LOS ANGELES—The median price of an existing, single-family detached home in the Los Angeles area rose to $725,000 in April, an increase of $45,000 from a month ago, mirroring a spike across California that brought the state’s median price above the $800,000 benchmark for the first time, a real estate group said May 17. The Los Angeles area’s median home price was $550,000 just one year ago. California’s median home price was $813,980 in April, with the rise fueled by heated market conditions and a shortage of homes for sale, according to the California Association of Realtors (CAR). “Not only do skyrocketing home prices threaten already-low homeownership levels and make it harder for those who don’t already have a home to purchase one, it also brings to question the sustainability of this market cycle,” CAR vice president and chief economist Jordan Levine said. “As vaccination rates increase and the state …