4 - The dynamics of production functions

Summary

Assume that the probability of success … of [a] collective action is … a function of the number of demonstrators.… This function is assumed S-shaped because a small demonstration is expected to have little impact up to a certain size, and again large numbers beyond a certain size would not make much difference either, whereas in the middle range, additional numbers increase visibility and impact.

Anthony Oberschall (1980, p. 48)

With this paragraph, Oberschall sought to move the analysis of social movements beyond the generally implicit assumption of a linear relationship between effort and effect that pervaded the previous literature. However, Oberschall gave us only this brief glimpse of a fundamental theoretical issue. He did not pursue further the relationship between the form of the production function and the probability of collective action. In this chapter, we take up this unfinished task.

Production functions can take many exotic forms, but the important dynamics of collective action can be captured with the five types sketched in Figure 4.1. Each of the figure's curves is intended to capture the entire production relation between individual costs borne and value received from the collective good. As discussed in Chapter 2, the overall shape is a composite of the relations between costs borne and resources contributed, between resources contributed and the level of the collective good, and between the level of the collective good and the value experienced. As our examples indicate, in different situations the overall shape of the production function is dominated by different links in the chain.