"In a market where there are no barriers to entry (i.e. perfectly competitive), the long-term price will tend to zero."

Yes, the price will gravitate towards zero because of competition or due to the fact that end users would not be willing to pay for the product anyway (who would use Facebook if it wouldn't be free?). But the marginal cost of such operation would not be zero and costs would have to be covered by other sources (VC funding, advertising, premium services...)