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Population-Consumption Model

This mathematical model relating world population and consumption of resources has gone through several versions. Most of the content on this site relates to Version 2. The implications of the latest, Version 4 (January 2014), are in the early phase of being fleshed out.

Version 4

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

Epop = ae * Ppop2 + be * Ppop + ce for Epop < Emax

F * Ppop = am * Emax2+ bm * Emax + cm for Epop < Emax

L = F / (aL * F + bL )

where:

Version 3 (for a detailed overview, see Population, Consumption, and the Future of the World)

Consumption = Mt * P2 / 2 + Me * P

Cmax = Mt * Pmax2 / 2 + Me * Pmax

Poprate = Ratemag * P / Pmax * (1 - P / Pmax)

where:

• Cmax is maximum consumption
• P is population
• Pmax is maximum population based on Cmax
• Poprate is the population rate (fractional change per year)
• Ratemag is the maximum normal population rate
• Mt is transaction mass
• Me is extraction mass

Version 2

Consumption = A * (r2/r1)F * tB*EXP(C*t^D+E*t^(D-1))

Population = G * Consumption0.5

Speed = H * Consumption

where:

• r2 is the previous year's resources
• r1 is the resources two years earlier
• t is the year
• The rest are constants

Happiness, Consumption, and Life Expectancy

Happiness = a * LN(Consumption) + b

Lifespan = c * LN(Consumption) + d

Where a, b, c, d are constants.

Good World

For each species s with population Ps and life expectancy Ls:

Ws = Ps * Ls

Where V is the total number of species, the total amount of good W in the observable universe is:

W = ∑s=1s=V (Ps * Ls)

If we integrate W over the entire lifetime of the universe, it should ideally be at large as possible.

Emissions = f * Consumption1.5

Temperature = g * Consumption3 + InitialTemperature

Where f and g are constants, Consumption is proportional to the Global Ecological Footprint.