This is not simply a question of how many people can be crammed onto the dry surface of the planet. For example, it is easy to calculate (as I indicate below) that if the present number of 6.7 billion of us were each allowed an area of one square metre, we would collectively occupy just 6,700 square kilometres, or an area enclosed within a square about 50 miles by 50 miles, which would fit with spare room within a county the size of Yorkshire.
This is a comically naive piece of arithmetic, but not much more so than many sums I have seen done as to how many might exist on Earth given a daily diet of, say, 2,500 Calories, in which case a figure of around 12 billion can be deduced. So, whoopee, we may well pass that WHO estimate of 9 billion by 2050 and maybe get to 12 billion by the end of the century. Beyond simple issues of how much food we might need, and water for that matter, along with fertilizers and other material resources to build shelters and clothe ourselves, are more complex but equally fundamental questions centred around quality of life and human dignity.
So, what do we mean by living and what standards of it might be considered acceptable? Would we in the West want to “fall” materially to the standards, say, of western Africa? Or, is the economic dream more wishful, to raise the living standards of the majority world to those of the West? The answer is really the proverbial elephant in the room. If the whole existing number of people on earth lived at the standard of an average American (if there is really an average anybody), it is said we would need five planets worth of resources.
It’s about 3.5 planets for a typical European (an even less average scenario), and four earths for that many Australians. Simply put, the latter prospect is not viable, and in the longer run neither is it for Americans, Europeans or Australians, let alone the whole world. Modern, chemically fertilized, mechanised farming is very successful. We can also kill-off pests with synthetic pesticides, and so crop-yields on Western farms are the best on earth, but they are unlikely to be sustainable.
So, in the absence of plenty of cheap oil and natural gas, what is the upper limit of population, or conversely, the lower limit of material quality. Well, O.K., let’s say that we are all allowed that 2,500 calories every day.
6.7 x 10^9 people x 2500 Cals/day. 1 Cal = 1000 cals, so 1 cal = 4180 J (4.18 J/cal).
So they would all eat, 6.7 x 10^9 x 2500 x 4180 x 365 = 2.56 x 10^19 J/year.
So, what might be grown in total?
We have 15 x 10^6 km^2 of arable land for crops. If we assume that 2 tonnes of edible food can be grown (from maybe 5 tonnes of crops mass) per hectare/year, and that this is in the form of simple sugars, i.e. C6H12O6, with an energy content of 2800 kJ/mol, we get:
2 x 10^6 g/year/180g/mol x 2800 x 1000 J/mol = 3.11 x 10^10 J/ha/year. And converting 1 km^2 = 100 ha, that’s grown on 15 x 10^6 x 100 ha of land, so we have:
1.5 x 10^9 ha x 3.11 x 10^10 = 4.67 x 10^19 J/year.
Now this might be seen as good news in that we can produce around 80% more food energy than is consumed by the present 6.7 billion humans, leading to the conclusion that the earth can support around 12 billion of us, so as I said, maybe we can meet the WHO targets of billion by 2050 and 12 billion by 2100.
But, we would all be living on the proverbial “bowl of rice a day” [(2500 x 4180)/(2800 x 1000) = 3.7 mol = 672 grams].
(This ignores growing any food for animals, that you could get these crop yields without artificial fertilizers and pesticides and there would of course be no crops grown for biofuels).
I have mentioned before a Hubbert type analysis that can be applied to human population growth which is already slowing down. This predicts that in 2024 there will be a maximum at 7.1 billion people (not many more than the 6.7 billion now) after which there will be a decline to 2.5 billion by 2100. I would not be at all surprised because resources to support population are limited.
Now that 2.5 billion at the end of the century may all be living equally and equitably on one planet's worth of resources, or more likely there will be even more poverty all over the world but with a smaller differential between the developing and industrialized nations, if either category are that by then. The level of poverty can only fall so far, because the lower limit of destitution is death.
I think many in the West particularly would sooner die than return to the conditions of a pre-industrialized society, even it that could be relatively well-provided for by agriculture.