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A. The per capita approximation means the whole world has to be brought at third world status.

At projected 2050 population levels of 10b, and 25GT/year emissions, per capita emissions allowance is 2.5t/year. There is no industrialized country with this level of emissions, the lowest being Sweden, Switzerland and France at 4.5, 4.7 and 5.13. These countries have moved >90% of their electrical production to nuclear and renewables and cut their emissions in half compared to the 1990s. Possibly they are also externalizing their food and industrials production.

B. What is 'fair' share? Population as of 2020? 2050? 1950? Land area? Forest mass?

The most obvious issue is population. Hard to believe, but in 1950, at the beginning of the current Golden Era, world population was a mere 2.5 billion people. At those population levels everybody on Earth could have had afforded the industrialized lifestyle of Japan, Germany or Netherlands, with about 10 CO2t/capita emissions.