  We investigate the environments of quasars such as number distribution of
galaxies using a semi-analytic model which includes both galaxy and quasar
formations based on the hierarchical clustering scenario. We assume that a
supermassive black hole is fueled by accretion of cold gas and that it is a
source of quasar activity during a major merger of the quasar host galaxy with
another galaxy. This major merger causes spheroid formation of the host galaxy.
Our model can reproduce not only general form of the galaxy luminosity
functions in the local Universe but also the observed relation between a
supermassive black hole mass and a spheroid luminosity, the present black hole
mass function and the quasar luminosity functions at different redshifts. Using
this model, we predict the mean number of quasars per halo, bias parameter of
quasars and the probability distribution of the number of galaxies around
quasars. In our model, analysis of the mean number of quasars per halo shows
that the spatial distribution of galaxies is different from that of quasars.
Furthermore, we found from calculation of the probability distribution of
galaxy numbers that at $0.2 \lesssim z \lesssim 0.5$, most quasars are likely
to reside in galaxy groups. On the other hand, at $1 \lesssim z \lesssim 2$
most quasars seem to reside in more varied environments than at a lower
redshift; quasars reside in environments ranging from small groups of galaxies
to clusters of galaxies. Comparing these predictions with observations in
future will enable us to constrain our quasar formation model.
