Expressions for the multipole polarizability and shielding factor for an atom are obtained using the model where the total electron energy is assumed to be a local functional of the electron density. This simple model correctly predicts the leading term in the 1/Z expansion of the polarizability. Further, the simple local density functional for the polarizability, when evaluated with ground-state Hartree-Fock densities, yields numerical values for atoms which are, in general, in reasonable agreement with those obtained from coupled Hartree-Fock theory.