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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.

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