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Critical debt and debt dynamics. (English) Zbl 1136.91541
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.

MSC:
91B64 Macroeconomic theory (monetary models, models of taxation)
91B28 Finance etc. (MSC2000)
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