The results are reported of molecular dynamics simulations of the static longitudinal dielectric and response functions for molten AgI at 923 K using two ionic models. The first one is a rigid ion model, while in the second the induced dipole moments of the anions are added to the effective pair potentials of the first. It is derived theoretically that the dielectric functions for the polarizable ion model are determined by spatial correlations of charge and dipole moment densities. The charge structure factor at long wavelengths is also studied.