The Paul Ehrlich Equation

Normally the Paul Ehrlich Equation is presented as:

I = P * A * T

I is the impact on the environment resulting from consumption
P is the population number
A is the consumption per capita (affluence)
T is the technology factor

Preventing I to increase due to growing consumption (P*A) requires the technology factor T to be reduced - i.e. resource productivity (or eco-efficiency) to be improved.

In a UNEP report of April 2002, "Sustainable consumption: A Global Status Report", it says under the heading 'The Consumption Equation':

The relationship between population, consumption and environmental impact can be described in approximate terms by an equation first proposed by Ehrlich and Holdren in 1971:

TEI = P x UC/hp x EE -1

where TEI is total environmental impact,
P is population,
UC/hp is (average) units of consumption of products and services per head of population
and EE is the environmental efficiency of the production, use and disposal of those units.

This equation makes it easy to visualise the importance of considering levels of consumption of goods and services (per head) and the resources used (and waste generated) to produce those goods and services. Patterns of consumption is a term that intends to capture both these variables. Consumption pressure per head describes the (aggregated) product of the two terms UC/hd and the inverse of EE.

It is from such an equation that the concept of factor 4 (etc) emerges being the level of change in EE that can be achieved through technical and organisational improvements (cleaner production; product re-design etc). If the intent is to reach some specific level of TEI (say for CO2 production) in a given period, then estimates of the likely population growth over that period, as well as the likely rise in the average level of consumption per head (from development, GDP growth etc), will define the factor of improvement in EE necessary to compensate for this rise.

Arguments that arise over the role of population growth in environmental degradation can also be clarified with reference to this equation, since it is clear that the issue is the product of population numbers times the average consumption pressure per head. Rebound effects arise from a relationship between UC/hd and EE, where improvements in EE generate increased consumption per head .