Joy, I believe what you have is a figural “celluloid” pencil sharpener.
Celluloid is a very early plastic invented in the 1800s to mimic the look of glass, tortoise shell, coral, and other things.
And “yes”, bout anything made of celluloid is “worth something”. And bout anything "elephanty" is a sought after collectible. Partly because it is a "Republican thingy", ya know.
Click the url below.
http://www.rubylane.com/shops/ogees/item/7499