Great post! It provides a good gedanken for sorting out how much inequality results from age and how much results from other factors.
If you made this scenario a little bit more complex, you could demonstrate how other forms of "inequality" are based, in part, on age:
1: Have everyone start with equal $50,000 salary at age 22, then get a raise of $3,000 per year until they hit 65. Everyone would still have equal lifetime earnings, but you would find significant income "inequality" when looking at the population as a whole.
2: Instead of a flat $3,000 per year raise, everyone gets a 3.5% raise each year until they hit 65. This is closer to real life than the scenario above, and would produce an even more "unequal" income distribution.
If you made this scenario a little bit more complex, you could demonstrate how other forms of "inequality" are based, in part, on age:
1: Have everyone start with equal $50,000 salary at age 22, then get a raise of $3,000 per year until they hit 65. Everyone would still have equal lifetime earnings, but you would find significant income "inequality" when looking at the population as a whole.
2: Instead of a flat $3,000 per year raise, everyone gets a 3.5% raise each year until they hit 65. This is closer to real life than the scenario above, and would produce an even more "unequal" income distribution.