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I'm a native French speaker.

In recent years, there has been a new concept of price in French that is "prix libre". A literal translation of "prix libre" is "free price".

This concept means that a seller proposes that the customer has to decide what amount of money he is willing to give for a given good or service. It especially applies to some cultural events. It implies that you may purchase something with a "prix libre" for free (0$/€/...), but the seller encourages the customer to pay something. It is not really seen as a "tip".

My goal is to put this expression on a website where we propose to download a document at "prix libre".

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    In terms of stocks you have a "bid price" which is the price investors are willing to pay. In second-hand goods, you will see the term "best offer" used to imply that if the buyer makes a reasonable offer, that becomes the selling price. "All offers accepted" would imply that no price would too low. There is no standard English phrase equivalent to the French. Jun 29 at 9:24
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    “Free with any donation”
    – Jim
    Jun 29 at 18:14
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    Another typical term might be "negotiated price". If I walk into a store and see a widget on sale for $25 and I say "hey, I'll give you $20 for that shiny widget over there", we've negotiated and come up with an agreed upon price. Other than that; the "Pay what you can" suggestion is probably best. It's been tried commercially (npr.org/2019/01/24/688372823/…). It seems that that attempt failed.
    – Flydog57
    Jun 29 at 19:00
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    @Flydog57, negotiated price implies that there can be some negotiation involved, which in turn implies that the seller need not accept the first amount that customer offers (in your example, the seller might say 'no, $20 is not enough, but I'll give it to you for $22). The OP has in mind the system in which there is no negotiation: the seller will accept whatever the customer offers, including $0.
    – jsw29
    Jun 29 at 22:22
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    A cultural event in English would be: Donation. In other areas where you are actually buying a good: NYPO. Name your own price.
    – Lambie
    Jul 1 at 16:14
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The phrase "Pay what you can" is used.

Pay what you can (PWYC) is a non-profit or for-profit business model which does not depend on set prices for its goods, but instead asks customers to pay what they feel the product or service is worth to them.[...]

"Pay what you want" is sometimes used synonymously, but "pay what you can" is often more oriented to charity or socially oriented uses, based more on ability to pay, while "pay what you want" is often more broadly oriented to perceived value in combination with willingness and ability to pay.

An example of this is at The Arcola Theatre's website

Arcola reserves a limited number of ‘Pay What You Can’ tickets for performances on Tuesday evenings. The average ticket spend is £5, but there are no restrictions either way; you simply pay what you can.

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    Regardless of what the link to Wikipedia says, what PWYC most strongly conveys, I would say, is that the price can greatly depend on the buyer's financial condition, rather than "what it is worth to" the buyer, which is a bit of a confusing standard. PWYW is relatively neutral on criteria, allowing each customer to wrestle with his conscience as he sees fit.
    – cruthers
    Jun 29 at 22:51
  • @cruthers Indeed, I've already seen PWYC offers and said that this would be waaaay too expensive Jun 30 at 0:00
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    This answer is correct in terms of French non-profits. The OP should clarify the question. Prix libre en France pour les associations sous la loi de 1901.
    – Lambie
    Jul 1 at 17:02
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    @smci PWYC is not the same as sliding scale. The payment structure for sliding scale is set (usually quite strictly, and sometimes requiring regulatory approval) based on a combination of some or all of a customer's income, family size, housing payment, age, or pre-existing medical or other debt payments. Jul 2 at 14:36
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    @EllieKesselman There are sectors where it is based on the honor system. I know therapists who charge on a sliding scale of their own free will.
    – Lambie
    Jul 2 at 14:54
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Common in English is "Name your price", or "Name your own price".

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    Be careful with these (particularly the former), as that's also used for the case of a seller (usually having a monopoly) who knows they can charge what they want and the customer will still pay. Context will normally make things clear, but I thought I should point this out. Jun 30 at 9:25
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    A good answer, but slightly more ambiguous than the top-voted one. Certain travel websites used to have a "name your price" feature, but it didn't mean you actually got to set the price of your ticket. You'd submit a price you were willing to pay, and could buy the ticket only if that value exceeded the un-advertised reserve price. In some "name your price" scenarios, the seller can still reject the offer, meaning the buyer cannot unilaterally decide how much to pay. Jun 30 at 14:18
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    Yeah, the most idiomatic use of "Name your price" is typically being said by some one who wants something (the customer) and is willing to pay any price to some one who is the only source of said thing. And more typically outside the context of normal commerce often in a blackmail scenario: Blackmailer: "It sure would be a shame if this information were made public", Person being blackmailed: "Name your price". Jul 1 at 16:14
  • @TobySpeight is correct, in a commercial context (which OP is asking about). A seller who can name their price, i.e. charge what they want, has pricing power, otherwise known as a monopoly. Jul 2 at 14:26
  • ....and @Shufflepants is correct too, in the most extreme scenario, of a desperate buyer/customer who will pay any price the seller asks. Jul 2 at 14:27
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One way of dealing with the matter, sometime used by museums and similar institutions, is to refer to the amount in question as a donation, rather than a price. This is often accompanied by creating subtle pressure that everybody give something, even though there is no legal obligation to do so.

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    This is posted as a wiki-answer, as it is, in essence the same as the comment previously posted by Jim, who was precluded from posting it as an answer, because the question was closed at the time.
    – jsw29
    Jun 30 at 16:50
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    Items sold like this are sometimes known as 'donationware' (see shareware, freeware etc) for that reason. It comes from software dev, but seems to have been borrowed by other areas such as the handcraft cottage industry and artisan fairs.
    – mcalex
    Jul 2 at 8:01
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Churches use "free will donation" or "free will offering" at meals or rummage sales. Even my church, which doesn't believe in free will, has a "Free Will Offering" box to put out at the end of the food line.

It means "pay what you will." No one should feel like they shouldn't come to the meal just because they can't pay. Wealthier people usually pay more in case there are people who can't pay much. Often, the event is a fund raiser, (say for the youth group) so people pay more than they think the meal/item is worth in order to support the cause.

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One expression that is common in the housing market is "offers".

The closest meaning to this usage in the free dictionary here is probably the noun meaning of "bid or tender". Owners of a house can put "Offers over" or "Offers around" in the selling summary. Houses here are often sold as a blind auction where all potential buyers submit their offers for a deadline and the best offer (which may or may not be the highest price) buys the house. Sometimes an offer is just accepted straight away rather than going to a blind auction. It’s also known that you can offer under the offers over (but your offer might be rejected immediately).

This might be a UK-specific phrase.

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    A slight distinction from the OP's intended usage - an offer is a price that a buyer proposes, with the hope that the seller will accept it. In the OP's scenario, the buyer unilaterally decides what to pay with no input from the seller. Jul 1 at 16:31
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The bid price

A bid price that is accepted is a price that is chosen by the customer

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    The OP is not looking for something that results in a price that is chosen by the customer.
    – fev
    Jul 1 at 21:07

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