Critical debt and debt dynamics

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 in"nity 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

[1]  The present value of resources with large discount rates , 1997 .

[2]  P. Dasgupta,et al.  Resource Management in a Trading Economy , 1978 .

[3]  J. Sachs,et al.  Growth and External Debt Under Risk of Debt Repudiation , 1985 .

[4]  A. Razin,et al.  Sharp Reductions in Current Account Deficits: An Empirical Analysis , 1997, SSRN Electronic Journal.

[5]  J. Sachs.  The Current Account in the Eacroeconomic Adjustment Process , 1981 .

[6]  G. Heal,et al.  Sustainable Growth and the Green Golden Rule , 1993 .

[7]  P. Sen.  Imported input price and the current account in an optimizing model without capital mobility , 1991 .

[8]  F. Ramsey,et al.  THE MATHEMATICAL THEORY OF SAVING , 1928 .

[9]  A. Razin,et al.  Current Account Sustainability; Selected East Asian and Latin American Experiences , 1996 .

[10]  M. Rauscher.  The Optimal Use of Environmental Resources by an Indebted Country , 1990 .

[11]  S. Fischer,et al.  Lectures on Macroeconomics , 1972 .

[12]  William A. Brock,et al.  Differential Equations, Stability and Chaos in Dynamic Economics , 1989 .

[13]  K. Nishimura,et al.  External debt cycles , 1995 .

[14]  R. Barro,et al.  Capital Mobility in Neoclassical Models of Growth , 1992 .

[15]  Colin W. Clark,et al.  Mathematical Bioeconomics: The Optimal Management of Renewable Resources. , 1993 .

[16]  A. Razin.  The Terms of Trade and the Current Account: The Harberger-Laursen-Metzler Effect , 1983, Journal of Political Economy.

[17]  P. Krugman.  Currencies and Crises , 1993 .

[18]  L. Berkovitz.  Optimal Control Theory , 1974 .

[19]  Assaf Razin,et al.  Origins of Sharp Reductions in Current Account deficits: An Empirical Analysis , 1997 .

[20]  Emilio O. Roxin.  Optimal Control Theory (L. D. Berkovitz) , 1976 .

[21]  C G Plourde,et al.  A Simple Model of Replenishable Natural Resource Exploitation , 1970 .

[22]  A. Razin,et al.  Current Account Sustainability: Selected East Asian and Latin American Experiences , 1996, SSRN Electronic Journal.

[23]  S. Turnovsky,et al.  Growth, External Debt and Sovereign Risk in a Small Open Economy , 1989, SSRN Electronic Journal.