Size, Bureaucracy, and Differentiation
In the 1950's there were conflicting studies on the relation between size and bureacratization. One difficulty in early studies was that they usually combined all the clerks, technical, professional, and managerial into one category "administration" and compared vs laborers. Later studies showed that in general the proportion of managers tends to decrease with size, but the proportion of technical and clerical people increases with size (Blau and Schoenherr, 1971).

Organizational size is positively associated with structural differentiation (levels, occupational categories (Blau and Shoenherr, 1971, Blau 1973, Pugh et al 1969). Larger organizations are more complex, and besides increasing the types of activities it increases the number of activities within each type.

Blau (1970) builds a theory to explain the impact of size. Large size increases structure, which increases pressure for more administration to control and coordinate the increased heterogeniety of work activities. But within subunits increased size increases the number of similar activities, which reduces the amount of adminstration required to coordinate them. Overall the effect of size is to decrease the managerial component (Blau and Shoenherr, 1971), though they tested their hypothesis with only one set of organizations. It's probably strongly affected by the type of organization and differentiation involved (Scott p. 261).

Note that differing environmental demands means that different subunits may grow at different rates, requiring more coordination to compensate (Katz and Kahn, 1978 p. 110). They reach two main conclusions from a survey of the size literature:

1. As organizations grow in size the proportion of workers in direct production decreases, but not as a monotonic function.

2. As organizations grow the % of people in managerial and supervisory positions decreases, but at a decellerating rate. They also note that rates are highly dependent on which organizational fields you are studying.