"Firm" is simply another word for company or business. The basic economic marketplace consists of transactions between households and firms. Firms use factors of production - land, labor, and capital - to produce goods that are consumed by households. They may be organized in many different ways - corporations, partnerships, sole proprietorships, and collectives are all examples of firms. Economists who study the theory of the firm attempt to describe, explain, and predict the nature of a firm, including its existence, behavior, structure, and relationship to the market.
The Evolution of the Firm
Not all markets and societies involve firms. In many medieval cities, most production was done by individual craftsmen who were loosely organized into guilds, or by tenant farmers who rented family-sized plots of land. Transactions took place primarily between individuals.
Firms generally appear and become prevalent as an alternative to individual trade when it is more efficient to produce in a non-market environment. For example, in a labor market, it might be too difficult or costly for firms or organizations to engage in production when they have to hire and fire their workers depending on demand/supply conditions. While the advantages of consolidation for efficiency are potentially many and varied, the underlying concept is that integrating operational paradigms enables potential synergy via the construct of a firm.
Firms also allow economic growth, not only for the firm but for the broader society in which it resides. Through separating the business from the individual(s) who starts it, the funding, insurance and liability of a firm can function independently of a person. The separation of a firm from the individual also allows more specifically applicable regulations and laws, broader accumulation of investment capital and more complex strategic alliances. While the detailed implications of a firm and it's relationship with individuals and society are complex, the important takeaway is that firms play an integral role in economic structure.
The Firm
Organizing production under firms reduces the transaction costs of coordinating production in the market.
The Transaction Theory of the Firm
According to Ronald Coase, people begin to organize their production in firms when the transaction cost of coordinating production through the market exchange is greater than within the firm. He notes that a firm's interactions with the market may not be under its control (for instance because of sales taxes), but its internal allocation of resources are: "Within a firm, … market transactions are eliminated and in place of the complicated market structure with exchange transactions is substituted the entrepreneur … who directs production." He asks why alternative methods of production (such as the price mechanism and economic planning), could not either achieve all production, so that either firms use internal prices for all their production, or one big firm runs the entire economy.
For Coase the main reason to establish a firm is to avoid some of the transaction costs of using the price mechanism. These include discovering relevant prices (which can be reduced but not eliminated by purchasing this information through specialists), as well as the costs of negotiating and writing enforceable contracts for each transaction (which can be large if there is uncertainty). Moreover, contracts in an uncertain world will necessarily be incomplete and have to be frequently re-negotiated. The costs of haggling about division of surplus, particularly if there is asymmetric information and asset specificity, may be considerable. Organization into a firm can considerably reduce these costs.