Is there a Market for a 'Premium Facebook Membership'?

With Facebook's IPO a week past and looking pretty lukewarm, it is a good time to look at their business model and explore whether or not there is a better alternative. Facebook essentially earns income through advertising and data mining. This model has worked in the past, with Google being the biggest success story, but even Google has spent the last three or four years expanding its business to include things as diverse as mobile phones, an operating system and virtual reality.
In the case of Facebook their greatest asset is not just the biggest social network in the world but one of the most engaged group of users ever conceived. Facebook's 2011 revenue was $4.27 billion which lead to a profit of approximately $1 billion. As of May 2012, according to Wikipedia, Facebook has about 900 million users; half of whom log in using mobile phones. Another way to break that down is to say that Facebook is earning a little more than $4 a year in revenue and $1 in profit per user.
With this in mind, is there a way for Facebook to generate more income and users to have a better experience on a subscription basis? That is to say, is there an annual fee high enough for Facebook to make more profit off a user through a subscription than through data mining and advertising while still being low enough that users would rather pay the fee to protect their data and remove advertising?
From Facebook's end how much would they need to generate for it to be a worthwhile venture? There are a few things to consider. Since data mining is a relatively new industry and presumably the geographical data gained from mobile connectivity will be more valuable than PC data and will lead to better advertising (for example a well-placed coupon for a restaurant 100m before you walk past it) Facebook would be reticent to accept a one time payout in the form of charging money for an app download. This may change as they produce more apps that work synergistically with Facebook but are outside of the core competency, like the messenger service, photo apps, etc. but for Facebook itself that does not seem likely. Likewise Facebook wouldn't want to risk alienating any user as Google+, among others, is just waiting for a major mistake on Facebook's part to jump in and be everyone's main networking tool.
So from Facebook side it would need to be a voluntary system - a two tiered website which at a fundamental level are not so different that those who are not paying for the premium service feel disenfranchised. There were reports of a Facebook test in New Zealand that allowed people to pay money to force their status through to all friends despite whether or not said friends had turned of status notifications from a particular user. Provided the users weren't spamming, or there was a limit on how many premium updates one is allowed per month, this is about the level of difference Facebook can get away with. Despite the marginal value of a single user being nearly zero (would you pay more to advertise on a site with 900,000,001 users vs. 900,000,000?), it is unlikely that Facebook would accept a rate of $4 gross which with, likely, lower marginal costs would lead to an equal or greater profit per user because the value of the company is based in this yet unknown but perceived future value of all this content being generated and the information that can be extracted from it. Since the majority of costs are probably marginal based on the user a fee of $1 per month would generate approximately $11 per premium user every year. That would mean if 10 percent of users signed up for premium service, Facebook would be earning as much from that group in subscription fees as they currently are generating site wide from all income streams.
From the user side, would this service be worthwhile at this price? That is difficult to say. The current advertisements do not bother me so if it merely turned off the tracking data and removed the advertisements I might not find it all that valuable. On the other hand, the newest form of advertising on twitter, where random tweets are found in your main feed, really bother me and I might be willing to pay some pittance to prevent that from happening on Facebook. Likewise there are plenty of users who take to Facebook to promote their side project, art work, political opinions, etc. who may find the idea of preferential treatment in the Facebook feed a valuable perk. Another perk that a lot of people might find alluring would be to have greater control and ownership of the content they upload and link to the site.
Facebook cannot try to force users to pay because users are their most valuable, albeit intangible, asset. That being said there is certainly room for this to be experimented with. Would I pay $12 a year for Facebook? Maybe.