We study the static density response function of the 2D quantum electr
on solid with analytic and quantum Monte Carlo techniques. The 'longit
udinal' response function at small and intermediate momentum transfer
from the simulation is well approximated by the analytic results using
phonons alone, provided the Debye-Waller factor is included. The 'tra
nsverse' response function and the large momentum transfer longitudina
l response function from simulations are larger than the analytic resu
lts from contributions with phonons alone.