It's not been a great year for Facebook, with security breaches and privacy scandals aplenty, but it turns out many of us still put a high price on the cost of quitting the social network – a price of around $1,000 in fact.

In a study in which over a thousand participants were asked how much they would take in return for closing their Facebook accounts for a year, the average price came out at more than $1,000.

Prices were set through an auction system where volunteers were given real cash in return for closing their accounts for a set period, from a day to a year. Based on these results, it would seem some of us are still rather attached to our Facebook accounts.

"Auction participants faced real financial consequences, so had an incentive to seriously consider what compensation they would want to close their accounts for a set period of time and to bid truthfully," says one of the researchers, economist Sean B. Cash from Tufts University in Boston.

"Students placed a higher value on Facebook than community members. A number of participants refused to bid at all, suggesting that deactivating Facebook for a year was not a welcome possibility."

After a test auction to familiarise participants, 133 students and 138 members of the wider community participated in an experiment to see what it would take to close their account. A third auction with 931 participants was hosted online using Amazon's Mechanical Turk service.

The group that put the lowest price on a year of Facebook was the non-student group from the second auction, averaging out at $1,139. The student group in the same experiment hit the highest average of $2,076.

In some cases individuals were bidding for a day or a week away from Facebook, but those figures represent the equivalent annual cost.

Based on Facebook's value as a company at the time of writing (nearly $400 billion), and its userbase (over 2.2 billion), each user is worth about $180 – much less than the amount people want in compensation for a year away from the social network.

Facebook only opened up to the general public in 2006, and while it may seem like forever ago, it's still early days when it comes to working out how the spread of the web and social media have affected us individually and as communities.

What this study makes clear is that it can be hard for a lot of us to walk away, because Facebook has become so entwined with our lives.

Some evidence points to worrying links between too much social media use and a downturn in health and wellbeing – including problems with attention and focus.

So even if you love Facebook, it's probably a good idea not to spend too long on there: make time for meeting people in real life, and relaxing away from phones and computers, and you'll be well set for minimising the problems that can come with social media use.

Indeed, there are signs that some people at least have had enough – reports suggest nearly half of young Facebook users in the US have deleted the app off their phones, even if their accounts are still considered active.

The debate about just how useful and rewarding Facebook and other platforms are will carry on, but now we have a figure on how much they're worth to us – and it's bigger than you might have thought. We can probably all do with re-evaluating the value we put on social media.

"Social media, and the internet more broadly, have changed the way we live and the way we keep in touch with friends and family, but it's hard to find evidence that the internet has made us richer or more productive at work," says one of the team, economist Jay Corrigan from Kenyon College in Ohio.

"We know people must derive tremendous value from Facebook or they wouldn't spend millions of hours on the site every day. The challenge is how to put a dollar value on a service people don't pay for."

The research has been published in PLOS One.