This post will attempt to work out, via some very rough back-of-the-envelope calculations, how rich an individual would be if everyone in the world had the same income. Incidentally, this is not meant to be a response to any particular argument; to my knowledge, nobody is currently advocating that the world's income be redistributed equally among its citizens.
According to the CIA World Factbook, the GWP in 2013 was $87.18 trillion. Since the global population in 2013 was 7.1 billion, the GWP per capita was approximately $12,300. In comparison, the current GDP per capita of the UK is about $37,300. Therefore, if the world continued to produce $87.18 trillion in output under a regime of global income redistribution, the average person in the UK would be about 67% poorer. However, because the UK's income distribution is skewed, the typical (i.e., median) person would only be about 37% poorer. Note that $12,300 is a pre-tax figure. Funding a government that spent 40% of GDP would leave an individual with about $7,400 in disposable income.
It is highly improbable that the world would continue to produce $87.18 trillion in output under a regime of global income redistribution. This is because, among other reasons, innovation and labour supply would be greatly reduced. Thus, the figure of $12,300 is almost certainly an overestimate. The table below provides four metrics for how rich an individual would be under alternative estimates of global income per person. Moving down the table, each successive estimate is approximately $1,230 smaller. The estimate in the second row reflects an assumption that output would be 10% smaller; the estimate in the bottom row an assumption that output would be 90% smaller. (One caveat is that the total population might also be smaller if many of the world's poorest people had slightly more income.)
The second column of the table gives the year at which the UK had the same income, based on data from the Maddison project. (Estimates were converted to 1990 dollars prior to comparison with the Maddison numbers). The third column gives the percentile of the current UK income distribution that each estimate corresponds to. The fourth column gives the percentile of the current world income distribution that each estimate corresponds to, based on the Global Rich List calculator. And the final column gives a country that currently has the same income.
If global income redistribution yielded an income per person of $12,300, an individual would enjoy the average living standard of: the UK in 1954, someone at the 23rd percentile of the UK income distribution, someone at the 87th percentile of the world income distribution, or Brazil. Comparatively, if global income redistribution yielded an income per person of only $1,200, an individual would enjoy the average living standard of: the UK in 1300, someone at less than the 1st percentile of the UK income distribution, someone at the 48th percentile of the world income distribution, or Eritrea.