Does Upward Income Mobility Depend on Your Starting Point? A Thought Experiment

Take a 40 year old male who makes in the neighborhood of $20,000 a year, and, adjusted for inflation, has made more or less the same amount for the past few years. Let X be the probability that in five years he will make $100,000 a year, adjusted for inflation. (i.e., X is the probability the person will increase his income by 5 times)

Take a 40 year old male who makes in the neighborhood of $100,000 a year, and, adjusted for inflation, has made more or less the same amount for the past few years. Let Y be the probability that he will make $1,000,000 a year, adjusted for inflation. (i.e., Y is the probability the person will increase his income by 10 times)

Take a 40 year old male who makes in the neighborhood of $1,000,000 a year, and, adjusted for inflation, has made more or less the same amount for the past few years. Let Z be the probability that he will make $20,000,000 a year, adjusted for inflation. (i.e., Z is the probability the person will increase his income by 20 times)

My guess… X
Is this guess accurate? And if so, does it say anything about how progressive the income tax should be?

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Follow-up.

Now take three two year old boys, each of whose parents died in an accident, and each of whom is brought up by a foster family. The first inherits a sum of $20,000 payable on his 25th birthday. The second inherits a sum of $100,000 on his 25th birthday. The third inherits $1,000,000 on his 25th birthday.

Which of these individuals is most likely to be making $20,000 a year fifteen years later? Which is most likely to be making $100,000 a year? And which is most likely to be making $1,000,000 a year fifteen years later?