This note offers a general proof of the converse of Hartwick’s rule, namely that – in an economy with stationary instantaneous preferences and a stationary technology – an efficient constant utility path is characterized by the value of net investments being zero at each point in time. In a one consumption economy with two stocks – a stock of a natural resource and a stock of man-made capital – this means that if consumption remains constant at the maximum sustainable level, then the accumulation of man-made capital always exactly compensates in value for the depletion of the natural resource.
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Withagen, C., Asheim, G.B. (2007). Characterizing Sustainability: The Converse of Hartwick's Rule. In: Justifying, Characterizing and Indicating Sustainability. Sustainability, Economics, and Natural Resources, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6200-1_11
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