Difficult economics question - please read carefully!!!?

Question

Suppose that an economic system has the following two features:

1. Per-capita income is growing at a steady rate of x percent per year.

2. The Gini coefficient is experiencing a slow and steady increase.

What percentage of the population is likely to see income growth rates BELOW x (slower than the per capita) and what percentage will see growth rates ABOVE x?

Answer 1

Since there is no limit for Gini coefficient growth (it can potentially reach 0.999(9)) so conclusion is: in infinitely long-run for all population except one person income will grow slower than x.

Answer: 99% (or 99.99%) will grow below X and 1% (or 0.01%) will grow faster than X.

But actually depending on speed of growth for Gini coeficient most population may go (only theoretically/mathematically - in real life nobody will allow it) to zero income (so their growth in income will be negative) - just because income will be distributed tremendously toward one person - and Gini coefficent will go to  0.9(9)> k >1.00