  We investigate the dynamical dielectric function of a monolayer of molybdenum
disulfide within the random phase approximation. While in graphene damping of
plasmons is caused by interband transitions, due to the large direct band gap
in monolayer MoS$_2$ collective charge excitations enter the intraband electron
hole continuum similar to the situation in two-dimensional electron and hole
gases. Since there is no electron-hole symmetry in MoS$_2$, the plasmon
energies in p- and n-doped samples clearly differ. The breaking of spin
degeneracy caused by the large intrinsic spin-orbit interaction leads to a
beating of Friedel oscillations for sufficiently large carrier concentrations,
for holes as well as for electrons.
