That's what an article (sub required for full version) in this month's HBR asks. As usual for business school professors, the authors don't give as satisfying an answer as one might want (and take a long time to make some pretty obvious points), but there are some interesting nuggets in the piece.
It starts like this:
Customers who pay little or nothing and are subsidized by another set of customers are essential to a vast array of businesses, including shopping malls, real estate brokerages, information technology providers, auction houses, print and online media, and employment and dating services. According to one estimate, this business model accounts for a majority of the revenues of 60 of the world’s 100 largest companies.
With the explosion in the number of free services offered on the internet, the prevalence of so-called two-sided markets is likely to grow. The rationale for this approach, of course, is that by charging one set of customers little or nothing, the business will attract the critical mass of them required to draw in large numbers of another set of customers, and the income generated by the latter will handsomely exceed the cost of acquiring and serving the former. The high-stakes challenge is figuring out the true value of each “free” customer. Although executives know that free customers matter, they tend to underestimate their significance for two reasons: First, managers naturally focus more on customers who generate the bulk of revenues, and second, they lack a rigorous method for calculating the lifetime value of free customers.
The authors base most of their analysis on one case study, a research project that they did for an undisclosed online auctions company that they call "auctions.com". Sellers paid, but buyers could use the service for free. The question was what these free buyers were worth.
The answer is this: more at the company's start than after it was a few years old. The early adopters, enticed by the free service, were more important in bringing in other buyers and sellers than later adopters. This is basic network effects, but they at least quantify it with this chart:
You can see an earlier paper from these authors that gives the models behind this here.