  In this paper, we study distributions that describe markets with linear
stochastic demand. We express the price elasticity of expected demand in terms
of the mean residual demand (MRD) function of the demand distribution and
characterize optimal prices or equivalently, points of unitary elasticity, as
fixed points of the MRD function. This leads to economic interpretable
conditions on the demand distribution under which such fixed points exists and
are unique. In particular, markets with increasing price elasticity of expected
demand that eventually become elastic correspond to distributions with
decreasing generalized mean residual demand (DGMRD) and finite second moment.
DGMRD distributions strictly generalize the widely used increasing generalized
failure rate (IGFR) distributions. In real life economic applications, they
arise naturally as mixtures of (possibly) IGFR distributions over disjoint
intervals. We further elaborate on the relationship of the two classes and link
their limiting behavior at infinity. We examine moment and closure properties
of the DGMRD distributions that are important in economic applications and
illustrate our results with examples.
