I never said you can’t have a free market. You factually cannot have a free market WITH property rights.
Incorrect, within labor costs is everyone’s compensation. Profits is what is above and beyond the cost to produce. If you studied worker cooperatives, you would know any “profits” go out as dividends or distributed back to the workers.
You can have privately owned companies in socialism, just not pertaining to life essentials or public commodities.
You save and invest your compensation.
