Maximum sustainable government debt in the overlapping generations model

The theoretical determinants of maximum sustainable government debt are investigated using Diamond's overlapping generations model. A level of debt is defined to be 'sustainable' if a steady state with non-degenerate values of economic variables exists. We show that a maximum sustainable level of debt almost always exists, and it normally occurs where variables such as capital are in the interiors, rather than at the limits, of their economically feasible ranges. This leads to a situation where, when debt is at its maximum, a further infinitesimal increase in debt causes a 'catastrophe', i.e. the economy embarks on a path of unchecked capital decumulation.