If per capita consumption is modeled linearly over time, rather than exponentially as I was doing it, there is a better fit to the footprint and population data in my theoretical model. The results are similar to what I found earlier.
With business as usual, the world’s population peaks near 8.1 billion people by 2049, then drops to a minimum of 590 million by 2280. It then may grow until the minimum per capita consumption is reached, with 51 billion people in 2621 before crashing abruptly. The sum of the Ideal World indices from 2000 (IWIsum) is less than 700.
If we stop population growth and cut per capita consumption by 0.2 hectare per year until we reach 0.89 hectare, there will be some population loss before the population levels out at about 6.4 billion people with an ideality of 54 percent.
The ultimate best case growth, with a maximum speed of half the speed of light allowing resource growth at 5.9 percent per year, would last until 4356 before the per capita consumption dropped below a minimum of 0.1 hectare (with an IWIsum of 6E+21, or 6 with 21 zeros).At that rate, we would need to consume a mass equivalent to the Earth in about 900 years, when the IWIsum would be 9 billion.