The division of labour and the firm: Stigler (1951)

"The division of labor is not a quaint practice of eighteenth-century pin factories; it is a fundamental principle of economic organization."
Stigler (1951: 193)
The following discussion covers material from Stigler (1951) which is one paper that offers a theory of the boundaries of a firm based on the division of labour. Interestingly Adam Smith, despite his famous discussion of the division of labour in the pin factory, did not develop a theory of the firm based on it.

Stigler begins his argument by saying that the division of labour, and its limit due to the extent of the market, lies at the core of a theory of the functions, and thus the boundaries, of a firm. Stigler outlines this theory in the second section of his paper.

In this theory a firm is seen as engaging in a series of distinct operations leading to the production of a final product. That is, the firm is partitioned not among its input markets but among the functions or process that determine the scope of its activities. And thus determine the firm's boundaries.

To allow the graphical representation of the firm's costs of production we will assume that the average costs of each activity depends only on the rate of output of the firm. In addition, if we assume that there is a constant proportion between the rate of output of each activity and the rate of output of the final product then all the cost functions can be drawn on the same diagram and the vertical sum of these costs will be the conventional average cost curve for the firm. With reference to the diagram below to produce q units of final output requires a given number of units of activity 1, costing C_1(q), a number of unit of activity 2, costing C_2(q), and a number of units of activity 3, costing C_3(q). These costs can be summed to give the average cost of production for q units of output, C_1(q)+C_2(q)+C_3(q).

With respect to the shape of the average cost curves for the various activities, some are increasing continuously (C_1), some are falling continuously (C_3) and some are conventionally U-shaped, (C_2).

Now consider the Adam Smith's idea that the division of labour is limited by the extent of the market. First take the activities for which there are increasing returns, Why doesn't the firm exploit the returns more fully and in the process become a monopoly in the output market? Because as the firm expands outputs other activities also have to be increased and some of these are subject to diminishing returns and these cost increases are such that they overwhelm the cost advantages of the increasing returns and increase the average cost of the final product. So why then does the firm not abandon these C_3-like activities and let some other firm (and thus industry) specialise in them to exploit the increasing returns fully? At a given time the market for these activities may be too small to support specialised firms. Given this firms must perform these activities for themselves.

But with an expansion of the market for the increasing returns activity firms specialised in that activity would develop. The firms currently carrying out this activity for its own consumption would forgo this activity and let it be taken over by a new (monopoly) firm. This monopoly could not fully exploit its market power however since it has charge a price which is less than the average cost of production for the firm abandoning the activity. As the market for this activity grows even larger the number of firms specialising in it grows. That is the industry becomes increasingly competitive.

The abandonment of this activity by the original firms will change the cost function for each firm. The cost curve, C_1, will be replaced by a horizontal line (the black dashed line in the diagram above) in the effective region. This also changes the average cost curve for the final product with the new curve (black dashed curve in the diagram above) being lower than the current curve.

What about the increasing cost case? Why not abandon or reduce use of those activities with increasing cost? Much of the previous discussion carries over to this case with the exception that as the market and the industry grows the original firms does not have to stop utilising that activity completely. Part of the needed use of that activity can still be produced in-house without high average (and marginal) cost, with the rest being purchased via the market.

Ref.:

• Stigler, George J. (1951). "The Division of Labor is Limited by the Extent of the Market", Journal of Political Economy, Vol. 59, No. 3 June, pp. 185-193.