We define a new complete sample of 13 optically-luminous radio quasars ( M _ { AB } ( 1450Å ) < -26 \hbox { $ . ^ { m } $ } 9 and \log P _ { 1.4 GHz } ( W Hz ^ { -1 } ) > 25.7 ) with redshift 3.8 < z < 4.5 , obtained by cross-correlating the FIRST radio survey and the APM catalogue of POSS-I .
We measure the space density to be ( 1.0 \pm 0.3 ) Gpc ^ { -3 } , a factor 1.9 \pm 0.7 smaller than the space density of similar quasars at z \approx 2 ( FBQS ) .
Using a new measurement of the radio-loud fraction of quasars we find that at z = 4 the total space density of quasars with M _ { AB } ( 1450Å ) < -26 \hbox { $ . ^ { m } $ } 9 is ( 7.4 \pm 2.6 ) ~ { } Gpc ^ { -3 } .
This is a factor 1.8 \pm 0.8 less than the space density at z \approx 2 , found by the 2dF quasar survey .
This z = 2 / z = 4 ratio , consistent with that of the radio-loud quasars , is significantly different from the ratio \sim 10 found for samples including lower-luminosity quasars .
This suggests that the decline of the space density beyond z \approx 2 
is slower for optically-luminous quasars than for less-luminous ones .