an:01454356
Zbl 1136.91541
Semmler, W. W.; Sieveking, M.
Critical debt and debt dynamics
EN
J. Econ. Dyn. Control 24, No. 5-7, 1121-1144 (2000).
00066397
2000
j
91B64 91B28
Summary: We study the debt dynamics and sustainable debt for an open economy which borrows from abroad in order to finance 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 \(B^*(R)\) of debt above which debt tends to infinity but below which it may be steered to zero. We demonstrate how to compute \(B^*(R)\) 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 \(B^*(R)\) may be reached in finite time. In such a situation slight perturbations of the optimal consumption lead to insolvency. The maximum principle ceases to be valid in this case.