What are the reasons for producing short-form anime? Short-form anime (or tanpen anime, see Is there official terminology for anime series that run less than the standard length?) are relatively common, with at least a few each season. 

It seems strange to me that this would be a worthwhile investment for studios. Sure, the production costs will be lower, but there are certain overheads that aren't going to scale with cost, and their DVD sales will surely be lower. So it seems like a losing deal for studios. 

Why, from a production standpoint, would studios decide to produce short-form anime over a full-length TV series?
Most of the short-form Anime that I've seen are comedies that have little to no character development. So it would be quite difficult to find enough content to "fill up" an entire full-length episode. It's the sort of thing where you sit down laugh for a few minutes and leave.

From another angle, the cost reduction of producing short form Anime is probably even lower than you'd expect.

A lot of short form Anime retain the standard 90-second OP and ED. Since each episode is already short to begin with, 3 minutes becomes a significant portion of the episode to get "for free" - thus even less content needs to be produced.