Inconsistency between a criterion and the initial conditions
What if an unsustainable economy decides to switch in finite time to a sustainable path of a nonrenewable resource extraction which is optimal with respect to some criterion? We consider this problem on the example of the Dasgupta-Heal-Solow-Stiglitz model (DHSS) using constant consumption over time as a criterion. It turns out that if the criterion has no connections with the "opportunities" of the economy (initial conditions) then the resulting "optimal" path of consumption can be inferior to the one along some sub-optimal sustainable paths of extraction calibrated on the original initial conditions. In our case we have obtained under the standard Hartwick Rule bounded and unbounded growth of consumption along these sub-optimal paths.
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