Unless I’m mistaken, if Alice pays 9% of $117,000 (i.e., $10,530), then Bob pays 11.7% of $234,000 (i.e., $27,400).
An 18% tax rate would apply to earners of $1,170,000 (i.e., $210,600 in tax).
The high end would be a 63% tax rate applicable to earners of $117 billion (i.e., $73.71 billion in tax).