It is worth noting for clarity's sake that the concept of a market does not logically presuppose the existence of "private property in the means of production" in the sense that private individuals or family households are the owners of land and capital and thus the recipients of profits, interest, rent etc. One may at least theoretically conceive of an economy of market socialism , in which workers' collectives, consumers' cooperatives, village communes or even autonomous state agencies leased from the state or held actual title to land, mines, factories, machinery and so forth -- so long as the socialist production organizations were free to buy and sell their output and and the use of their assigned land or capital assets to each other at freely negotiated prices responsive to conditions of supply and demand (assuming, of course, they are allowed to keep effective control of the bulk of the proceeds). There are, of course, both theoretical and practical problems with market socialism , and the costs and benefits of capitalist markets cannot be uncritically attributed to such a system. The larger point is that socialist economies have historically included varying proportions of "remnant" market elements in their make-up, and the theoretical possibilities for additional "hybrid" forms are numerous.
[See also: market , property rights , factors of production , contract , microeconomics , transaction costs , competition , capitalism , socialist ]