You might want to try The Fountain Pen Network for a more definitive answer.
Just a random stab in the dark, but the streamlined look would indicate that it was produce as part of a Duofold set made sometime after 1929 into the late 1930s. I'd guess that it's part of a Duofold Junior set. The three bands indicate that it was probably a part of a slightly more expensive Duofold Junior Deluxe set. That colour/pattern isn't common at all. Usually you see them in black, orange red or a jade pattern. Of course, it may also mean that it was part of a Parkette set, which was the lower end of the Parker line, but it was offered in a magnificent amount of colours and patterns.
Mechanical pencils weren't really sold on their own, but in compliment to fountain pens. You could buy a Dufold Senior for $7.50 in 1929, and for $9 with the matching pencil.
Can't really tell you too much more.