A linear response expression for the Hall conductance ${\ensuremath{\sigma}}_{\mathrm{xy}}$ of interacting two-dimensional electrons in a strong magnetic field is derived. When the system is dissipationless, ${\ensuremath{\sigma}}_{\mathrm{xy}}$ can be written solely in terms of the density-density response function ${\ensuremath{\chi}}_{\mathrm{nn}}$(q\ensuremath{\rightarrow}) of the electron liquid. Thus, a specific behavior of ${\ensuremath{\chi}}_{\mathrm{nn}}$(q\ensuremath{\rightarrow}) is required on a Hall plateau. This behavior is ${\ensuremath{\chi}}_{\mathrm{nn}}$(q\ensuremath{\rightarrow})\ensuremath{\propto}${q}^{2}$ for small wave vector q, with a proportionality constant given by the Hall quantum number.