The quasar sample selected by cross-correlating the Faint Images of the Radio Sky at Twenty cm (FIRST, <VIII/71>) survey and the 2-degree Field Quasar Redshift Survey (2QZ, <VII/223>) allows us to explore, for the first time, the faint end of the radio and optical luminosity functions up to z=~2.2. We find indications (~3{sigma}) of a negative evolution for these faint sources at z>~1.8, both in radio and optical bands. This corresponds to a decrement in the space density of faint quasars of approximately a factor 2 at z=2.2 and confirms the presence of a differential evolution for the population of radio-active quasars. The faint end of both luminosity functions flattens and the comparison with the (optical) number density of the whole quasar population supports a dependence of the fraction of radio-detected quasars on the optical luminosity. A progressive decrease in the fraction of quasars in the whole radio source population can be consistently accounted for within the receding torus scenario. The population of low-luminosity quasars, which the FIRST-2dF detects, appears to depart from the classical scheme for radio-loud quasars.