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4.3.1. Within-Group Radicalism. We shall examine here the effects of a change in the distribu-
tion of radicalism within one group without perturbing the correlation between radicalism and
wealth. To this effect at every wealth level w we shall redistribute population over x generating
a Lorenz-worsening change in the distribution of radicalism. Religious attitudes will become
more dispersed at each wealth level.
Making radicalism more dissimilar across the population of a given group decreases its in-
ternal cohesion. However, this decreased cohesion has the effect of increasing the extremism of
the most radical part of the population — and decreasing the radicalism of those who already
were more lukewarm. We want to examine which of these two forces will prevail. Will more
religious heterogeneity decrease or increase group aggressiveness?
In order to examine this question we start by recalling that the group equilibrium best re-
sponse is determined by the intersection of the aggregate cost of mobilizing a number Ah of
activists with the funds individuals will willingly supply when Ah activists are being mobilized
in response to the Am activists mobilized by opposing group. The aggregate cost of mobilization
is not altered by the change in radicalism. Hence we just have to focus on how the supply of
funds will be modified as the distribution of radical feelings becomes more dispersed.
The aggregate demand for activists at any compensation rate is the sum of the individual
decisions to contribute money to finance activists. We have already seen in Proposition 3 that
an increase in radicalism leads to higher individual contributions. Therefore, we will have to
balance the decreased contributions by the moderates who are now even less committed and the
additional contributions coming from the most radical who have become more radicalized. This
depends on how the marginal rate of substitution between consumption and religious attitudes
varies as radicalism increases. When the marginal utility of consumption is convex, the fall in
contributions by the more moderate (now even more so) will exceed the increase in contribu-
tions by the more radical (who have become more radicalized). Hence aggregate contributions
will come down and with it the mobilizing capacity of the group.
Indeed, it is well known that a Lorenz-worsening in the spread of x over the population will
produce an decrease (increase) in the aggregate contribution ^z rh(z)nh(z) if r is a concave
(convex) function of x. Condition (3) implicitly defines r as a function of x. The assumed con-
cavity of u with respect to consumption guarantees that r is increasing in x. It can be easily seen
that the condition for the concavity (convexity) of r with respect to x is that the marginal cost
u'(.) is a convex (concave) function of consumption.
PROPOSITION 4. For a given group, suppose that for each level of w, the distribution of radicalism
becomes more disperse in the sense of Lorenz-worsening. Then the group will display less activism if the
marginal utility of consumption is convex, and more activism of the marginal utility of consumption is
concave.
When will the marginal utility function be convex? Notice we have assumed that u'(.) be-
comes unboundedly large as consumption goes to zero. By itself, this implies that marginal
utility cannot be concave on its entire support. For utility functions with a third derivative that
does not change sign, this has to be positive. This is the case for the constant-elasticity utility
functions in the family u(y) = ι-1ηy1-η , η > 0.
Turning the proposition around, we see that greater cohesion in group radicalism increases
group agression if the marginal utility of consumsption is convex. We have seen that this is
indeed the case for the standard assumption that the utility of consumption is concave and of
constant elasticity.