• Some resources, the best example being mineral deposits, exist in given stocks at given locations. For all the intents and purpose, they can be withdrawn and used up, but no more can be made or recreated. If we use S t to denote the existing stock, R to denote the amount extracted to provide raw materials, and the subscript T = 0,… t,…∞ to indicate the time, the current stock of an exhaustible resource can be expressed as

S_t = S 0 – ΣR_T

That is, the current stock at time t is equal to the initial stock (S 0 ) minus the

sum of all previous withdrawals through the time t-1.

If ” S indicates the known stock, discovered can add to known stock just as

extraction subtracts from them. Thus,

S_t= S₀– Σ (R_T – H_T)

Where C T is the amount recycled in period T and is limited by amount of resources previously used but not recycled.

• The quantity and time dimension of exhaustible resources are seldom homogenous introduces the quality and space/place dimensions.
• Quantity is measurable, usually in terms of mass or volume.
• Quality is often measurable in terms of chemical composition, for instance, mineral contents of ores, or ash content of coal but may also have ore nearly intangible aspects, such as aesthetic properties.