I have a pretty good handle on the duties, decisions of a business owner in a capitalist market. Supply/demand, profit margins, etc. But what a business owner/manager have to deal with under a Communist economic system? How involved was he in any decision-making? Who did he report to on a day to day basis?
EDIT: Let's say I'm talking about the Soviet Union, in particular.
In the USSR if you were self-employed then you could still own your own business, in certain fields like owning a cafe, being a hairdresser or other service industries of this type. This was however strictly limited as you could not have employees yourself on any level more formal than family members helping you (or off the books moonlighters)
If the business was of any size then you would not be an owner, but a manager on behalf of a state owned enterprise. You would have a production target that would be allocated from a planning board, which you would have to ensure, whether by inspiring your team, or cheating the system in various ways, you fulfilled. Your local planning board would make its decisions based upon previous production levels in the 5 year planning cycles, as well as be influenced by political planning demands from higher regional planning offices and the central GOSPLAN ministry in Moscow.
As for who a manager reported to, there was the twin system of the CPSU Party structure (which any mid-senior level manager would be a part of as part of the nomenklatura system of assigning responsible jobs), as well as the formal power structure of the factory/business. This was designed to produce a power structure in society where those who had power were both politically reliable and competent in their work. In practice however the political reliability trumped the competency requirement in almost all cases, so someone who was better at framing his reports from the perspective of the changing 'party line' would often be promoted faster than those who showed actual skill. Also the widespread patronage networks that developed from the 1960s onwards further degraded managerial inefficiency.
This describes the system in the USSR covering the period from about 1960-1985, though there were some minor experiments that varied this situation over the period. I personally would love to hear from anyone about the situation in other socialist states.
This depends heavily on which state you are talking about. For example Cuba was much different than USSR, Yugoslavia much different from USSR, PRC much different from Yugoslavia etc. etc. etc.