  Does a new product spread faster among heterogeneous or homogeneous
consumers? We analyze this question using the stochastic discrete Bass model,
in which consumers may differ in their individual external influence rates
$\{p_j \}$ and in their individual internal influence rates $\{ q_j \}$. When
the network is complete and the heterogeneity is only manifested in $\{p_j \}$
or only in $\{ q_j \}$, it always slows down the diffusion, compared to the
corresponding homogeneous network. When, however, consumers are heterogeneous
in both $\{p_j\}$ and $\{q_{j}\}$, heterogeneity slows down the diffusion in
some cases, but accelerates it in others. Moreover, the dominance between the
heterogeneous and homogeneous adoption levels is global in time in some cases,
but changes with time in others. Perhaps surprisingly, global dominance between
two networks is not always preserved under "additive transformations", such as
adding an identical node to both networks. When the network is not complete,
the effect of heterogeneity depends also on its spatial distribution within the
network.
