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Sintel, an animated production was funded similarly: http://www.youtube.com/watch?v=eRsGyueVLvQ. It consisted of a DVD 'pre-sale' which allowed people to pre-purchase a DVD, before the movie was produced, hence raising funds. But I believe the Dutch government sponsored it too. Kickstarter.com, Flattr.com have notable alternatives to funding as well.

- "Given two choices: 'download and pay nothing' and 'download and pay something', people will generally opt for the first. It costs less."

Not true. My understanding of the Radiohead scheme was that the majority of people normally opted to pay something (http://www.bnet.com/blog/intercom/first-results-of-radioheads-pay-what-you-want-experiment-are-in/1214). I know economic theory suggests the first, but this is one area where there are shortcomings in the theory.

- There is a difference between how Wikipedia and Radiohead framed their products. To get to the Radiohead album, you were prompted for a donation. Wikipedia doesn't prompt you for a donation before you access their website. Sure, there are ads, but it's not the same as asking someone directly to make a donation to access an article. Also, there's a difference between the products; once you download a song, you own it; you can put it on your iPod, burn it on a CD, give it to a friend. Website access is a little less tangible; I don't think most people view it as a product in the same way they view a song.

- "But imagine that 7,499 other people have aready donated $10 to Public Enemy. My $10 donation brings the total up to $75,000, enough to generate a new Public Enemy album. I have no incentive to withdraw my donation, because if I do, the project won't be funded. My donation is a "pivotal contribution. Indeed, if any one of the 7,499 people pull out, the project won't be funded. Each one of those 7,499 donations are pivotal, so no one has an incentive to pull out."

This seems a little strong. It seems to rely on an assumption that Public Enemy only has 7,500 fans. Surely there is probably a significant group of fans that donate nothing and are free-riding; if one fan pulled out their donation, it's very likely that a free-riding fan would step up to the plate. So the incentive to keep your donation parked with Public Enemy isn't seem as strong as you make it out to be.

The music industry is constantly evolving. When was the last time a band had a member with an economics background (not including Mick Jagger - he was a LSE dropout)? Would these models evolve if they did? Supply/demand?

Adopting a new funding formula requires innovation. And there is much inertia to overcome. I cannot more concisely state the problem than what was profoundy stated here.

I particularly enjoy the criteria for a failing grade in the marking scheme in your solution. Students should realise just how desperate profs sometimes are to give partial marks.

"how desperate profs sometimes are to give partial marks"

Sorry for the OT ... That must be a new development at University. I never detected any inclination towards clemency on the part of the profs I had in the early/mid 90's. I once had a prof grade a lab report with the following comment: "Without a doubt this is the absolute worst work I've ever had the misfortune to grade: 0".

No chili peppers for him.

JVFM: Rick rolled!

David, yes, about 2/3 of people did give with the Radiohead scheme. It feels good to believe that you're participating in the development of a whole new funding paradigm. (Actually, if you work through the sample question attached, you'll see that it's set up so that if Radiohead tries to sell their tunes through itunes for $1 each, they sell nothing at all, so they would do as well or better relying on warm glow giving). Perhaps their experience is generalizable. But I don't think so.

Your point about that the set up of web sites matter is well taken.

I'm not assuming that Public Enemy has only 7,500 fans. I'm pointing out that there exists a Nash equilibrium with 7,500 fans donating $10 each. There are a whole lot of other Nash equilibria as well. The problem is, when there's tens of thousands of fans, how do you settle on one particular equilibrium?

*Once you're in the equilibrium* AND if it's a *one-shot game* there's no incentive to deviate. But that doesn't solve the problem of how to get there in the first place.

Stephen, I'm just happy to amuse. It was actually a pretty unclear question the way I had set it up initially - I edited it a bit before I posted it on-line. I think often my students would prefer a little bit less creativity at exam time!

If the market for digital media were utility maximizing, each producer would be paid the MC of production and all consumers would be able to use it as much as they desired since the MC of use is zero. The Radiohead model may achieve some definition of fairness but it doesn't achieve efficiency. The band may in fact get paid vastly more (or less) than they would have required as compensation to produce the album. Sellaband.com gets half way there. What's missing is the part where everyone gets to consume the content for free after it's released. This is a big loss of value. What we need is like Sellaband but without copyright.

Someone needs to design a better market.

I once received an assignment back where we had to grind through the RSA public key encryption algorithm to decypher a message. Essentially this involves large amounts of long division of big numbers. I correctly decoded the message, but received a grade of 5/20 and the helpful comment "There's a better way to do this".

Andrew F: Man, that is harsh. At least in my case I probably deserved it.

Seems like if I was one of the 7,500 people donating $10 and I thought that someone else would take my place if I withdrew my contribution (a likely scenario), then my incentive would be to withdraw my contribution and free-ride (assuming standard economic assumptions about me being a selfish jerk who only cares about money, of course). I don't see how that is an equilibrium situation.

In other words, I agree with David, above. I guess if, hypothetically, it was a one-shot game, then I wouldn't want to defect. But since it isn't a one-shot game, it seems misleading to act as if it was.

It seems as though an entirely different model is needed to deal with 0 marginal cost situations like this.

"But the long-run feasibility of the strategy is better evidenced by Wikipedia - 400 million users and $14.5 million in annual donations, revealing an average willingness to pay of about 4 cents per year."

Wikipedia is built on anonymous donations of highly skilled labor. Given a choice between "use Wikipedia and don't contribute to articles" and "use Wikipedia and contribute" the former costs a *lot* less but enough people choose the latter option to make the scheme viable. Same with Yahoo! Answers. This really is the worst example to use in making this point.

David, Declan: "I don't see how that is an equilibrium situation."

There's lots of different types of equilibria in game theory. A Nash equilibrium is one where each person is doing what is best for herself *taking the other person's behaviour as given*.

A Nash equilibrium is *potentially* a sustainable situation - if we could get there and somehow support it with social norms, no one individual has an incentive to defect in the middle of the night. The Radiohead example is not, even potentially, sustainable. People always have an incentive to defect.

Rajiv Sethi - well we can argue about the "highly skilled" part of it! But the point with Wikipedia is that even one of the most highly used sites on the web hasn't been very successful in getting people to donate money.

Donations of time don't pay the bills. And actually it's interesting to look at some of the stats on time donations:

http://stats.wikimedia.org/reportcard/RC_2010_09_detailed.html Sept, 2010: about 400,000,000 users worldwide, 82,500 active editors. The interesting thing is that the trend in user numbers is steeply upwards, whereas the trends in editors, editor numbers etc are much more stable.

So the overwhelming majority of people free ride on Wikipedia, too.

Wikipedia works for the same reason that blogging happens - there's a bunch of people out there who derive enormous pleasure from the act of writing (I do). But it is really seriously lacking in clearly written entries on just slightly more advanced topics - basically the incentives for free riding start getting really high it comes to high cost activities like drawing a clearly labelled diagram and posting it.

By the way, eventually I got so fed up of bad cut-and-pasted definitions from Wikipedia that I gave up and started editing definitions of terms that I use a lot in teaching myself, so at least I get cut-and-pasted definitions that please me!

The interesting question in terms of Wikipedia is - will those 82,500 active editors continue to be so enthusiastic about working for free as they see the millions accumulate in the wikipedia foundation?

K: "If the market for digital media were utility maximizing, each producer would be paid the MC of production and all consumers would be able to use it as much as they desired since the MC of use is zero."

For efficiency what is vital is that the marginal cost of downloading an extra song is zero. One way of achieving that is with a subscription-based model: pay a fixed monthly fee for unlimited (or lots and lots) of downloads. I think a cell phone company was recently experimenting with this - the cell phone contract came with unlimited downloads from a particular site (yes, I do have exam questions on that too if anyone is interested).

So marginal cost *per download* = zero is not the same as saying price charged to the consumer = 0.

Rajiv - on Wikipedia.

Thousands of people voluntarily post music recordings on Youtube. That says nothing at all about people's willingness to pay money for on-line music and, critically, the ability of musicians to support themselves through on-line sales.

I kind of day dreamed my way through auction theory in Micro II, but could sellaband.com design an auction that could solve the coordination problem?

Frances, there's a good discussion of this in Boldin/Levine's book Against Intellectual Monopoly, where they argue that British authors in the 19th century who had no copyright protection in the US nevertheless made more money in the US market than the British one.

Here's an extract:

"How did it work? Then, as now, there is a great deal of impatience in the demand for books, especially good books. English authors would sell American publishers the manuscripts of their new books before their publication in Britain. The American publisher who bought the manuscript had every incentive to saturate the market for that particular novel as soon as possible, to avoid cheap imitators to come in soon after. This led to mass publication at fairly low prices. The amount of revenues British authors received up front from American publishers often exceeded the amount they were able to collect over a number of years from royalties in the UK."

How could it work for music? Direct sale of songs/albums to an identified fan base bundled with autographs, concert tickets, etc. prior to broad redistribution. Not exactly the Radiohead model but still distribution at near-zero prices for copies that have negligible marginal cost of production. Similar to the sale by for-profit publishers of the 9/11 Commission Report which was not copyright protected and had massive distribution (combining sales and free downloads).

Here's my post on Boldrin/Levine, which contains a huge number of other fascinating examples:


Rajiv - I agree with you that live performance is the practical answer to the question of 'how do musicians earn a living?' But as you rightly point out, lots of people have already said this, which is why I didn't include a digression on the topic in my post. I just find it kind of cool how the Nash equilibrium for the public goods contribution game changes depending on how the game is constructed, and that there are positive contribution Nash equilibria.

Two observations on the 19th century parallel:
- high up-front fee/low marginal cost is a bit like the subscription model for music downloads discussed above.
- How much money do you think Dickens would have made if he could have credibly committed to the following stance: "I am not going to tell you what is happened to Little Nell until $1 million has been contributed to www.dickens.com"?

A (mostly) unrelated digression: These days conferences, not individual journal subscriptions, are the way that academic associations, like the Canadian Economics Association, make money. When I was Secretary Treasurer of the CEA people would call and say "I'm presenting a paper, why do I have to pay to come to the conference?" I would then patiently explain that we had a surfeit of people willing to stand up and talk, indeed the privilege of talking was what we were charging for. Now if they would promise to attend sessions, listen and ask questions...

One minor detail. Musicians never made money from record sales, the record companies did (and didn't pay the musicians).

JDUB has the right of it, I think. Targetting the fans quickly would win the artists the majority of the funds they could reasonably expect. Downloading has never been as costly to the music industry as they portray, because the low marginal cost i.e. zero, of downloading leads to activity that would not be occurring in a marketplace. In other words, of the thousands of songs a particular user has downloaded, the loss to the providers is the loss of compensation for the handful of songs the user would have purchased, if she had been forced to pay for music.

"Declan: "I don't see how that is an equilibrium situation."

"Frances: A Nash equilibrium is one where each person is doing what is best for herself *taking the other person's behaviour as given*."

Sure, but I didn't say anything about Nash, did I? The point is, it's only an 'equilibrium' with the completely unrealistic assumption that each person will make a decision based on the assumption that nobody else will react to their decision.

It's about as useful as arguing that me aiming a soccer penalty kick 3 inches to the left of the goalkeeper is a nash-equilibrium choice for me, because, assuming the goalie doesn't move, the ball will go in.

Declan -

- you know that the goalie will move - not moving is clearly the wrong decision for him (the equilibrium strategy on a professional penalty kick is not obvious, in fact, because basically a keeper doesn't always have enough time to react, he just has to more or less guess which way to go).
- Suppose Fred's giving $10 and George is giving nothing. Why would Fred think "if I don't give, George will." George might think "if I don't give, Fred will." Fred risks losing the album if he pulls out his contribution.

It's a fundamentally different problem than the conventional Radiohead or Wikipedia donating-after-the-good has been produced type situation.

Though it's still hard in the real world to solve - because how do you get to that equilibrium in the first place?

Clearly it's a different situation asking for money up-front vs. asking for money afterwards, primarily the shift in intended motivation from gratitude to greed, I'm just skeptical that the Public Enemy approach would solve the problem of free-riding or that individual contributors would really believe that their particular contribution was important, let alone critical to the success of the venture.

I suspect that, much like in the case of Radiohead, Public Enemy's album will be financed by people who believe they are paying more than they 'have to' but are doing so out a spirit of willingness to contribute to the band rather than out of a purely material self-interested calculation. The only sense that this would be an 'equilibrium' is in the sense that if everyone has made their decision to contribute or not voluntarily, there's no reason why you'd expect them to change their mind without the circumstances changing. But of course this sort of 'equilibrium' definition would include the Radiohead model as well.

P.S. The example of Fred and George with just 2 people is completely irrelevant to the case of Public Enemy with thousands of potential contributors. Try, 'suppose Public Enemy has 100,000 fans and Fred is giving $75,000 and the 99,999 other Public Enemy fans are all giving nothing and waiting to download for free the album that Fred is paying for. Does this seem like a situation in equilibrium?'

I'd worry folks have incentive to hold out to see whether they'd be the marginal contributor or not, in which case you can get coordination failure. Sure, you're pivotal if you're in and the thing goes ahead. But somebody else could have held the pivotal spot instead of you, right?

In that kind of case, dominant assurance contracts might have worked a bit better. Suppose all folks pledging money and who didn't pull their pledges got to download an exclusive track, regardless of whether the project wound up going ahead. Then folks have stronger incentive to sign up early on instead of dithering. It's still not perfect, but it's an improvement.

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