A
Figure 1. The Supply of Activists
The endogeneity of s means that over and above best “responses” at the individual level,
which are defined by (3) and (4), there is an implicit aggregation at the level of each group.
This gives rise to the notion of an equilibrium response for each group, which we now proceed to
discuss.
Fix a group i, with compensation s for its activists. Notice that all types in that group with
w ≤ s will be willing to join the ranks of the activists. For every s the number of available
activists will be
(5) Ai (s) = ni(x, w).
w≤s
This is an increasing step function. Figure 1 plots its inverse, by showing the compensation
rate(s) s that will elicit various quantities of activism A. Of course, this inverse correspondence
si (A) is also an increasing step function; we’ve filled in the jumps in the obvious way by includ-
ing all compensation rates between the extremes at each jump. These jumps will be small if the
gaps between wage rates of neighboring types are small.
3. Equilibrium
Consider group H, and fix some level of activism Am for group M. The pair (Ah, sh) is an
equilibrium response to Am (by individuals in H) if there is a profile of individual contributions
rh (z ) such that
(i) For each z = (w, x), r = rh (z) satisfies (3),
(ii) ^rh(z)nh(z) = shAh, and
z
(iii) sh ∈ sh(Ah).