This photo on Shorpy comes from a Life Magazine archive, dated 1953.
According to the Marilyn Sites in LA webpage, in 1953 she lived at 882 N. Doheny Drive, Apartment 3--right up to January 1954 when she married Joe DiMaggio. There's even a picture of the place at their site, if you scroll down less than half-way through the page. The apartments are still there. Actually, LALife says condos are there, and #3 is less than 650 sq. ft.
Mark Bellinghaus' blog shows another photo of Monroe against the same planked background, and identifies it as the yard of her Doheny apartment. So I guess that settles it. Alfred Eisenstadt is the photographer and the sweater is black cashmere.
BTW, the Bellinghaus blog really rips at the authenticity of the Marilyn paraphernalia displayed in Long Beach in 2005--including her own hair curlers, that he claims were actually manufactured in the 1970s!