The maximization problem in (2) is straightforward. Each H -individual of type z = (w, x)
takes as given the contributions of everyone else in society and selects his own contribution r. If
we denote by Ah- the aggregate contributions by the rest of the H -individuals, then r is chosen
to maximize
p (a- H—hh, Am) x + u(w — r),
It follows that the H-individual’s “best response” r is uniquely described by the first order
condition
(3) p1 (Ah, Am) χh^ ≤ u'(w — r), with equality if r > 0,
where Ah is just the sum of Ah- and r/sh .
For an M -individual of type (x, w), the conditions are entirely analogous:
(4) —p2 (Ah, Am) — ≤ u'(w — r), with equality if r > 0.
So far the present model is not too different from a standard model of lobbying. There are
two variations though, with a third — the most important — to be introduced presently. First,
we allow for heterogeneity in individual attitudes towards religious policy, something that will
permit us to remark later on the correlation between wealth and extremist attitudes. Second,
each individual makes his choice of contributions; the choice is not dictated by a group decision.
On this matter, we are agnostic regarding the alternatives of group-based versus individual-
based contributions.7
The third and most important way in which we depart from the standard literature is by
endogenizing the costs of activism, sh and sm . It is hardly a novel observation8 that social
and political activity, especially of the potentially violent kind that we have in mind, is costly.
Individuals who earn a lot of money with their labor time are generally not out on the streets;
they would rather contribute monetarily to an extremist cause than participate in it physically.
On the other hand, individuals who are poor can be easily “bought” and compensated for their
violent activity. The compensation can include meals, money, and promises of reciprocal favors
or job opportunities. The term si generally includes these compensations.
The easiest way to model the effects of economic circumstances on this sort of activity is to
suppose that all those whose earning capacities are low enough join up, though they cannot
switch religious alliances in the process. Thus a person with religious affiliation i can only be
compensated by si should he decide to take to the streets, and he must join the i-activists. We’ve
already used w as a proxy for overall earnings capacity; we now use precisely this variable to
determine a cutoff: all i-types with w ≤ si become activists.
Notice that this does not imply that every individual with w < s must become a full-time
activist. There are generally limits on the extent of this sort of activity. Presumably, an individual
cannot participate in a religious riot 365 days per year, but the point is that he should be ready to
do so if called upon to instigate or assist in one. Thus we suppose throughout that the decision to
participate or not in activism represents a small fraction of working time, so that for all practical
purposes an individual’s earnings capacity is not endogenously altered thereby.
In particular, this allows us treat an individual’s (gross) contributions r as a decision that isn’t
intertwined with his activism. Of course, his net contributions may well be: part of his r may be
imputed payments to himself (if he is also an activist at the same time).
7Esteban and Ray (1999) employ a group-based approach, and Esteban and Ray (2001) address the Pareto-Olson
group size paradox by taking an individual-based approach.
8See, e.g., Becker (1968).