Some Economics of Pay What You Want Pricing

A number of musicians and game developers have experimented with pay-what-you-want pricing (e.g. see the important field experiment by Gneezy et al. and less formal reports from Radiohead, Norwegian composer Gisle Martens Meyer and the video-game makers 2D Boy and Joost van Dongen.)

Imagine that under the pay-what-you-want model consumers choose to split their consumer-surplus with the seller. Here is a neat little proof for the linear demand case that under this heuristic profits are as large as under monopoly pricing!  I have also assumed MC of zero which makes sense for digital goods and is also quite important to the result as pay-what-you-want can result in negative profits should consumers choose to pay less than marginal cost.

Split the consumer surplus is optimistic for the seller although splitting the gains does happen quite often in the dictator game so it is not without interest. Probably more importantly, pay-what-you-want pricing is going to be advantageous when the seller also sells a complementary good, such as concerts, which benefit from consumption spillovers from the pay-what-you-want good.


Static analysis. What will happen if you repeat the game when someone knows that others pay (offer) much less than him/her ? Of course in such cases the seller can decide to give up or to ask for a fixed price. In other terms the perspective of a seller's give up is enough to convince the potential buyers to pay as much as they can ?

You could do as most orgs do and list major patrons publicly to increase their status.

I don't think this kind of game theoretical setup is proper in this settings. What we know from "Ultimatum game like" behavioral analysis is that people are not always economic agents and they do not always maximize. Or, at least, you should factor a lot of different things in the maximization problem. Only in this kind of heuristic setup a post like Alex's is meaningful, why people should otherwise chose to pay one half? When you happen to give money to a guy playing a wonderful clarinetto at the corner of the street, it's not cause you are thinking about "how little can I give him so that he keeps playing?", but "how much money does he deserve?"

It's generally accepted in behavioral studies that contest is the main issue. If they ask you money, you respond as the "economic you". If they ask you an offer, you switch to the "not maximizing you". A good example of this is that a couple of maximization exercise, or even unrelated math exercise, done before the experiment can switch the Ultimatum game equilibrium back to his "logic" 99%-1% splitting.

It would be like using a game theoretical setup to explain how much money people gives as an offer during mess. I wouldn't think that "how little money can I give to the church such that messes keep going?" plays an important role in this reasoning. People pay more then average to show higher then average willingness to pay. Either cause you are a bigger then average fan of the product, or because you have an higher then average income. What I think is really needed is some kind of better signaling about how much you have paid to support, the kind of thing many Kickstarter projects do offering limited edition merchandising, or in-game token for multiplayer games.

So the big unknown here is how much individuals will pay. Game theory would suggest they'd pay $0.01. But I hear you that the actual payments reflect some sense of equity and fairness.

I'm not sure that assuming a 50-50 split of the surplus is a reasonable assumption (and BTW, your diagram shows social surplus, not consumer surplus -- alternatively, it only shows consumer surplus when the price is set to 0).

Will the really high reservation price consumers really pay 50% of their reservation price?

Isn't it more realistic to say that consumers would pay max {50-50 split of the surplus, the sticker price that had been set previously}?

I think it follows trivially that profits cannot be higher.

Your point about spillovers/externality stands. But it is also something that could, and presumably would, be addressed by the supplier in setting his sticker price lower than indicated by the static/no externality MR=MC condition (since he internalizes the externality/spillover on concert sales or whatever it is -- you could model it simply by raising MR by the value of the spillover -- that will raise quantity and lower price).

You should also address the problem about piracy however. This is twofold.
First, if you set a price, and that's around my reservation price, I would have a very low surplus buying. That has to be confronted with the alternative option, download it for free, with his risks and (possibly) lower quality. On the opposite, a "pay what you want" offer is always better then piracy.
Second, if you propose me "Will you pay X$ for this?", I'll answer as a maximization user, thinking about reserve prices. And the rational thing to do, even if I have a very high reserve price, is almost always to download it for free. Content producing firms, with respect to piracy, are always better off dealing with the non-maximizing part of our brain, the one thinking about deserved income and decency instead of "how can I obtain the maximum for the least money?".

Why not auction?

Are there any auctions of MC=zero commodities; none come to mind easily.

Telecoms spectrum?

Can't auction goods that can be infinitely reproduced at 0 cost.

Interesting post. Are there any academic papers on this subject? Seems like a place where interesting work could be done. I too am interested in dynamic effects -- such as reputation elements and quality (dynamic informational) issues.

Personally there's no way I'm splitting my consumer surplus evenly. My surplus from a book or song is usually many times the standard cover price, and I'm not about to give the author $100 just because it's worth $200 to me.

Maybe people with lower surpluses are relatively more generous.

If my claimed surplus is unusually high (and it probably is) then I guess that violates your linear demand assumption anyway. So the proof, while correct, looks unrealistic in at least two ways.

Indeed. There's a ton of quite good "donate-if-you-want-to" software, phone apps, firefox plugins etc.

What's the typical amount donated? On a few sites that list the donations the earnings are very low as compared to what I'd expect the consumer surplus to be.

Some sites even have to beg people to turn their ad-blockers off. There are lots of people who resist paying anything.

There seems to be a whole lot of stuff hidden inside "imagine that consumers choose to split their consumer-surplus." Might as well imagine it rains gold.

A classic case of elegance wins over messy reality. The triangle area equivalence trick was cute, though.

Is it actually worth $200 to you? If you saw your favorite author's next book on Amazon at $180 (or $15/mo x 12mo), would you buy it?

(I've bought books just to support an author whose previous work I liked, even if I didnt expect to like that particular book. There are a few authors for whom I've bought multiple copies).

How much is, say, Wikipedia worth to you? If they went pay-what-you-want how much would you?

Wikipedia asks for donations from users, so they have already gone to pay-what-you-want.

"Split the consumer surplus" would be a more compelling theory if consumers knew what their surplus was ex ante. Indeed we rarely can quantify it ex post.
Humble bundles, limited time offered collections of games from indie game developers, come around pretty frequently, use a pay-what-you-want model, but also post their aggregated stats in real time, and often will use an incentive to give "above the average".
You definitely have your $0.01 donations, as well as purchases(donations) in the thousands. We linux folk point to the humble bundle all the time to show developers that there is a market to create games natively for linux OSes.
Oh, and World of Goo is a wonderful game!

This assumes linear relationships amongst the variables of the kind Total Revenue = PQ*Q = PQ^2 hence derivative of TR = 2PQ. see: Also it assumes various things about elasticity of demand and as noted herein about marginal costs being close to zero, see generally:

But if revenue vs quantity is not a straight line you cannot do these simple geometric proofs. Still, a nice academic proof of possible no real world significance.

This might change the analysis a bit (and it certainly makes it less risky for the producer) but I think I remember that to get Radiohead's album, you had to pay at least $2 for handling, or whatever.

That more than covered their marginal cost of distribution.

Pay What Its Worth has different results in different contexts.

In a social context, if you are in a group, PWIW causes other members of the group to pay, even if they would not if they were alone.

For experience goods, PWIW is sample pricing--you experience first before you pay. For music, since the MC of music distribution is 0, any contribution is a contribution to fixed. In addition, you get word of mouth and audience effects even if someone doesn't pay.

For goods that signal our identity, PWIW in small amounts indicates that you are committed and will be willing to pay more if you are asked in the future. If you just give a charity a dollar, you will actually be more willing to give it much more later because you gave earlier. PWIW works for public radio stations because if a student contributes a buck, they are more likely to contribute more later It becomes a habit.

PWIW has a charitable aspect as well. If there are some who take (such as those who get a free lunch at the PWIW diner) others view their payment as a payment for themselves and others and actually contribute more to the diner than if the diner hadn't been known to feed those who could not afford it. There may be self interest involved as well--you have a concern that the diner may go out of business.

The scariest PWIW scheme is called Borrow What Its Worth (If You Cannont Pay For It). It was very popular in the housing industry.

wow seems to me that they would save a lot of money on one hand and that the other party could get ripped off if they didnt make many sales.

Baen Publishing has the Baen Free Library. Authors who wish can post a DRM-free book, available for download in several formats. I gather the general experience of the authors is that by putting up the sample books, they get more sales for their works--including more sales for the book which is available for free.

Great topic. As an armchair-economist, am I thinking about this correctly?

I'm a long-time Grateful Dead fan, and I think I've seen spill-over effects dominate. The Dead allowed taping at their shows (admission to the venue bought you full access to the sound waves within the venue). A broad community/network evolved around trading (not selling) recordings of shows, and the band built a loyal, massive, multi-generational fan base. Their tours were huge, and the venues were full, and now there is a market for higher-quality soundboard recordings (which are rightly controlled by the band).
Their taping policy might have adversely impacted record sales. But then, they were never really a big studio band anyway.


One problem with the "make money on touring" model is that it's completely dominated by older bands whose fans are now middle-aged with huge amounts of disposable income. Those older bands have kind of double-dipped, making money off record sales in their youth and touring in middle age.

and this is a problem because?

There is another source for study. Waiters' and bartenders' income is almost entirely pay-what-you-want. While the "next time" is perhaps more obvious than with an author, and the "personalized" service is more realisticly expected than with a song writer, it is nevertheless true that people who are tipping at the end of an experience and who never expect to return to the establishment could be expected to leave no tip at all, in practice if it happens it happens very seldom.

Donations to political campaigns are similar in that donors generally don't expect to receive direct compensation. They probably donate in a hope that the world will become more what they want in a general way.

Ok, stupid post coming from an economic illiterate. What economic rationale is there for a consumer wanting to split the consumer surplus if they can just take all of it? I don't understand how an economic model can account for consumer activity under pay what you want pricing, if they can get the item for free. I thought the people who do pay do it out of a sense of moral obligation, even though they know they'd be better off if they didn't pay anything. Is it a way to signal to suppliers that they shouldn't get rid of pay-what-you-want pricing?

Probably for some people giving money to people they like and think are worthy is a source of pleasure.

Splitting surplus is a way of saying "I want to give back what I think you are worth"

rationale is easy: A likes Radiohead, A says go ahead take some surplus, because A wants Radiohead to be successful

That may be the case, but then it wouldn't be in his self interest to do so, as he would be better off if he just took all the surplus for himself. Splitting consumer surplus in that situation seems contrary to basic assumptions about economic behavior.

I think as you're interpreting the setting, you are correct; there is little rationale for the buyer to offer more since there's a presumption of an existing producer surplus captured or at least the market return to the producer.

I think someone else pointed out that since zero marginal costs were assumed we're really talking about total surplus in the trade. In this case it's a pricing model that differs from the standard one of p=MC for market clearing and efficiency. That it produces the same monopoly profit as standard monopoly pricing model is interesting.

It's also worth noting that the Consumer Surplus increases significantly over the monopoly model.

One might also wonder if this is the way a smart opportunistic monopolist deals with the problems indicated by the Coase Conjecture.

But why then not make all products free and have a single charity/donate bucket? It makes it much simpler as there's less overhead and transaction costs are lower too.

I don't know why this is being looked at as some sort of spectacular new way to solve old problems. The shareware concept is decades old (basically two prices, 0 and purchase price) and it didn't work for close to anyone who didn't time- or nag-bomb their software. The spyware/adware model seems more realistic and successful.

Panera is doing it too:

Many pay what you want bundles (such as the humble bundle) include charity donations.

Perhaps this causes people to be more willing to split the consumer surplus?

Pay What You Want scheme takes in considerations only money. Well, unfortunally, I dont print money, so dont have any control on it. But I do have time, plenty of time, and those seller could certainly benefit more if they accepted a time currency instead.

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