Details and Projections
This page provides details about version 3 of the PopulationConsumption model.
In the newest version of the PopulationConsumption model, consumption and population are related according to a simple formula:
Where C is consumption, P is population, M_{t} is transaction mass, and M_{e} is extraction mass. See the blog post Discontinuity for more explanation. The percapita consumption, represented here by the ecological footprint F, is therefore:
where: M_{t} = 5.5E11 M_{e} = 1.80E02 (P ≤ 2.64E+09) M_{e} = 2.50 (P ≥ 3.14E+09) 

The rate of population change has declined linearly since the 1960s. If this trend were to continue, the rate would reach zero (the population would peak) in 2065 and consumption of ecological resources would be the equivalent of 2.1 Earths.


Looking at the larger picture, the population rate (Poprate) seems to follow the relationship
where Ratemag is the maximum normal population rate (approximately 0.07 = 7%), and population Pmax is derived from the maximum consumption Cmax:
From the historical data, Cmax appears to have been one Earth (1.19E+10 hectares) until about 400 BC, and from then on it was two Earths (2.38E+10 hectares).


Assuming current conditions can be maintained (extraction mass M_{e} stays at its current value – energy and other resources can support it; and the maximum consumption Cmax doesn't decrease), the population will approach the maximum (Pmax = 8.69E+09) and stay there.


Consumption likewise approaches its maximum. This is currently envisioned to be the best case scenario, because there are good reasons to believe that the conditions cannot be maintained, primarily:
For a discussion of these results, see the blog post Approaching the Peak.


Happiness is projected to be as shown, rising to nearly 20% until after World War Two, then rapidly increasing to over 60% and increasing relatively slowly afterward. 
See also:
© Copyright 2011 Bradley Jarvis. All rights reserved.