Blue is print revenues, and red is a slice of digital revenues on top. (Newspaper Association of America)

The collapse of newspaper advertising revenues has been lamented and puzzled over for so long that it has its own jingle. There's no shortage of study of what caused the problem, or debate over what to do about it.

What's been missing, of course, is theoretical econometric analysis. Into the void, then, charge Stanford's Susan Athey, the University of Toronto's Joshua Gans, and Bocconi University's Emilio Calvano, to bust some conventional wisdom about how ad prices respond to the explosion of digital content.

The key, they say, is understanding "consumer switching" -- which is their term for people getting news from multiple sources, rather than just one newspaper as they did in the good old days. That may lead to a richer reading experience, as my colleague Tim Lee explained, but it also means that a publication can't charge for monopoly access to its readers, so the value of their presence is degraded. Once you've got that down, some surprising conclusions emerge: For-profit outlets should love non-profits, for example, and the newspaper industry might want to fight efforts to track where their readers go online.

The problem is that the paper is written in the mellifluous language of formulas and equations. Let's break out some key points, rendered in English:

- On the web, bigger is much better, because advertisers don't want duplication: Space on the internet is infinite, but consumer attention is scarce, and now divided between many outlets. So companies that want to reach consumers run the risk of hitting the same person more than once if they advertise with multiple publications, or only hitting a slice of them if they advertise on just one. That allows publications with a wider reach to command higher prices for their ads, since they can reach more people with a lower risk of duplication.

- For-profit outlets should love non-profits: Some private publications have opposed government support of public media outlets. That makes no sense, since subsidized publications are less likely to sell advertisements, and lower ad capacity raises prices for those that do sell it. Same goes for blogs, which rarely take much advertising, if any.

- Go for viral hits, not longreads: A publication can do well with limited content as long as it's "magnet content," regularly attracting a large share of consumers, rather than the focused attention of a few consumers. Ergo, Facebook--which reaches lots of people every day, if only for a few seconds--sucked up 30 percent of all display ad impressions in 2011, while in-depth news outlets like CBS and Fox News got less than 2 percent each.

- On face, paywalls are dumb: No matter what model you use. Both subscriptions and micropayments for individual pieces of content just send traffic to other outlets, and also reduce switching for non-paywalled outlets, allowing them to charge higher prices. Now, that's less true for outlets with intensely loyal reader bases and essential news that they can't get anywhere else. Also, it might change as people get more used to the idea of paying for news, which newspapers hope the New York Times' pioneering paywall will do.

- Big Media is better off: When news outlets have common ownership, since they're able to track consumers across publications, they can coordinate ad sales to charge more for reaching eyeballs more efficiently. That could have antitrust implications down the line, the authors write.

- Newspapers may not actually want to track eyeballs: The digital advertising industry has viciously fought proposals to let consumers more easily avoid being tracked online, on the theory that not knowing who people are will make it more difficult to target relevant ads. But the authors argue that news outlets may not actually want advertisers to know, in hopes that the biggest ones -- like AT&T, which purchased 19.5 billion ad impressions in 2011 -- will just keep paying for as many as it takes to reach as many consumers as possible.

How bad is all of this for newspapers? Well, it certainly doesn't bode well for the provision of deep, expensive, quality content. But we're pretty sure that doesn't pay for itself anyway. And as for the mid-level, Gans is optimistic, because people sure still are reading on the Internet, and their eyeballs are still valuable.

"One of these days someone's going to figure out the advertising bit," he said in an interview. "The economic fundamentals to us seem to point to the content providers will be rewarded in the end."