Discontinuous functions and environmental regulation

Environmental economics generally employs marginal logic. This is often useful for conceptual demonstrations even if not always literally proffered for policy. This paper argues that more realistic discontinuous schedules, arrived at by drawing on the development economics literature, have interesting and counter-intuitive policy implications. The cases examined suggest more stringent environmental regulations and the use of continuous fine functions.

 
By Shahrukh Rafi Khan
Last Updated: Sunday 07 June 2015

Environmental economics generally employs marginal logic. This is often useful for conceptual demonstrations even if not always literally proffered for policy. This paper argues that more realistic discontinuous schedules, arrived at by drawing on the development economics literature, have interesting and counter-intuitive policy implications. The cases examined suggest more stringent environmental regulations and the use of continuous fine functions.

Discontinuous functions and environmental regulation This essay is based on a paper I published in International Journal of Ecology and Development, Vol. 26, No. 3. Most students of economics study neo-classical economics and take for granted a world of continuous functions since that facilitates the mathematics. Following from this, environmental economics also generally employs marginal logic. This paper argues that more realistic discontinuous schedules arrived at by drawing on the development economics literature have interesting and counter-intuitive policy implications.

I examine two cases to examine this point and in each case more stringent environmental regulations are suggested than when using continuous functions. For example, environmental economics textbooks use continuous marginal abatement cost functions and optimal emissions are derived from the intersection of the marginal abatement cost function (MAC) and the marginal damage (MD) function. Since sound science is needed to compute a continuous marginal damage function with precision and since even the most advanced countries are researching their way towards that ideal, the framework above could be viewed as relevant for conceptual points rather than practical policy. Given uncertainties pertaining to damage to the environment and human health, most ecological economists would urge the precautionary principle when the science is uncertain in establishing outcomes with precision.

This is more so the case when there is no guarantee that the forthcoming optimum would not have too large an aggregate impact in a “full world” (Daly, 1996). The fiction with regards to an optimum level of emissions is compounded by the assumed continuity of the MAC function. For most industries, there is no continuous technological option but rather discrete choices. This point has been made in the context of the choice of technology debate as applying to production functions and discontinuous isoquants (Stewart, 1972), but that point logically carries over to this production context also. I show that by utilizing a discontinuous function it is possible to suggest more stringent regulations without violating marginal conditions. The same principle could be applied when the marginal damage functions differ, for example due to rural and urban pollution.

There may be lower damage from rural pollution due to diffuse population but a discontinuous abatement cost functions would suggest equally stringent standards in urban and rural areas. Environmental economists argue that if the standards are too stringent, agents will simply spend more funds lobbying for relaxing standards since on the margin the expected returns from lobbying against stringent standards would become higher relative to more productive activities. While this may be so, ecological economists point out that there are off setting incentives created for the clean technology industry.

The second case considered pertains to how discontinuities might apply to sanctioning pollution. The fine function is normally drawn as a continuous step leading off from the marginal damage function i.e. fine only applies if damage exceeds a stipulated amount of emissions. The ideal fee would be one that simulates damage and so an upward sloping continuous fee would make most sense. If the damage rises exponentially, then it would make most sense for the fine function to rise exponentially.

Once again it may be logical for environmental bureaucracies to use a step fine function to reduce information and transaction costs and this is what is used for pollution charges based on self-regulation. However, we show that a realistic step function creates perverse incentives of polluting too much and a more finely tailored continuous fine function would avoid this perverse incentive To sum up, this essay urges students to work with more realistic scenarios than the stylized world imposed upon us by neo-classical economics. REFERENCES Daly, H., 1996, Beyond Growth: The Economics of Sustainable Development, Beacon Press, Boston. Stewart, F., 1972, “Choice of Technique in Developing Countries,” Journal of Development Studies, 9, 99-121.

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