When do we use 値 (あたい) instead of 価値 or 値段?

Question

I would like to know

1) when do we use 値 (あたい) to say "value" instead of 価値 ?

2) when do we use 値 (あたい) instead of 値段 to say "price, cost"?

I don't see the difference between these words. Please feel free to give example sentences so I can see the difference.

Thank you so much in advance for your answers!

Answer 1

値 readings: 「ね」 vs. 「あたい」

「ね」:

For the vast majority of native speakers in almost all daily communications, the word 「値」 is read 「ね」 to refer to a price or value.

「値{ね}が上{あ}がる」 means "to rise in price"

「歌手{かしゅ}としての値{ね}をあげる」 means "to raise one's value as a singer"

「あたい」:

「値」 is read 「あたい」 to refer to a price or value only in literary, old-fashioned or fixed expressions.

「値{あたい}が高{たか}い」 means "a/the price is high".

「～～に値{あたい}をつける」 means "to put a pricetag on ~~"

「一文{いちもん}の値{あたい}もない」 is a fixed expression meaning "not worth a penny"

Thus, the two readings are not always interchangeable for natural use and you would sound very weird if you used the 「あたい」 reading in your daily conversations where inappropriate.

「値」 is read 「あたい」, however, by everyone everywhere when it refers to a "numeric value" in math, graphs, charts, etc. Read it 「ね」 for that purpose and you will again sound quite weird.

Answer 2

I think あたい as a standalone noun to mean value/price is not very common in modern Japanese. All the usage I can think of are more idiomatic and feel old, such as 千金に値する (highly valuable) 一見に値する (worth a watch), etc. I don't think value vs price are distinguished that strongly either; I mean, they are basically the same concept --- valuable things cost more, and expensive things generally has more value!

The other use of あたい is in mathematics and computer programming, where it refers to a specific number/value that a variable takes at any given time. I think this use came from a literal translation of "value" from English.