  We present a simple model for the relationship between quasars, galaxies, and
dark matter halos from 0.5<z<6. In the model, black hole (BH) mass is linearly
related to galaxy mass, and galaxies are connected to dark matter halos via
empirically constrained relations. A simple "scattered" light bulb model for
quasars is adopted, wherein BHs shine at a fixed fraction of the Eddington
luminosity during accretion episodes, and Eddington ratios are drawn from a
lognormal distribution that is redshift-independent. This model has two free,
physically meaningful parameters at each redshift: the normalization of the
Mbh-Mgal relation and the quasar duty cycle; these parameters are fit to the
observed quasar luminosity function (LF) over the interval 0.5<z<6. This simple
model provides an excellent fit to the LF at all epochs, and also successfully
predicts the observed projected two-point correlation of quasars from
0.5<z<2.5. It is significant that a single quasar duty cycle at each redshift
is capable of reproducing the extant observations. The data are therefore
consistent with a scenario wherein quasars are equally likely to exist in
galaxies, and therefore dark matter halos, over a wide range in masses. The
knee in the quasar LF is a reflection of the knee in the stellar mass-halo mass
relation. Future constraints on the quasar LF and quasar clustering at high
redshift will provide strong constraints on the model. In the model, the
autocorrelation function of quasars becomes a strong function of luminosity
only at the very highest luminosities, and will be difficult to observe because
such quasars are so rare. Cross-correlation techniques may provide useful
constraints on the bias of such rare objects.
