The rise, fall and sustainability of capital-resource economies

In debates about green accounting it is sometimes argued that a positive value of aggregate investments indicates that an economy is developing sustainably. Asheim (1994) and Pezzey (1994) have shown that this is wrong, using a version of the well-known Dasgupta-Heal economy (with one capital and one non-renewable resource stock) as a counterexample. Asheim's proof referred to the unproved assumptions that in such an economy a higher rate of time preference induces higher initial consumption and vice versa, and that "optimal" consumption is initially rising and then falling. Here we show that these assumptions do hold true under certain circumstances, thereby also proving some of Dasgupta and Heal's other conjectures about sustainability.