Population – Wealth Equations

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The formulae:

Annual-wealth-created = total-work-done + asset-wealth-accessed

Total-work-done = average-personal-productivity * population

Per-capita-wealth  =  average-personal-productivity  + (asset-wealth-accessed / population)

Asset-wealth-accessed = accrued-wealth + natural wealth-accessed

The Terms

Total Wealth.

The total wealth is simply the wealth of the society overall.  The sum of the wealth that is available for the total society to enjoy.  This wealth is available to be share evenly or not, but it represents that which is available to share.

Asset-wealth.

Asset wealth is the sum of durable wealth which remains from year to year such as housing and infrastructure as opposed to wealth which is consumed such as food and holidays.

Assets can be man made such as housing, or natural, such as the land under the housing, fertile farm land and water to grow crops or mines as a source of mineral wealth.  For natural wealth,  only those natural resources which are being utilised add to the wealth of the community at the time being considered.  Unused land or undiscovered minerals which may potentially be part of future wealth, do not add to current wealth.

Per Capita Wealth.

Simply the total wealth divided by the number of people.  In a society with perfectly even distribution of wealth, each individual would hold the per capita share of wealth.  Raising the Per Capita wealth would raise the wealth of all in the society.  However, simply adding to the wealth of one individual will still raise per capita wealth, even though there is no distribution of the increase in wealth.  Per capita wealth only is a sound indicator of overall wealth if wealth distribution remains static, and the rich remain in the same ratio of wealth to the poor.

Per capita wealth creation follow the formula above and combines individual wealth creation with the share of natural resource wealth.  Growing population should allow specialisation which can have a positive impact on the ability of an individual to produce wealth, but as the population grows this effect reaches a limit.  While there are untapped resources, growing the population can also allow accessing more resources,  but eventually all resources are already leveraged.  The result is that there is a phase where as population increases per capital wealth should increase, followed by a tipping point when all resources are fully exploited after which per capita wealth will be driven to decrease by further population grown.

The Implications: Pre-Finite world

Logically, total work done should increase in proportion to population. However, increased opportunities for specialisation and economies of scale can result in an increase in total work done slightly beyond the logical proportional increase. Simplistically, it is feasible for a team of 200 to do more than 10x the work of a team of 20 because of economies of scale and ability to specialise.  But a team of 200 trying to dig the same 3meter diameter hole in the ground may not be 10x as fast as team of 20.

Pre-finite world, natural asset wealth could never fully utilised, as there was always new natural assets to be found and utilised.  As population expands, more land can be utilised, more minerals discovered and the accessible total natural wealth expands as the population expands.  The result is that increase in population has the potential to increase per-capita wealth.

Finite World Implications

Once we reach ‘finite world’ where all new land has been found, and there is already sufficient people to exploit all available resources, more people simply means a smaller share of available land and resources per person.

Like digging the hole in the ground, there is an optimum number of people on the team.  Less than the number the work takes longer,  but past a certain point adding more becomes counter productive… or a least results in no further increase in production and the proceeds of the work on a per person basis start to decrease.

Once finite world is reached, further increases in population simple mean less wealth per person.  This is the same with any creatures in nature, within a given habitat, there is a maximum population of each creature which can be sustained by the habitat before living conditions start to decline.

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