The density functional theory of Hohenberg, Kohn, and Sham has been used to derive an exact variational expression for the spin susceptibility (χ) of an inhomogeneous electron gas. This variational expression allows one to simultaneously treat band and exchange correlation effects among the conduction electrons and, furthermore, includes the influence of core electrons on the latter. The use of a simple trial function and a local approximation for the exchange correlation functional in the variational expression results in a simple formula for χ (lower bound). The above approach is developed in parallel and compared with the self consistent single particle equations for a magnetized paramagnetic system including exchange correlation. These equations are used to obtain explicit expressions for the paramagnetic response functionals for noninteracting and interacting systems.