The local density approximation is used to construct a model for the reactivity parameters defined in density functional theory, Starting from a model for the hardness kernel, equations are derived to compute the softness kernel, local softness and local hardness, global softness and global hardness, the Fukui function and also the electric dipole polarizability, A very simple functional is used to test the equations in some atomic systems. The results are promising. Extensions and applications of the model are discussed.