A. There is obviously nothing like THE carrying capacity of earth¹, it heavily depends on the consumption per capita and the technology available. I never did the math but I always wondered what would happen if we upgraded every human in existence to the first world. I think seven billion people with first world living standard are possible but I am not sure it would end well today, resource consumption would increase by a factor of maybe two. So I can imagine that we are not in big trouble with seven billion people and current technology and consumption only because we still have a lot of relatively poor people.
C. We improved living standards and decreased mortality in early years, so a pyramid shaped population structure is a thing of the past. And countering this with continued population growth is not an option because it is not sustainable. Some countries could nonetheless use a few more babies to get back to 2.1 children and avoid an inverted pyramid due to a shrinking population.
¹ There is certainly some theoretical upper limit but that is also certainly not relevant here.
resource consumption would increase by a factor of maybe two
That's significantly lower than most estimates I've seen. Jared Diamond for example says that the first world versus developing world resource consumption ratio is 32, with the majority of the world's population being much closer to the developing world:
The estimated one billion people who live in developed countries have a relative per capita consumption rate of 32. Most of the world’s other 5.5 billion people constitute the developing world, with relative per capita consumption rates below 32, mostly down toward 1.
He goes on to say that if China was to increase to match US consumption levels --- with no change in population or change in consumption elsewhere --- that alone would double the worlds consumption:
Per capita consumption rates in China are still about 11 times below ours, but let’s suppose they rise to our level. Let’s also make things easy by imagining that nothing else happens to increase world consumption — that is, no other country increases its consumption, all national populations (including China’s) remain unchanged and immigration ceases. China’s catching up alone would roughly double world consumption rates. Oil consumption would increase by 106 percent, for instance, and world metal consumption by 94 percent.
Your numbers are probably closer to the truth, as I said, I never did the math or looked for existing calculations. I just looked up the energy consumption in 2008 - EU-27 40,821 kWh/capita, World 21,283 kWh/capita - which gives a factor of 2 and hoped that energy consumption would be a reasonable proxy for resource consumption. I definitely expected something more than 2 but would not have guessed more than maybe 5.
A factor of 32 is a lot but that is also the extreme. China at 11, that leaves 5 billion people. If they were all at 1 that would drag the average down to 2.7. So maybe between 3 and 5 in the end? That still means a 5 to 10 fold increase in their resource consumption and matches my expectation. Suddenly needing twice as much of everything is probably already way harder than it first sounds, but up to 10 times...
I'm not familiar with the numbers either, but your estimate sounds plausible to me. Tom Murphy has a nice presentation from which a more exact figure can probably be extracted, but I don't see it there directly: http://physics.ucsd.edu/do-the-math/2013/09/the-real-populat...
C. We improved living standards and decreased mortality in early years, so a pyramid shaped population structure is a thing of the past. And countering this with continued population growth is not an option because it is not sustainable. Some countries could nonetheless use a few more babies to get back to 2.1 children and avoid an inverted pyramid due to a shrinking population.
¹ There is certainly some theoretical upper limit but that is also certainly not relevant here.