What is a firm? It is a collection of assets with one owner that contracts with other assets to produce and sell goods. An example might be a steel company we will call Apex: a steel blast furnace owned by one man who hires workers to produce and sell steel. But this is too easy. We do not say that the iron mine which sells to Apex and other steel companies is part the same company as Apex. We could say that blast furnace by itself is Apex, but that neglects the value of its relationship with its workers.
We want to think of a firm as a collection of long-term relationships. But this is hard to pin down.
Tirole's book suggests three ways: Technological, Contractual, and Incomplete-Contracting.
For the Technological approach, think of the firm as a production function. Someone decides what inputs to buy and uses a production function to produce outputs that he sells.
The technological approach is convenient, but it avoids the real question, because in it, the decisionmaker effectively owns none of the inputs-- he buys them all, and thus it doesn't capture the idea of the firm as a longterm relationship. The technological firm is formed and dissolved each period. Only the market is used, and never command-and- control (which is why Coase[1937] criticized the technological view).
For the Contractual approach (Oliver Williamson, others), think of the firm as a "nexus of contracts". Different people own different assets, but they have made contracts with each other to produce and sell something.
In Tirole's chapter 0, he looks at this as a situation where a complete contract can be written, specifying everything that might happen in any future event. Contracts can be useful even in a certainty model with symmetric information, though. Suppose a professor would like to move from Ohio to Alaska and work for a university there. If there were no contract, then after incurring the cost of moving, the university could renegotiate the wage downwards. The professor wants a longterm contract in advance.
Longterm contracts are also useful because of bargaining costs under asymmetric information. Suppose the professor and the university are in a bilateral monopoly once they start working together, but the professor's enjoyment of the job will go up and down over time and cannot be observed by the university. That means the minimum wage he will accept goes up and down too. There would be a bargaining situation each year, and sometimes bargaining would break down and he would not work that year, an inefficiency. It is better to have all the bargaining over in advance. (Think of post-contractual adverse selection contracts' superior efficiency compared to pre-contractual adverse selection.) Note that this stretches the meaning of "complete contract" a bit, though, because we cannot contract on the professor's utility function.
The contractual approach gives us the idea of a long-term relationship. Since breaking contracts introduces a new bargaining problem, it also tells us why sometimes contracts are *not* used, and the market is used instead: when efficiency requires changing the relationship frequently. Moreover, since a long-term contract is similar to ownership, it suggests why the firm owns some assets outright.
But the contractual approach does not tell us why a firm has a boss and workers: why the contracts say that one asset owner can tell the other what to do.
The Incomplete Contracting, or "Authority" approach (Oliver Hart, others) adds control to the contractual approach. It retains the idea of bilateral monopoly. Now let us use a model of uncertainty, and say that the uncertain variable cannot be contracted upon because a court cannot observe it (it is "observable" by the parties but "nonverifiable"). The value of the uncertain variable determines what action is efficient.
Now the contract should say which party gets to make the decision-- which party has "authority". Otherwise, they will bargain over it, and we get the two problems of hold- up and bargaining breakdown again. If the contract specifies authority, though, the "boss" is the one with authority. Commonly, contracts give the boss authority over many of the worker's decisions.
The incomplete contracts approach can also be driven by contract-writing costs (and contract-reading costs-- see Rasmusen, 2001, http://www.bepress.com/bejeap/advances/vol1/iss1/art2). Giving authority over lots of decisions makes the contract shorter. Tirole's book does not mention this reason, I think.