Shares in social media company Facebook Inc. could fall below the initial public offering price of $38, Barron's wrote in its May 21 edition.

Facebook saw its shares rise a scant 0.6 percent to $38.23 on Friday in the first day of trading.

The stock stayed above the $38 IPO price, supported in the market by the deal's underwriters. But Barron's said the "big question" this week will be whether they continue to do so.

Its shares still look overpriced compared with rivals such as Google Inc., and all the more so given Facebook's challenges in drawing revenue from mobile device users, the financial weekly wrote.

Facebook's shares also face the prospect of pressure from heavy sales of stock between now and the end of 2012 if early and inside investors get rid of shares ahead of a potential rise in capital gains taxes, according to Barron's.