We investigate how the fraction of broad-line sources in the AGN population changes with X-ray luminosity and redshift . We first construct the rest-frame hard-energy ( 2 - 8 keV ) X-ray luminosity function ( HXLF ) at z = 0.1 - 1 using Chandra Lockman Hole-Northwest wide-area data , Chandra Deep Field-North 2 Ms data , other Chandra deep field data , and the ASCA Large Sky Survey data . We find that broad-line AGNs dominate above \sim 3 \times 10 ^ { 43 } ergs s ^ { -1 } and have a mean luminosity of 1.3 \times 10 ^ { 44 } ergs s ^ { -1 } . Type II AGNs can only become an important component of the X-ray population at Seyfert-like X-ray luminosities . We then construct z = 0.1 - 0.5 and z = 0.5 - 1 HXLFs and compare them with both the local HXLF measured from HEAO-1 A2 survey data and the z = 1.5 - 3 HXLF measured from soft-energy ( 0.5 - 2 keV ) Chandra and ROSAT data . We find that the number density of L _ { x } > 10 ^ { 44 } ergs s ^ { -1 } sources ( quasars ) steadily declines with decreasing redshift , while the number density of L _ { x } = 10 ^ { 43 } -10 ^ { 44 } ergs s ^ { -1 } sources peaks at z = 0.5 - 1 . Strikingly , however , the number density of broad-line AGNs remains roughly constant with redshift while their average luminosities decline at the lower redshifts , showing another example of cosmic downsizing .