  We use the spectra of 22,000 nearby early-type galaxies from the Sloan
Digital Sky Survey (SDSS) to determine the age distribution of these galaxies
as a function of their velocity dispersion sigma_v in the range 100 km/s <
sigma_v < 280 km/s. We then combine the inferred age-distributions with the
local abundance of spheroids, including early-type galaxies and late-type
bulges, to predict the evolution of the quasar luminosity function (LF) in the
redshift range 0<z<6. We make the following simple assumptions: (i) the
formation of stars in each galaxy, at the epoch identified with the mean
mass-weighted stellar age, is accompanied by the prompt assembly of the nuclear
supermassive black hole (SMBH); (ii) the mass of the SMBH obeys the
M_bh-sigma_v correlation observed in nearby galaxies; (iii) the SMBH radiates
at a fraction f_Edd of the Eddington limit for a fixed duration t_Q, and is
identified as a luminous quasar during this epoch, (iv) the intrinsic
dispersions in the Eddington ratio and the M_bh-sigma_v relation produce a
combined scatter of Delta(log L_Q) around the mean logarithmic quasar
luminosity <log L_Q> at fixed sigma_v. These assumptions require that the SMBH
remnants of quasars with bolometric luminosity below L_bol=10^{12.5} f_Edd
L_sun reside predominantly in bulges of late type galaxies. We find that
evolution of the observed quasar LF can be fit over the entire redshift range
in this simple model, 0<z<6 with the choices of Delta(log L_Q)=0.6-0.9, t_Q=
(6-8)x10^7 yr, and <f_Edd>=0.3-0.5. We find no evidence that any of the model
parameters evolves with redshift, supporting the strong connection between the
formation of stars and nuclear SMBHs in spheroids.
