EME 504
Foundations in Sustainability Systems

5.4 Renewable vs. Non-Renewable Resources

Whether a natural resource can be considered renewable or not depends on the time needed for it to be replenished to levels that allow continual extraction. Therefore, a renewable resource may become non-renewable at a tipping point.

Lamberson and Page (2012) create a simple model that results in different tips, depending on the chosen assumptions. The tipping function in this case is the available natural resource. They evaluate how the amount of the available resource changes with time. If this rate is positive, the amount of the available resource will change. If the rate equals zero, equilibrium is attained. If the rate is negative, the resource becomes non-renewable.

In their model, the following terms are defined:

xt = available resource A

C = total existing resource A

(C-xt) = excess capacity

α = portion of resource used at any given time

min {A, xt} = fixed amount of resource A that is consumed regardless of supply

They choose the following replenishing rate:

xt (C-xt) = replenishing rate

Such that:

ẋ = xt (C-xt) - αxt -min {A, xt}

If C,α, and A are held constant, the resulting tipping point is Direct.

If any of these terms are allowed to vary, the resulting tipping point is Contextual.