I'm kinda a semi-authority on the Marx Brothers and want to share what an incredible piece of movie history this is.
This was the Marx Brothers first feature length film and one of the first "talkies." They took their stage act and basically put it on screen in 1929. Most of the shots are done in one take with no editing. This scene, with its rapid-fire dialogue and memorable exchanges, is one of these one-take wonders. Notice the blueprint? The soundman had so much trouble with the sound of crackling paper, when Groucho would open it up on the table, that it had to be saturated with water so the two characters' voices could be caught on microphone.

The screenplay was done by Kaufman and Ryskind, two incredible writers that appealed to the lowbrow vaudeville audience yet threw in incredible witticisms. The music was scored by Irving Berlin. The director walked off the job during the filming; the Marx Brothers had to be directed on their own terms, so they had to go through a couple to get a good match.