# 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

where:

• 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