LAST week The Economist gave warning in a leader that a new bubble seemed to be forming in private-market valuations of some kinds of internet companies. It also cautioned that this could ultimately spill over into public markets. The initial public offering (IPO) on May 19th of shares in America's LinkedIn, a social network for professionals, looks like a sign that this is already starting to happen.

Before the flotation, LinkedIn's advisers had set the price for the company's shares at $45 each. No sooner had trading begun on the New York Stock Exchange than LinkedIn's shares soared as investors rushed to buy them, ultimately closing the day at almost $94. That propelled the company's market capitalisation to a whopping $8.9 billion—some 578 times its net earnings in 2010.

That is an eye-wateringly high multiple and it is reminiscent of the ones that young start-ups going public were getting in the heyday of the last dotcom boom. Some commentators such as Paul Kedrosky have argued that the company's stratospheric valuation (which is the largest initial price tag for a tech firm since Google staged its IPO in 2004) reflects the fact that LinkedIn is the first big American social network to go public, giving investors their first chance to profit from the social-networking revolution. Others have claimed that the heady valuation the firm has been given may well turn out to be justified.

LinkedIn is undoubtedly a solid company. It is focused on a lucrative demographic—executives looking to manage their careers actively—and, unlike other social networks, it has developed a fairly balanced set of revenue streams. These include fees from users for premium services, advertising revenues and money from companies and recruiters that use its services to find talented people. The firm also has an impressive senior management team led by Jeff Weiner, its chief executive.

But there will be a limit to just how fast LinkedIn can scale up, given the nature of its audience. So far its revenue growth has been steady, not spectacular. The $353m that it has raised from the IPO should help the company to expand more swiftly, but it will still have to navigate tricky markets such as China if it is to succeed. And it will need to come up with many more creative ways to monetise its audience without abusing the trust they have in the service. Mr Weiner and his team have a long, hard road ahead to satisfy the investment community's great—no, make that worryingly inflated—expectations.