Sustainability screw: role of relative production and abatement time scales

Abstract

We postulate that reasonable notions of sustainability must include a time-scale synchronization of both the processes of human development and those of the natural environment. We perform our analysis within a simple system of five differential equations where non-renewable and renewable resources are coupled with production capacities, abatement and human capital as functions of time. A ‘sustainability screw’ phenomenon is demonstrated describing a spiral like trajectory of three key variables—the non-renewable resources, the renewable resources and the production capital. This spiral may tend to an undesirable steady state, however, by adjusting a ratio of intensity parameters, time scales of production and natural recovery processes can be altered to produce more sustainable trajectories.

Keywords:

• sustainable optimization systems
• viability
• multiple time scale

Acknowledgements

Jacek B. Krawczyk thanks the Institute for Sustainable Systems and Technologies at the University of South Australia and also the Center for Operations Research and Econometrics (CORE) in Louvain-la-Neuve, Belgium, for hosting him during several stages of writing this paper.

Jerzy A. Filar and Manju R. Agrawal acknowledge the support from the Australian Research Council under grant DP0987148 and Prof Phil Howlett’s comments and improvement suggestions.

Notes

1 For example, the New York city councillors feared at the beginning of the 20th century that, given the rapid increase of horse driven street cars, the amount of the horse manure would be unbearable for the city by the early twenties.

2 A PPP adjusted dollar has the same purchasing power over GDP (or GNI) as a US dollar in the United States and buys an equivalent amount of goods or services irrespective of the country. PPP rates provide a standard measure allowing comparisons of real price levels between countries, just as conventional price indices allow comparison of real values over time. Values are in current dollars and are not adjusted for inflation.

3 Gathering historical data enabled those authors to develop a quantitative theory to link population density to human capital formation.

4 We remind the reader that the growth function in Equation (2) is logistic and that the corresponding time profile of R can converge (bifurcate) to a ‘low’ or ‘high’ steady state.

5 Again, without specific claims about the pace and levels of those changes.