I made the math on excel and looks like it would require 100% of the global gdp to offer 10.4k $ of income to 7.4 billions people. If it is possible to apply it on a global scale, given the current gdp, why are there experiments on it?
There is no global fiscal authority; you'd have to do this at the national level, if not the subnational level. For a particular country, you'd probably want to look at this problem using a microeconometric framework (see for instance http://ftp.iza.org/dp4781.pdf), and/or a heterogenous agent framework (see Dirk Krueger and co-authors for examples on optimal dynamic tax policy http://economics.sas.upenn.edu/~dkrueger/research.php).
The size of the cake (GDP) is not fixed. It depends on people's choices: work, occupation, education etc. Choices depend on incentives, which in turn are affected by how the cake is expected to be shared. If you give everyone an unconditional basic income some people might decide to stop working, or work less and so on (say because of a negative income effect; other people might instead work more, or become more productive or invest more in their human capital (say because a larger opportunity set allows better choices). As a consequence, the size of the cake to be shared would in general change (especially in the long run, in my view). Experiments and econometric or simulation exercises, such as those mentioned by Stephen, try to understand how the incentives work towards changing the cake's size. You might also look at: http://wol.iza.org/articles/is-unconditional-basic-income-viable-alternative-to-other-social-welfare-measures#link.
Ugo, I like Figure 1 in your linked document. It seems to me that one good thing about a basic income equal to 100% of the poverty line, instead of a fraction of the poverty line, is that it could make net income like a call option: you limit the effects on the downside, but can take on the upside.
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