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If you have a person A and a person B, and A replicates by having 2 children, and B replicates by having 16 - then two generations in A's camp has 4 young people in it while B's camp has 256. Should A's family be deprived of earned income to the extent that B replicated with no plan to pay for them?
A society without income inequality will not be able to attract workers to essential roles. For example, how will society ensure that doctors are available in unattractive locations? Currently, a higher income can serve as an incentive.
In our current society, money translates into power, income inequality leads to abuse and anxiety.
It depends on other conditions. To have equal access to employment and the basic securities of life in a socialist (referring to Marxist definition) framework is great, but capitalism as a socioeconomic system disintegrates with equal income. It is an impossibility under capitalism.
If everyone had equal income, then there would be no motivation to strive or go the extra mile for your job.
You can't just have goal in mind, propose a solution and then disregard any other side consequences. Why would someone go through hell to become a doctor, graduate with $250,000 in loans (on average) and then earn as much money as the person microwaving his food at McDonald's.