  We consider a model of socially interacting individuals that make a binary
choice in a context of positive additive endogenous externalities. It
encompasses as particular cases several models from the sociology and economics
literature. We extend previous results to the case of a general distribution of
idiosyncratic preferences, called here Idiosyncratic Willingnesses to Pay
(IWP). Positive additive externalities yield a family of inverse demand curves
that include the classical downward sloping ones but also new ones with non
constant convexity. When j, the ratio of the social influence strength to the
standard deviation of the IWP distribution, is small enough, the inverse demand
is a classical monotonic (decreasing) function of the adoption rate. Even if
the IWP distribution is mono-modal, there is a critical value of j above which
the inverse demand is non monotonic, decreasing for small and high adoption
rates, but increasing within some intermediate range. Depending on the price
there are thus either one or two equilibria. Beyond this first result, we
exhibit the generic properties of the boundaries limiting the regions where the
system presents different types of equilibria (unique or multiple). These
properties are shown to depend only on qualitative features of the IWP
distribution: modality (number of maxima), smoothness and type of support
(compact or infinite). The main results are summarized as phase diagrams in the
space of the model parameters, on which the regions of multiple equilibria are
precisely delimited.
