Why do the Ferengi keep their "females" naked, instead of allowing them clothes?
the wiki entry gives several decent explanations. Another one, not mentioned but logical, would be economics. The clothing of the male Ferengi can be seen as more easily facilitating his economic transactions with other species that have problems with nudity (such as humans for example). As the females aren't involved in that activity, there's no reason to spend money on clothing them.
Of course as de facto sex slaves their main duties would be performed naked, in fact clothing would be a hindrance there, another reason to do away with it :)
Out of universe, no Ferengi female AFAIK ever showed up in the movies or television series, so there was no reason to design clothing for them, which made it a lot easier for people writing fan-fic in the 1970s when erotic sci-fi was popular (and indeed many authors wrote it because there was good money in it) to create a society where women were kept naked for the pleasure of the men. Remember this was the same period where John Norman wrote the best of his Gor novels which also emphasised that female slaves were often kept naked, wearing minimal clothing mostly only as needed for performing their duties.
15Quark's mother Dec 4, 2015 at 7:09
3Also Pel Dec 4, 2015 at 7:11
1@Dreamwalker "The Ferengi Commerce Authority had the authority to punish Ferengi females who earned profit, an illegal activity for them" it was illegal for Ferengi females to earn profit, thus to engage in business transactions (which of course are all intended to produce profit).– jwentingDec 4, 2015 at 9:01
17Ferengis in the 1970's? Were you living in an alternate timeline yourself? There were no Ferengis in Star Trek until the The Next Generation came out in 1987.– JREDec 4, 2015 at 9:02
7This answer is simply wrong. Why is it accepted? Feb 8, 2018 at 16:48
They keep their women naked, so they cannot make profit (and lead a normal life)
QUARK: Would somebody please tell me what's going on?
ISHKA: It's one of those good news bad news type of things. Give them the good news first.
ZEK: If you insist. Three days ago, I added a new amendment to the Ferengi Bill of Opportunities giving females the right to wear clothes.
ROM: In public?
ISHKA: Anywhere we want.
QUARK: That can't be the good news. If Ferengi females can wear clothes in public, then they can leave their homes. If they can leave their homes, they can go to work. If they can go to work, they can make profit.
ISHKA: What's the matter, Quark? Afraid of a little competition?
Why do the Ferengi keep their women naked?
In a few words, the Ferengi live in a male-dominated culture where women are not valued as anything more than domestics.
This subject was addressed in several episodes of Deep Space Nine, including "Rules of Acquisition", Season 2 episode 7, and "Family Business", Season 3 episode 23.
3If you could find the exact episode and add a quote from it, this answer would be greatly improved. You may find Chakoteya's episode transcripts useful.– Rand al'Thor ♦Feb 11, 2016 at 0:07
We are left with best guesses and opinions if we want a historical answer to this question, but are told many times throughout Deep Space Nine and TNG that the Ferengi consider Cloths, at least with respect to Ferengi women, as extremely erotic and as an indication of sexual desire/submission towards the viewer. In their words: wearing clothing is paramount to offering yourself sexually to whoever sees you.
From what we have seen of Ferengi family life and morals, primarily from the DP9 episodes set on Ferenginar, their morals and family life are rather similar to America's in this regard. They do not value promiscuity and are monogamous. Ferengi families, don't seems to want to see their daughters/mothers/wives flirting or having sex others/strangers anymore than American humans would.