## Sunday, December 16, 2007

### Consumption and Population

At the heart of my dire projections of the world population’s peak and decline has been the apparent parabolic relationship between cumulative consumption and population. As each year’s consumption is added together, population grows to a maximum and then drops to zero. This implies that there is a maximum amount of total resources that we can consume, beyond which more people will die than are being born.

I have now created a theoretical model which explains this relationship, showing the parabolic relationship to be only an approximation.

Consider a system with a fixed amount of resources, of which a maximum amount can be replenished each year (the “capacity,” which increases exponentially each year). The world population has a basic, exponential rate of growth that it attempts to maintain. Each person consumes a certain amount of resources each year, which increases exponentially. As long as the amount of resources consumed by the entire population does not exceed the capacity, the amount of resources doesn’t change; if it does, then the amount of resources decreases by an amount equal to the excess. If the amount of resources changes then the population adjusts itself in proportion to the change (that is, if the resources decrease by one percent in a year, the population after its basic rate is applied also decreases by one percent).

The best fit of the model to the data starts in 1961 with a population growth rate of 2.0 percent, capacity growth rate of 0.5 percent, 2,800 billion hectares of resources, per capita consumption at 1.44 hectares, growth in per capita consumption at 1.6 percent, and a capacity of 3 billion hectares. When this model is applied to footprint and population data, the world’s population peaks in 2035 at 8.4 billion people, and drops to under one billion people by 2093, reaching zero by 2287.