On production and abatement time scales in sustainable development. Can we loosen the sustainability screw ?

In this paper we carry out a preliminary exploration of a time scales’ conjecture, which postulates that “reasonable” notions of sustainability must include a suitable synchronisation of time scales of both the processes of human development and those of the natural environment. We perform our analysis within a coarse, five variable, model of man-nature interactions expressed as a system of differential equations where production and human capital are coupled with both renewable and non-renewable natural resource. We demonstrate a phenomenon that we name the “sustainability screw” that describes a spiral like trajectory of the three key variables: non-renewable and renewable resources as well as the production capital. Under many plausible scenarios, this spiral tends unacceptably fast to an undesirable equilibrium. However, we also show that by adjusting the ratio of “intensity of production effort” and “intensity of abatement effort”, parameters of the relative time scales of production and natural recovery processes can be altered in a manner that produces, arguably, more sustainable trajectories.