What are you talking about? Private property refers to the ownership of the organs of economic production - factories, steal mills, whatever - by private institutions (e.g shareholder-managed organisations). If your referring to markets in general, they have existed since the dawn of urban human civilisation, thousands of years before capitalism. Markets can even exist in the most despotic communist dictatorship, or decentralized anarchist collective. Buying and selling goods or having personal property is largely orthogonal to the mode of production employed by a given society.

Right now in spain, the largest buisness group in basque (10th largest overall) is the Mondragon corporation. It’s worker-owned (but not worker managed), although each worker has voting rights. Clearly it is possible - even within capialism - to have some worker autonomy over production.

In 1936, during the civil war in Spain, around 60-75% of urban industry and agriculture was restructured by anarchist labour unions and run and managed by the workers to varying degrees of collectivization. Some towns abandoned the use of fiat currency entirely and instead used systems of vouchers, in small villages goods where distributed even more informally. Industrial production is reported to have increased during this time, and agricultural yields rose by around 30%.