ON THE SUSTAINABLE GROWTH IN AN ECONOMY WITH PERFECTLY SUBSTITUTABLE EXHAUSTIBLE RESOURCES

Authors


Margaréta Halická, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska dolina, 842 48 Bratislava, Slovakia, e-mail: halicka@fmph.uniba.sk. The research of this author was supported by ERDF-017/2009/4.1/OPVaV-CESIUK project and VEGA grant 1/2429/12 of Slovak Scientific Grant Agency.

Abstract

Abstract A model of sustainable economic growth in an economy with two types of exhaustible resources is analyzed. The resources are assumed to be perfect substitutes with marginal rate of substitution varying over time. The optimal control framework is used to characterize the optimal paths under the maximin criterion. It is shown that the resource with increasing productivity is not used before the constant productivity resource is depleted. Afterwards the resource with an increasing productivity is asymptotically depleted as well. The results are based on an assumption that transversality conditions hold. A new sufficient condition for the transversality conditions is derived. Finally, an analogue of Hartwick’s rule for this non-autonomous case is established.

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