, as default is permissible in an economy and its penalty prescribed in terms of utility, indispensable to the existence of equilibrium. And the resulting equilibrium relies heavily on the prevailing penalty level. We propose, in this paper, a path-following algorithm for calculating the level of penalty that leads to a Pareto efficient equilibrium—Pareto efficient among the set of equilibria of the economies with distinct penalty levels. This algorithm brings off those rational expectations by identifying their upper and lower bounds iteratively until the discrepancies between them are admissible.