The product of the electronic width of the $J/psi$ meson and the branching fractions of its decay to hadrons and electrons has been measured using the KEDR detector at the VEPP-4M $e^+e^-$ collider. The obtained values are: $Gamma_{ee}(J/psi) = 5.550 pm 0.056 pm 0.089 , text{keV}, $ $Gamma_{ee}(J/psi) cdot mathcal{B}_text{hadrons}(J/psi) = 4.884 pm 0.048 pm 0.078 , text{keV}, $ $Gamma_{ee}(J/psi) cdot mathcal{B}_{ee}(J/psi) = 0.3331 pm 0.0066 pm 0.0040 , text{keV}.$ The uncertainties shown are statistical and systematic, respectively. Using the result presented and the world-average value of the electronic branching fraction, one obtains the total width of the $J/psi$ meson: $Gamma = 92.94 pm 1.83 , text{keV}.$ These results are consistent with the previous experiments.