The static properties of the dielectric response function for an electron liquid, obtained previously by one of the authors, is investigated. It is shown that the resulting pair correlation function has the correct long-range and short-range behaviors so that the correlation energy calculated therefrom reproduces the known exact values to the order of ε2, when an expansion with respect to the plasma parameter ε is carried out. The compressibility sum rule is satisfied to the order of ε2ln ε. It is found that within the accuracy stated above the short-range behavior of the pair correlation function is not sensitive to the form of the ternary correlation function.