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> I don’t think middle class refers to median income. At least it certainly didn’t used to. How else could a population have a small middle class?

Well, it could if it meant “near median income” if few had near the median income. Median doesn't mean particularly common (or even the most common, which is the mode.)



The median is what you get if you sort all people by income and pick the middle person. If one forces the median to be in the middle class then this forces the upper class to be large when the middle is small: Example with a large middle class:

  |...|...........|...|
    ^       ^       ^
    |     median    |
  (working)      (upper)
Example with small middle class:

  |.......|...|.......|
    ^       ^       ^
    |     median    |
  (working)      (upper)
Real life example with small middle class:

  |.............|...|.|
  (working) ^     ^  ^
          median  | (upper)
                middle


> If one forces the median to be in the middle class then this forces the upper class to be large when the middle is small

It doesn't force the working and upper class to be equally large unless you further assume the distribution is symmetric, but yes, there is a limit to how small the upper class can be since at least half of the distribution has to be split between the upper and middle class.




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