Currently the world economy is $74 trillion on a purchasing power parity basis. the IMF is forecasting about 6% per year growth through 2015 for a world economy of $99 trillion.
Robert Fogel, nobel prize winning economist has projected China to have 123 trillion GDP in 2040 China’s share of global GDP — 40 percent — will dwarf that of the United States (14 percent) and the European Union (5 percent) 30 years from now. So the World economy he is projecting is $307 trillion in 2040.
A world economy ten times larger will be a quadrillion dollar economy. Inflation and using future dollars will accelerate that milestone.
Increasing growth every 20 years Year flat 6% 6-11% 6-18% 2015 100 100 100 (trillions of dollars, World GDP PPP) 2020 134 134 134 2030 241 241 241 2.5 times energy 30K per cap 2040 431 474 571 3-4 times energy 50-70K per cap 2050 770 940 1390 5-10 times 80K-140K per cap 2060 1380 2000 4300 10-20 times energy 140K-430K per cap 2070 2500 4500 13700 15-40 times energy 250k-1.37 Million per cap 2080 4400 11600 56000 20-80 times energy 440K-5.6 M per cap 2090 8000 30000 230000 35-200 times energy 800K-23 M percap 2100 14000 86000 1200000 60-500 times energy 1.4M - 120 Million per cap
Up through 2040-2060 the gains to the world economy come from some continued growth in the developed countries and China, India, South east asia, and other countries catching up. The per capita assumes that world population grows to about 10 billion and then stays flat.
Assuming energy intensity of 10 megajoules/todays dollar and 10 billion people for a Kardashev level one civilization would mean $5.5 million dollars per person per year. Energy usage would be 55 terajoules per person (15.28 million kwh, 100 GW at 90% capacity factor produces about 800 billion kwh. 1.9 megawatts to generate the 15.28 million kwh)
The highest growth rate path on the table (increasing 3% growth rate every 20 years, 6% for 2010-2030, 9% for 2030-2050, 12% for 2050-2070, 15% for 2070-2090 and 18% for 2090-2100). It would be an economy 12000 times larger than in 2015. Assuming increased energy efficiency relative to GDP generation, I am assuming they will only need about 500 to 1000 times more energy. This would need less than the energy of Kardashev level one. 2* 10 ^16 watts. Kardashev one is about 100 Petawatts (10^17 watts).
A yottawatt civilization would be roughly equivalent to a Kardashev 1.75 civilization. It would have one billion times more energy than Kardshev level one. This level of energy requires factory mass produced nuclear fusion or nuclear fission.
The Wealthy of 2100 will be different from the Wealthy of 2010
William Randolph Hearst was one of the richest men in 1903. He had 28 newspapers read by 20 million people (did not reach that level until 1925). He also had big property. Hearst Castle, but did not own that land until 1919 (construction from 1919-1947).
A more modest modern approximation would still be a multi-millionaire. Someone with a bunch of popular blogs or websites to reach 5 million (lower than the 1920 figure to the 1903 level). Instapundit/Pajamasmedia gets 500,000 page views per day, 12 million per month. Online estimate $10/cpm for about $1.4 million per year in revenue. However, the staff to achieve that went way down. Nice big modern homes (30,000+ sf) are still very expensive, but not Hearst Castle. It would be easier and cheaper (but still expensive) to make a modern approximation of royalty from an earlier period. Certain things become cheaper and easier to make with better technology.