Critical debt and debt dynamics

Abstract

We study the debt dynamics and sustainable debt for an open economy which borrows from abroad in order to nance consumption. To service the debt the country may exploit a renewable resource. We show that there is for every resource stock R a critical level BH(R) of debt above which debt tends to innity but below which it may be steered to zero. We demonstrate how to compute BH(R) using an ODE of steepest descent. If the economy maximizes a discounted integral of utility depending on consumption and the resource stock, the critical debt BH(R) may be reached in nite time. In such a situation slight perturbations of the optimal consumption lead to insolvency. The maximum principle ceases to be valid in this case. ( 2000 Elsevier Science B.V. All rights reserved. JEL classixcation: C61; F32; F34; O16