Assuming a Pareto Distribution [1], it's commonly known that 20% of the effort gives 80% of the results.
The "80–20 law", according to which 20% of all people receive 80% of all income, and 20% of the most affluent 20% receive 80% of that 80%, and so on, holds precisely when the Pareto index is
$$\alpha =\log _{4}5=\frac{\log _{10}}{5\log _{10}4}\approx 1.161 \alpha =\log _{4}5=\frac {\log _{10}5}{\log _{10}4}\approx 1.161$$
Given such a fixed index (alpha = 1.161), how do I derive how much effort to get 50% of the output? I've found around online that ~0.8% gives ~51% but have not found a formula to give that result.
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