In a democratic capitalist environment the price mechanism automatically becomes the planning tool for its homeostasis; what is the significance of the public sector in this environment?

In a market economy, the price mechanism is indeed the primary coordinator of the decisions of buyers and sellers, because the price for goods and services adjust to an equilibrium point, where demand and supply are equal.

However, the public sector still has two important functions in this enviroment:

Correcting market failures - a market failure is a situation in which the market does not produce a good outcome. An example of market failure is pollution. Market failures can be corrected by government intervention, for example, by setting anti-pollution regulations.Providing public goods - some public goods are not provided by the private sector because they are not profitable. The public sector can therefore step in and provide this type of goods.