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I have heard about:

What's the price of the book.

What's the price for the book.

Today I have seen a sentence:

We aim to bring down prices on all our computers.

What are the uses of "on" with the word "price"?

Explain.

Thank you.

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    As an aside, your questions frequently include the one-word sentence, "Explain." You should be aware that this comes across as demanding and impolite: the command "explain" without a softening modifier like "please explain" is more typical for a situation like an angry parent confronting a naughty child. You should avoid this usage unless you want to convey impatience or anger. – Canadian Yankee Mar 30 at 19:32
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You can think of this as referring to a price label. That's not literally what it's doing, but it's a convenient way to think about it.

Each product has a (conceptual) price label saying how much it costs. That is referred to as the price, and because you can think of it as a label on the product, you can use on. It has no difference in meaning to of.

"You want the blue one? Let me check the price on that."

However, that's not all that's going on when you have the "bring down prices* example. There, you have different ways of phrasing it depending what preposition you use:

We aim to bring down prices on all our computers.
We aim to bring down the prices of all our computers.

Essentially, you can have bring as a transitive verb, prices as the subject, and down as an adverb, in which case prices needs a definite article and of is acting genitively, and you could say "all our computers' prices" rather than "prices of all our computers". You could use other prepositions that act to form genitives instead of of.

Alternatively, you can have bring down prices as an intransitive phrasal verb, with on all our computers acting as an adverbial. That adverbial can't use as many prepositions as the genitive would, and on is the only one you would use naturally.

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