"Isn't it cheap?"
When you say yasuku nai desu ka you're really emphasising that the thing you're taking about isn't cheap. It's like you're commiserating/seeking empathy from others in a way. Think of it like when you take your whole family to the movies and after the ticket prices, and all the treats per person, drinks, an icecream each, popcorn, Tommy likes peanut MnMs but Jill doesn't, after all the tickets and communal and individual goodies are tallied up the final total floors you and you might turn to people behind you in the line or just say aloud to no one in particular - Phoarrrrr!!!! It's NOT cheap, IS IT??!?!!! To which you would no doubt get murmurs of heartfelt agreement and sympathy from other parents.
Hey asdf, I think you've misunderstood what I was trying to say - I was attempting to explain the feeling behind the Japanese and the difference between ~nai desu ka and desu ne in English. I wasn't trying to explain English. Rather I was trying to explain what the Japanese meant in English by appealing to English phrasing that is similar to the Japanese meaning.
Given your explanation, the connotation of the English phrase "isn't it cheap?" (and all "isn't it ?" phrases, at least in AmE) would mean that this isn't the best answer for this Japaniese phrase even if it literaly is correct. From my English speaking mind, "isn't it " is an empathetic form of "is it _" where one asks for agreement or approval ("isn't it great" where the speaker thinks that "it" is great and is asking if the listener agrees; kind of similar to "is it great or what") or one is clarifying what one thought ("isn't it supposed to be on" where the speaker thought that "it" was ment to be on but has come across some knowledge that brings doubt about that assumption and is asking for clarification. Although this does match up to what you describe, it is does not feel nearly as forceful and is almost neutral to me without a very strong tone behind it). There also seems to be a trend for positive things to be of the approval nature while negative things to be of the clarification nature ("isn't it expensive" feels like the speaker may not want to do something because of a preceived cost while "isn't it cheap" feels like the speaker is saying that the object is quite inexpesive for what it is. Although, cheap can also be negative in which case it feels more like the speaker may not want to do something because of a preceived low quality).
I had a really hard time with this type of sentence construction when i first learned it. As another person mentioned, it was confusing to me because my instinct would be to express this idea by saying やすいですね rather than やすくないですか. It helped me to think of the strict literal translation: 1) it's cheap, isn't it? 2) isn't it cheap? Both versions convey the same general idea, but they're slightly different ways of saying it.
I think the other poster's comment about the difference in tone makes sense, too, and it's kind of difficult to get used to because it doesn't readily carry over like that in English.
Quick story: first time i encountered it in class, we were talking about the day. Sensei asked 月曜日じゃないですか, is it not (or, isn't it) Monday? and I was just like... um... yes, it is Monday. Why are you saying it like that? It sounded as if she was confused, expecting it to be a different day, and i thought, why not say "it's Monday, isn't it?" Or "today is Monday, right?" She explained it as being a kind of gentler/more polite way to confirm the date rather than using 月曜日ですね.
No, it's not the same as saying is it expensive. It's actually more like a rhetorical question. The speaker has just found a great deal and is so impressed/surprised/incredulous of the loss cost of the item (surpassing all other deals with similar items at other stores) that it's led them to exclaim - Isn't it cheap??!?? The speaker knows the item is cheap, they're not really asking for confirmation, it's more like a rhetorical exclamation of surprise/thinking aloud.
I could be wrong but during my time in Japan, it seemed like Japanese might be more likely to use question tags to communicate this, since it could otherwise be confused with an exclamatory statement (Wow isn't it cheap!).
I know the above negative question is functionally and grammatically different than a negative question tag but they both get at the same answer.
BTW How do you do positive question tags to negative statements? Google translates seems to show them not existing and gives me a funny translation with arimasen ka and oddly makes yasu into a noun:
It isn't cheap, is it? 安くはありませんか？ Yasuku wa arimasen ka?
Is this right, or do Japanese say it another way? I always said positive question tags to negative statements (eg Yasui desu ne?) when I was there.
Yes, that is wrong, assuming you mean English speakers say "isn't this cheap" when they mean to say it's cheap. In Japanese it's an actual question ("is it not cheap?"), rather than a statement conveying the opposite (that'd be やすいですね), though it may express the speaker's assumption that it is cheap (e.g. in response to someone claiming it's expensive).