Background: I worked in a social networking startup Jaiku (acquired by Google) in the early days of social media boom (2006-2007) and have thought about these things since.
Trying to monetize social network service through subscriptions or other type of payments from users have been tried several times since the dawn of digital social networks, and I think there is quite much evidence that it doesn't work for generic social networks such as Facebook and Twitter.
I think pg himself once said that "Information wants to be free". There is a certain truth to it that also applies to social networks.
Social networks that have been able to monetize by subscription model mainly deal with some kind of exclusivity. For example, three types of social networks that people are willing to pay for:
1) networks in which people share information that can be used to gain financial benefit. An example: ValueInvestorsClub.
2) exclusive networks that offer an access to hard-to-reach people. There are digital versions of these, but good examples from physical world are invite-only social clubs popular in London, New York, and other cosmopolitan cities.
3) Social networks targeted as internal communication tools to companies and other organizations. These usually monetize explicitly by offering a better controls who you can invite, remove and how you can restrict access in finer granularity. Examples: Yammer, Slack.
Fourth kind of successful monetization strategy involving payments from users is mostly seen in games and other types of virtual worlds. People buy digital outfits, avatars or other digital goods that help them to express themselves or stand out from other users. I haven't seen this model working very well in social networks in which users use their real identities: dating sites are an exception, but they usually are not considered social networks, even if there are elements of social networking in Tinder, OkCupid, Match.com etc.
If I were you, I would study history of failed and successful social networks and community tools both deeply (try to understand the details of mechanisms that the services were using) and broadly (don't restrict your study just to what we currently consider social networking platforms like FB).
Understand what has been tried, what works, what didn't work. It will be very enlightening.