who controls the factors of production in a free market economy
Market economies do not logically presuppose the existence of private ownership of the means of production. A market economy can and often does include various types of cooperatives, collectives, or autonomous state agencies that acquire and exchange capital goods in capital markets. These all utilize a market-determined free price system to allocate capital goods and labor. In addition, there are many variations of market socialism, some of which involve employee-owned enterprises based on self-management; as well as models that involve the combination of public ownership of the means of production with factor markets.