I modified my theoretical model of consumption and population, introduced in the last post, to include exponential growth in the amount of resources available. I also accounted for the restriction of that growth after a maximum speed is reached (assuming a constant density of mass in an expanding sphere, and a constant mass per global hectare of consumption). In addition, I set adjustable minimum and maximum values for per capita consumption, and added a logarithmic curve fit of ideality (the average of lifespan and happiness) as a function of per capita footprint. While resources are increasing faster than they are being consumed, the population rate stays at its maximum level. When per capita consumption falls below the minimum, the population crashes.
Multiplying the size of the population by the ideality (as a fraction) for any given year results in a measure of the magnitude and quality of our experience as a species. Normalizing these values to the value for a particular year, yielding what I’ll call the “Ideal World Index” (IWI), allows us to compare experiences over time: the higher the IWI, the better we’re doing. Based arbitrarily on the year 2000, the IWI is projected to rise to 1.5 (times what the product of population and ideality was in 2000) by 2038, drop to 0.05 by 2144, and then rise to 20.4 where the per capita consumption drops below minimum (0.09 hectare) and the population crashes.
If the IWI is summed over infinite time (or a sufficiently long period) different scenarios can be compared. Those scenarios with a fixed IWIsum will have the population crash, while those that have a minimum value indicate that the population is sustainable. I have chosen the period from 2000 to 5000 for the scenarios I’ve studied. For all cases where resources are growing as long as possible, per capita consumption falls below the minimum by the year 4500.