Population-Consumption Model v4

This and related pages describe and discuss Version 4 of the Population-consumption model. Version 4 introduces a new definition of "happiness," which ties population growth to consumption of ecological resources.

The model is an empirically-derived theoretical construct that simplistically represents the dynamics involved in the most essential aspects of humanity's future: those affecting our survival. Like any hypothesis, it is subject to test.


Basic equations:

H = MIN(P, E) / MAX(P, E)

Fe = Ppop * F

Emax = Eo * (1 - aE* Fe )

Epop = ap * Ppop2 + bp * Ppop + cp for Epop < Emax

h = Ppop / Epop = F / (ah * F + bh), Epop >= Emax

Eh = h * Ppop

L = F / (aL * F + bL )

G = Eh2

W = Eh3


  • E is the environments inhabited by part of a population
  • Eh is the number of happy environments
  • Emax is the number of maximum environments in people-equivalents
  • Eo is the original number of maximum environments (prehistory)
  • Epop is the preferred number of inhabited environments in people-equivalents
  • F is the global ecological footprint in Earth/person/year
  • Fe is the total ecological footprint in Earths/year
  • G is the value of the economy, which is proportional to Gross World Product
  • h is average happiness of a population, H is happiness of part of the population
  • L is life expectancy in years
  • P is the number of people in part of a population
  • Ppop is the size of the human population in people (also, the number of "occupied" environments)
  • W is the wealth, or size, of the economy, which is proportional to total wealth
  • The rest are constants

Additional information

Technical Details: Non-technical Discussion and Implications:



© Copyright 2014 Bradley Jarvis. All rights reserved.