The Firm as a Collective Action outcome

By firm, I mean the entity which is involved in production process in an economy. Why does the firm exist? If "price mechanism" was the director of factors of production as many economists claim, there would be no need for the firm to exist. Indeed all the factors of production would enter into contracts with other factors of productions in a "market exchange" process.
The firm exists as the aforementioned costs are reduced when an entrepreneur through a firm "directs" these factors of production. The costs involved of absorbing many factors of production under the "firm" and co-ordinate their activities is less than pure "market exchanges" of the same.
Thus the firm as a collective action outcome reduces cost of production and hence exists in the "market" thereby benefiting everyone economic agent