1. Exhaustible Resources:

• 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 For all the intents and purpose, they can be withdrawn and used up, but no more can be made or recreated.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.

Reserve:

• The nature of reserves is dynamic and reflects prices, technology and exploration effort, as well as the pattern of previous extraction and use.
• As increase in raw materials prices will increase the extraction, thus diminishing reserves; but it may also increase reserves, as some of the previously sub-economic resources become profitable to extract.

Exhaust:

• Exhaustion is defined as a state in which the extraction rate falls to zero. Obviously, a reserve is exhausted when there is literally none left.

2. Flow Resources:

• Some resources, a good example being the radiation from the sun, are called flow resources.
• Their distinguishing characteristics are that they are provided in some predetermined quantity and quality beyond human control and must b used when provided or otherwise wasted.

i.e. F_t= R_t +W_t , Where Ft is the flow provided in period t and W indicates the amount wasted.

3. Fund Resources:

• A good example is storing solar energy in forms more readily available for heating and cooling and by converting it to electricity that is more readily transmissible.

i.e. S_t = Σ (F_T– R_T-W_T)

• This period’s use cannot the cumulative net storage from previous periods plus this period’s flow.
• Another example of fund resources is water in a typical watershed system that includes natural groundwater deposits and aquifers and managed reservoirs.

4. Biological Resources:

• Biological resources such as crops, forests and animal populations represent a complete category of resources.
• They use the flow of solar energy, the flow or fund of hydrological resources and the fund of soil nutrients.
• At any given time the stock of biological resource, its biomass is determined by

S_t = S₀ – Σ (R_T – H_T)

Where, H refers in this context, to net recruitment (R is the excess of additional from reproduction and growth over losses from mortality and like occurring independently of harvest). In bad time, H could be negative and at other times, it could exceed R, for a net increase in biomass.

Generally, H is determined by

H_t = h (S_t ,N_t , X_t )

Where, N and X define the support provided by the environment, N being the inputs provided by nature and X the inputs under the control of people. Assuming that, X and N are given and constant across the time periods, we can consider the relationships between

– H_t and S_t

• In a stable unmanaged ecosystem, the biomass of any species tends towards S, the carrying capacity.
• If for some reason the biomass were to fall below S, it would continue to fall to zero. S is the extinction threshold.