  In this paper, we consider the mean residual life (MRL) function of the
Cantor distribution and study its properties. We show that the MRL function is
continuous at all points, locally decreasing at all points outside the Cantor
set and has a unique fixed point which we explicitly determine. These
properties readily extend to the parametric family of p-singular, Cantor type
distributions introduced by Mandelbrot (1983). The findings offer evidence
that, contrary to common perceptions, Cantor-type distributions are tractable
enough to be considered for practical applications. We provide such an example
from the field of economics in which Cantor-type distributions can be used to
model markets with recurrent bandwagon effects and show that earlier
anticipated bandwagon effects lead to higher monopolistic prices. We conclude
with a simple implementation of the algorithm by Chalice (1991) to plot
Cantor-type distributions.
