No they aren't. Markets tend towards monopoly, or at least an oligopoly. Market 'equilibrium' where prices are 'right' is an ideological fantasy.
That said - this is an example of how the legitimacy for private commercial corporations being run dictatorially based on formal property ownership kind of blows up in people's faces when such corporations grow to the level of encompassing a significant part of some sector of the economy, or a significant part of social interaction altogether.
As for government intervention - the government is involved: Its basic role is to set this up and support it. Government checks corporate/capitalist power mostly in the face of very strong public pressure and the threat of uprisings / mass strikes / violent redistribution etc.
