Taylor Swift has pulled her entire library of songs from streaming service Spotify, a move that illustrates the long and continued struggle between artists, labels and tech companies to find an economic model for music on the Internet that everyone can like.

The pop and country music sensation has criticized piracy, file-sharing and streaming services for hampering album sales and for the meager payments they return to artists. Spotify says it has given 70 percent of $1 billion collected back to labels and publishers. But artists see very little of that. Every time a song is heard on Spotify, the artist gets back less than one penny — 7/10 of a cent — in return.

In a blog post Monday, Spotify announced that Swift had removed her music from the app–and said it hopes she returns.

“We hope she’ll change her mind and join us in building a new music economy that works for everyone,” the company wrote. “We believe fans should be able to listen to music wherever and whenever they want, and that artists have an absolute right to be paid for their work and protected from piracy.” Spotify said it pays nearly 70 percent of its revenue “back to the music community.”

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Few artists have Swift’s sway in music. Her latest hit album, “1989,” has sold 1.3 million copies in one week, the most of any album since 2002. On Monday, she announced a world tour to promote the new album. Spotify said 16 million of its 40 million users have listened to Swift’s music in the last month. Other artists have expressed similar frustration with Spotify. Radiohead’s Thom York has bashed the company and its business model. Jimmy Buffett has criticized the services’ meager payment to artists too.

But the 24-year-old singer has expressed her concern about the music industry and how piracy and new online models will discourage other young artists to follow her path.

In July, she wrote an op-ed in The Wall Street Journal explaining the complicated ecosystem of the music industry today.

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“Piracy, file sharing and streaming have shrunk the numbers of paid album sales drastically, and every artist has handled this blow differently,” Swift wrote. “Music is art, and art is important and rare. Important, rare things are valuable. Valuable things should be paid for. It’s my opinion that music should not be free, and my prediction is that individual artists and their labels will someday decide what an album’s price point is.”

Few artists can afford to reject a popular service such as Spotify. Beyonce, Radiohead, and others have experimented with new ways of distribution online and new business models.

For now, Swift has decided to shake off one of the world’s most popular streaming services.

“Taylor, we were both young when we first saw you, but now there’s more than 40 million of us who want you to stay, stay, stay. It’s a love story, baby, just say, Yes,” Spotify pleaded.

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