Red Type-1 Quasars after Cosmic Noon and Impact on $L_{\rm UV}$-related Quasar Statistics

Over the past decades, nearly a million quasars have been explored to shed light on the evolution of supermassive black holes and galaxies. The ultraviolet-to-optical spectra of type-1 quasars particularly offer insights into their black hole activities. Recent findings, however, raise questions about the prevalence of red type-1 quasars of which colors might be due to dust-obscuration and their potential influence on luminosity-related properties of quasars. We examine the fraction of red type-1 quasars within the redshift range of $0.68\leq z < 2.20$, applying spectral energy distribution (SED) fitting using optical-to-MIR photometric data of Sloan Digital Sky Survey Data Release 14 quasars. Approximately 10\,\% of the type-1 quasars exhibit red colors suggestive of dust obscuration. There is an association between the brightness of the MIR luminosity and a higher fraction of red type-1 quasars, albeit with negligible redshift evolution. By employing $E(B-V)$ values from the SED fitting, we obtained dereddened luminosity of the red type-1 quasars and reassess the quasar luminosity function (QLF) and black hole mass ($M_{\rm BH}$) estimates. Result shows a modest increase in the number density of bright quasars, linking to more flatten bright-end slope of QLFs, while $M_{\rm BH}$ adjustments are minimal. Current SDSS selections in optical could miss a significant population of heavily dust-obscured quasars. As future MIR surveys like SPHEREx expand, they may reveal enough obscured quasars to prompt a more profound revision of fundamental quasar properties.