The Manager and the Competitive Firm's Supply

A firm is typically defined by a production technology. A competitive firm is further characterized by a profit-maximizing objective and a market environment of given prices for inputs and outputs. For these reasons, the theory of the competitive firm ensues completely from the properties of the production function. Thus, specific assumptions on the production function are required to exhibit the traditional insights on the competitive firm. In particular, a rising supply price by the firm requires eventual diseconomies of scale. A U-shaped average cost function then requires the additional property of initial economies of scale. Finally, the insight that relative efficiency and opportunity costs determine membership in the industry is diminished to a computation of how many production functions can profitably operate for a given demand. In short, with the production function approach, the substance of the theory of the competitive firm is technological rather than economic. This paper modifies the definition of the firm along the lines suggested by Gary Becker [1, 119-124] in his discussion of the firm. By so doing, we can explicitly derive the traditional cost curves without ad hoc technological assumptions. Furthermore, this derivation highlights the traditional insights concerning the competitive firm. In particular, we identify the firm by its owner and/or manager. The owner provides a system for coordinating productive activity, while the manager conducts the system. An owner-manager would conduct the system himself. However, the owner could hire a professional manager to conduct the system. Either way, we assume that the system would be operated efficiently. A production technology exists and is freely available to the firm. However, the production process is replicable to any scale, i.e., constant returns to scale. This is a pleasingly restrictive assumption. By eliminating economies or diseconomies of scale, our theory of the competitive firm will be independent of these technological properties. Since input prices are given, technical costs are linear in output. If X is the output per period, then T(X) = t X is the technical cost function, where t is the constant marginal-average cost. The theory of the competitive firm now depends upon characteristics of the owner and the manager. The manager's labor services are required in order to consummate production of the output. For an owner-manager, the firm's objective will be utility maximization. Participation in the industry will depend upon the relative efficiency of the owner's system and on his alternative opportunities. If the owner employs a manager, then the firm's objective