I modified my consumption model to project price elasticity of consumption, using U.S. consumer expenditures as a function of ecological footprint (representing annual consumption or demand). The result, the ratio of change in footprint to the change in expenditures, closely matches published estimates of price elasticity of carbon used in projecting the magnitude of carbon taxes required to fight global warming. In addition to agreeing that elasticity will increase as the time interval increases (from one to ten years into the future), the model predicts that the elasticity will increase as the rate of change of annual consumption becomes more negative (by about 2.6 percent for each percent decrease in rate).
I added another major variable to my model: the year that reductions in annual consumption (by mass) would stop and consumption would stay constant, rather than continuing indefinitely. This change plus a correction to the calculation of when population would drop (using a population of zero instead of what it was in 1989) yielded unexpected results. No matter what rate or interval (years of reduction) that I used, the final footprint per capita required to stop population loss was much less than one acre. For example, if we reduced consumption for 50 years starting some time in the next year or so, we could need to halve annual consumption every six years, ending with an average of about 50 people using each acre of bio-productive land. If we waited until 2015, we would need to halve annual consumption every three years, ending up with over 7,200 people per acre. The projected population loss would also increase over time, starting with about 500 million if we start soon, and over a billion if we wait until 2015.