The arguments that the alarming level of Gini coefficient is 0.4 are widely reported. However, to the authors' knowledge, it is not based upon any rigid economic theories. In this paper, they show that Rawls' fairness is compatible with the standard model of competitive markets. This finding reveals that the exponential income distribution not only satisfies Pareto optimality (or efficiency) but also obeys social fairness in Rawls' sense. Therefore, the authors specify the maximal value of Gini coefficients when income follows exponential distribution as a minimal basic reference point of the alarming level (calculated as 0.5), above which efficiency and Rawls' fairness cannot be guaranteed simultaneously. Their empirical investigations show that during peaceful times, worldwide Gini coefficients approximately obey asymptotic normal distribution with a mean around 0.4, contradicting the implication of alarming level; while the two-sigma rule shows that in our sample the alarming levels are all larger than 0.5, conforming to our prediction.
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