  We analyze systematic effects in the determination of the galaxy luminosity
function in clusters using a deep mock catalogue constructed from a numerical
simulation of a hierarchical universe. The results indicate a strong tendency
to derive a rising faint end ($\alpha \lsim -1.5$) in clusters selected in two
dimensions, using a galaxy catalogue constructed with a universal flat
luminosity function with $\alpha \simeq -1.0$. This is due to the projection
effects inherent in catalogues of clusters constructed using 2 dimensional
data. Many of the clusters found in 2d have no significant 3d counterparts, and
most suffer from massive background contamination that cannot be corrected for
by subtracting random offset fields. The luminosity function of high surface
brightness galaxies in the field and within small groups follows a Schechter
function with a fairly flat faint end slope, $n(L)\propto L^{\alpha}$ with
$\alpha = -0.9$ to -1.2. On the contrary, observational studies of clusters
constructed using Abell, EDCC and APM catalogues are systematically found to
have steeper luminosity functions with $\alpha = -1.4$ to -2.0. This may be
attributed to projection effects rather than a dominant population of high
surface brightness dwarf galaxies ($M\gsim M^*+2$) in clusters. It should be
straighforward to confirm our results by measuring redshifts of these faint
cluster galaxies.
