In the Real Existing Socialism[*] this side of the Cold War, the type of economy was state capitalism.
The means of production weren't owned by the people or their elected government, but the party elite.
Personally I received this eye-opener from Gásár Miklós Tamás, a Hungarian publicist-philosopher who made through a more extreme version of my own ideological journey. A liberal dissident in the eighties, in the early nineties a self-described small-r republican (roughly = libertarian), taught at a US university, got his doubts seeing Real Existing Capitalism there, boiling over upon his return to see the side effects of the march of freedom for markets here, going 'far'-left and greeting the globalisation-critical movement.
The above framing of Real Existing Socialism should also help Westerners (of any ideological stripe) to better understand what's going on since 1989 in my region. To a large part, privatisation here resulted in former factory heads and other party cadre turning owners. While the picture of post-communist Left vs. post-dissident Liberals and Right would be wrong - all parties have their share of former cadre, and many if not most leading members of the Right weren't exactly active members of the opposition -, one can say that 'centre-Left' parties are dominated by former cadres. And they are also the constituency they serve - and if you consider what I wrote previously, you'll see why they are largely pro-business.
This is also why, tough that may not be well known outside my region[+], here decrying elites
is a rhetorical weapon mostly utilised by the Right
Of course, the best example of communist capitalists is in China. Where the Party razes workers' homes to make way for gated communities
. Blood & Treasure
, always with an eye on China, has a good post on this.[*] To the uninitiated: this was an actual propaganda term of the regimes, which - at least in Hungary and Germany - became catchphrases with a mocking undertone in popular usage.
[+] For example the libertarian loon posting as 'Hayward' in the comments @ Lenin's Tomb.