Socialism does not mean the absense of a market system!
"Contrary to conventional wisdom the defining characteristic of socialism is not the abolition of market relations and its replacement by centrally planned, top-down production. Economic planning has no bearing whatsoever on whether a set of social relations are exploitative or not.
The essence of socialism is a hoped-for system of property relations, which we’ll call the “communal system”. In this system, the renting of people has been abolished (just as liberal democracy abolished the selling of people, i.e. slavery). People no longer are workers available to rent by the owners of firms. Instead, people are workers available to join as equal members of a democratic firm, who together lay claim on the residual income.
A socialist firm is owned by its working members who hire-in capital at pre-agreed rental prices (compared to capitalism, the contracts are reversed). Capital, not labour, is now the ex ante cost of production. In consequence, the working members democratically distribute the firm’s residual income to themselves.
What’s right with this?
The communal system is an inherently egalitarian system because all income from production is earned in essentially the same manner: by the contribution of labour. Absentee owners no longer lay claim to the fruit of others’ labour in virtue of a piece of paper (e.g. “equity”). The systematic economic theft, characteristic of capitalism, has been abolished.
Socialism is not merely just, however. It also eradicates extreme income and wealth inequality for the simple reason that the entire working population earns the same kind of economic income, which is a kind of profit share. The split of the population into two main economic classes, that is workers (wage-earners) and capitalists (profits via ownership of firms), disappears along with the major social ills caused by extreme inequality." (https://ianwrightsite.wordpress.com/2016/12/14/first-blog-post/)