Short answers, pulled from the story.
The theory of the firm explains why firms exist and how they differ from markets by superseding the price mechanism with internal resource allocation. It addresses transaction costs such as discovering prices, negotiating contracts, and haggling over surplus division in uncertain environments.
Ronald Coase published his transaction cost theory of the firm in 1937 as one of the first neo-classical attempts to define the firm theoretically in relation to the market. This work established that a firm's existence stems from the inability of markets to handle all production efficiently without internal direction.
Neo-classical theory of the firm was seriously challenged in the 1960s by alternatives including managerial theories developed by William Baumol Robin Marris and Oliver E. Williamson. Behavioral approaches emerged through Richard Cyert and James G. March of the Carnegie School emphasizing bounded rationality and satisficing rather than profit maximization.
Armen Alchian and Harold Demsetz argue that firms emerge because extra output is provided by team production but requires monitoring to overcome shirking. They assert that the monitor must be the recipient of residual income to effectively manage the team and avoid infinite monitoring loops.
The property rights approach to the theory of the firm was developed by Sanford J. Grossman Oliver D. Hart and John H. Moore through their incomplete contracting paradigm between 1986 and 1995. This framework posits that ownership structure influences investment incentives when contracts cannot specify every contingency, making the party with the more important investment decision the owner.