No, it yields a Gini coefficient very close to zero.

The Gini coefficient is defined as 1/2 the mean absolute difference considering all pairs of households:

https://en.wikipedia.org/wiki/Gini_coefficient

A group of people where everyone has the same income as a Gini coefficient of exactly zero. Adding a single outlier will increase it a little. A group of 1001 with 1000 people earning $1 and one person earning $100 has a Gini coefficient of 0.09.

>> If everyone in Tajikistan has $5 except the president

> That distribution will yield a very high gini coefficient of very close to 1.

It yields (n-1)|5-p|/(2n(5(n-1)+p)) which is about p/(5n+p).

So it depends on whether the president (p) has $10 or $n^2.

indeed. If everyone in tajikistan has $5 except the president, who has $1, the gini coefficient will be different.