We investigate whether the parsec-scale jets of quasars 3C 345 and 3C 279 are dominated by a normal (proton-electron) plasma or a pair (electron-positron) plasma. We first present a new method to compute the kinetic luminosity of a conical jet by using the core size observed at a single very long baseline interferometry frequency. The deduced kinetic luminosity gives electron densities of individual radio-emitting components as a function of the composition. We next constrain the electron density independently by using the theory of synchrotron self-absorption. Comparing the two densities, we can discriminate the composition. We then apply this procedure to the five components in the 3C 345 jet and find that they are pair-plasma dominated at 14 epochs out of the total 19 epochs at which the turnover frequencies are reported, provided that the bulk Lorentz factor is less than 15 throughout the jet. We also investigate the composition of the 3C 279 jet and demonstrate that its two components are likely pair-plasma dominated at all the four epochs, provided that their Doppler factors are less than 10, which are consistent with observations. The conclusions do not depend on the lower cutoff energy of radiating particles.