There are three pieces to this set It does look like Bakelite but is probably Each piece is a type of celluloid called Acwalite (sometimes called "French Ivory". The box was used as a powder box, the button Hook matches the Box. the shoe horn is just a little different color. The bottom of the powder box is a translucent amber color and the lid is marbled Amber color. The set is not marked and is in very nice condition for its age of the 1930s.
Vintage Vanity Dresser Set Acwaite Powder box, Shoe Horn & Button Hook