I can't directly answer your question, because I haven't found any documents related to the price of dynamite in the 1930-1940 interval. However, I did find and old brochure named Farming with Dynamite by the DuPont Explosives company that explains some of the practical applications of dynamite (namely their "Red Cross" variant) farmers could benefit from and the money they would be spending/saving. Unfortunately, it is from 1910 and does not give the price per stick like you asked. Either way, here's some citations:

On August 11, 1910, at the demonstration of Ivor, Va., above referred to, a ditch 85 feet in length, 3 feet deep and 4 1/2 feet wide at the top, was blasted with dynamite, at a cost not exceeding 10 cents per yard, or about $2.75 for the entire work.

A little farther down:

"Red Cross" Dynamite can be used with complete success to turn up an entirely fresh, fertile soil, and convert a $10 an acre "worked-out farm" into land worth $50 to $100 an acre. The cost in dynamite would be about $10 to $15 an acre (...).

I don't want to risk and give you a (likely wrong) estimate on how much a stick would cost (moreover in the 1930's) based solely on this information, but I think it helps you get a general idea.