Given that production could be carried on without any organization, Coase asks, "Why and under what conditions should we expect firms to emerge?" Since modern firms can only emerge when an entrepreneur of some sort begins to hire people, Coase's analysis proceeds by considering the conditions under which it makes sense for an entrepreneur to seek hired help instead of contracting out for some particular task.
The traditional economic theory of the time suggested that, because the market is "efficient" (that is, those who are best at providing each good or service most cheaply are already doing so), it should always be cheaper to contract out than to hire.
Coase noted, however, that there are a number of transaction costs to using the market; the cost of obtaining a good or service via the market is actually more than just the price of the good. Other costs, including search and information costs, bargaining costs, keeping trade secrets, and policing and enforcement costs, can all potentially add to the cost of procuring something via the market. This suggests that firms will arise when they can arrange to produce what they need internally and somehow avoid these costs.
There is a natural limit to what can be produced internally, however. Coase notices "decreasing returns to the entrepreneur function", including increasing overhead costs and increasing propensity for an overwhelmed manager to make mistakes in resource allocation. This is a countervailing cost to the use of the firm.
Coase argues that the size of a firm (as measured by how many contractual relations are "internal" to the firm and how many "external") is a result of finding an optimal balance between the competing tendencies of the costs outlined above. In general, making the firm larger will initially be advantageous, but the decreasing returns indicated above will eventually kick in, preventing the firm from growing indefinitely.
Other things being equal, a firm will tend to be larger:
the less the costs of organizing and the slower these costs rise with an increase in the transactions organized.
the less likely the entrepreneur is to make mistakes and the smaller the increase in mistakes with an increase in the transactions organized.
the greater the lowering (or the less the rise) in the supply price of factors of production to firms of larger size.
The first two costs will increase with the spatial distribution of the transactions organized and the dissimilarity of the transactions. This explains why firms tend to either be in different geographic locations or to perform different functions. Additionally, technology changes that mitigate the cost of organizing transactions across space will cause firms to be larger—the advent of the telephone and cheap air travel, for example, would be expected to increase the size of firms. On a related note the use of the internet and related modern information and communication technologies seem to lead to the existence of so-called virtual organizations.
Coase does not consider non-contractual relationships, as between friends or family.