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The basic income can't make all people equal. Generally, it reduces the inequality. 

But in some cases it could even ensure an inequality - where needed to keep alive people's work incentive. Namely, it ensures that the income of active and inactive working age people would remain inequal in favour of those who have job or enterprise. Current traditional social welfare systems could, in worst cases create a "reversed" inequality which means that receiving social transfers is more useful than having job. Literally, one has a choice - to stay home and receive social transfers 500 euros per month or to have a job and get 500 euros per month. With a basic income, the choice with the same numbers would be - to stay home and get 500 euros per month or to have and job and get 500+500=1000 euros per month.

Inversely, the communists tried to build a money-free society where all people would work according to their abilities and get the goods according to their needs. I other words the amount of goods would not depend on their work at all. The Commune of the Working People of Estonia, an unrecognized communist state with short lifetime (Nov 1918-Jan 1919) even found the salary being a "capitalist hangover" and therefore paid a "living wage" that depended on the profession (but not on the real work). In Soviet Union that tried to build communism, having a job was compulsory, people without job were punished with short term imprisonment. At the same time, people with job often spent their working time in queues fearing otherwise not to get different goods. Private enterpreneurship wasn't allowed, there were no concurrence and many other things that are usual in market economy. 

Unconditional basic income would still use the money and keep alive the market economy.