Using the same methodology, Apple said this month that its app business had generated 291,250 jobs for the American economy, as varied as developers and U.P.S. drivers. That number rose 39 percent in less than a year. During that time, the number of United States developers paying the $99 annual fee to register with Apple rose 10 percent to 275,000. Some of these registered developers have other full-time jobs and write apps in their spare time.

Apple has become increasingly assertive in promoting the economic benefits of apps as its own wealth and prominence have grown and its employment and other business practices have come under scrutiny. The company issued a statement for this article saying it was “incredibly proud of the opportunities the App Store gives developers of all sizes,” but declined to answer questions.

At the company’s annual meeting this spring, the chief executive, Timothy D. Cook, noted that just a few years ago “mobile app” wasn’t even in people’s vocabulary. “Now there’s this enormous, entirely new job segment that didn’t exist before,” he said. “Apple has become a jobs platform.”

Michael Mandel, the economist who conducted the TechNet study, said it was problematic to slice the jobs data as Apple had done. “The guy who writes an Apple app one day will write an Android app the next day,” he said. “You can’t add up all the numbers from every study to get the total number of jobs.”

For many of the developers not working at traditional companies, moreover, “job” is a misnomer. Streaming Color Studios, a game developer, did a survey of game makers late last year. The 252 respondents, while not a scientifically valid sample and restricted to one segment of the app market, indicated what many people had suspected: the app world is an ecology weighted heavily toward a few winners.

A quarter of the respondents said they had made less than $200 in lifetime revenue from Apple. A quarter had made more than $30,000, and 4 percent had made over $1 million.

A few apps have made it extremely big, including Instagram, the photo-sharing app that was bought by Facebook in April for $1 billion. When app developers dream, they dream of triumphs like that.