We have made radio observations of 87 optically selected quasars at 5 GHz w
ith the VLA in order to measure the radio power for these objects and hence
determine how the fraction of radio-loud quasars varies with redshift and
optical luminosity. The sample has been selected from the recently complete
d Edinburgh Quasar Survey and covers a redshift range of 0.3 less than or e
qual to z less than or equal to 1.5 and an optical absolute magnitude range
of -26.5 less than or equal to M-B less than or equal to -23.5 (h = 1/2, q
(0) = 1/2). We have also matched other existing surveys with the Faint Imag
es of the Radio Sky at Twenty Centimeters and NRAO VLA Sky Survey radio cat
alogs and combined these data so that the optical luminosity-redshift plane
is now far better sampled than before. We have fitted a model to the proba
bility of a quasar being radio-loud as a function of absolute magnitude and
redshift, and from this model we infer the radio-loud and radio-quiet opti
cal luminosity functions. The radio-loud optical luminosity function is fea
tureless and flatter than the radio-quiet one. It evolves at a marginally s
lower rate if quasars evolve by density evolution, but the difference in th
e rate of evolutions of the two different classes is much less than was pre
viously thought. We show, using Monte Carlo simulations, that the observed
difference in the shape of the optical luminosity functions can be partly a
ccounted for by Doppler boosting of the optical continuum of the radio-loud
quasars, and we explain how this can be tested in the future.