The dizzying stock decline of Facebook, a wealthy company with nearly a seventh of the world’s population as users, has revived a key debate of the Internet age: Can anyone get rich while giving their product away?

Investors have cut Facebook’s value nearly in half since the May public offering. One of its first outside investors, Peter Thiel, sold 20 million shares last week, deepening questions about how such a highflying technology icon could falter so quickly.

Part of the answer, say analysts and academics, lies in Wall Street’s skepticism of a founding principle of Silicon Valley’s business culture — that the best way to build a company is to ignore profits in favor of building a huge audience.

Few companies have a larger or more loyal audience than Facebook, with more than 900 million users and reams of the personal information that marketers covet. Many analysts expect that Facebook will continue to find ways to make money from that vast global reach; it already brings in $3.7 billion a year.

Yet Wall Street’s evident frustration with the stock price reflects growing concerns about the long-term prospects for companies that are popular but do not charge users for services.

Another social-media company, meanwhile, the business-
oriented LinkedIn, has seen its stock climb 65 percent this year as it relies on a mix of advertising dollars and fees for premium services.

“Free serves purposes, but you have to go beyond free to make some money,” said professor Rita McGrath, who teaches corporate strategy at Columbia Business School.

Facebook’s troubles bear some resemblance to those experienced by traditional media companies that depend mainly on advertising for profits. They once built empires by helping department stores, automakers and beer companies reach customers but have struggled to make similar profits while moving their businesses online, where ad rates are lower and content is often free.

The most striking success story for free content is Google, which brought in $38 billion in revenue last year, mostly from advertising. Because consumers use search engines when they are looking to buy products, Google provides an ideal opportunity for advertisers, much as the Yellow Pages have for generations.

Yet for most other online businesses, display ads are an intrusion on the user experience. People wanting to connect with old friends, or get the latest news on the presidential race, may tolerate commercial messages, but they are not seeking them.

Such a disconnect did not keep radio and television companies from making billions of dollars serving commercials to captive audiences over many decades. But analysts say the online world is different — users are in charge. Off-point messages get tuned out. Alternatives are just a click away.

“Facebook is in a pickle,” said Donna Hoffman, co-director of the Sloan Center for Internet Retailing at the University of California at Riverside. “The advertising broadcast model is dead wrong for this medium. . . . It can never work.”

Facebook declined to comment for this article. (Washington Post Co. chief executive Donald E. Graham is on the board of Facebook.)

A key to the profitability of traditional media companies was scarcity, as most markets had only a handful of broadcast stations and newspapers. The glut of new outlets in the digital era has stoked competition, driving down online ad rates. Retailers also seek customers directly through their own Web sites or through Internet retailers such as

“Whoever coined the phrase ‘information wants to be free’ was blowing smoke,” said John Morton, who has analyzed the newspaper business for more than 40 years. “Information is valuable, and it has to be paid for.”

Such arguments have prompted newspapers increasingly to charge those who regularly read their stories online. The New York Times, for example, reports more than 500,000 digital subscribers since it started charging readers last year for heavy use of its Web site or its apps on mobile devices.

Facebook, whose stock closed at $19.16 on Tuesday for a total market value of $46 billion, is far from a bad business, analysts say. Many say the decline of its stock price is the result of a sloppy initial public offering and excessive expectations from investors.

The company is trading at more than 40 times its reported earnings — an extraordinary ratio that signals that buyers are investing more in potential growth than current profits. Apple, which this week became the most highly valued company in U.S. history, trades at 15 times its earnings. General Motors trades at seven times its earnings.

“Facebook is probably a successful business, perhaps a hugely successful business, but may not be worth 40 times profits,” said Danny Sullivan, editor in chief of Marketing Land, which covers Internet marketing.

Investors are pushing the company to find new ways to draw profit from Facebook’s massive traffic, though this is complicated by privacy concerns from users and rising scrutiny from government regulators, who have set limits on how Facebook collects personal information. Consumers’ increasing use of mobile devices, which have less screen space than desktop computers, also makes it more difficult to make money by selling ads.

Even so, ­Facebook as a social-media company has opportunities that producers of other kinds of online content do not. Users frequently express their preferences for products by hitting a “like” button, improving opportunities for targeting ads. They also discuss products with each other — as they search for a dentist or a new car — which could be the trigger of a well-timed ad to a ready consumer.

Whit Andrews, a technology company analyst for Gartner, said some social-media company probably will succeed at getting its members to express their consumer desires in a way that entices advertisers to spend massive dollars — perhaps enough so that it can stay free for users while satisfying Wall Street’s demands for more profit.

“The key question is,” Andrews said, “how will Facebook react to this?”