On Saturday, Stockholm hosts the final of the Eurovision song contest: a camp, televised event that draws nearly 200 million viewers.

Bands competing for votes and fame relish exposure; the city gets to promote itself for tourists and businesses. And a big selling point for the Swedish capital is its status as home to a string of successful digital firms, exemplified by a large music-streaming business, Spotify.

Tech and Stockholm have long thrived together. "Programming is the single most common occupation in Stockholm today," said Mikael Damberg, Sweden's minister of enterprise. An estimate, by the city itself, suggests the tech sector employs 18 percent of workers.

A digital boom is one reason the Swedish capital region has one of Europe's fastest-growing populations (2.3 million people, up by 10 percent since 2010). It also explains why the city's economy as a whole is rattling along about 5 percent annualized growth. .

Since 2003, Stockholm ranks as the fifth city, globally, in nurturing unicorns, private firms valued over $1 billion. It got one-fifth of all European investments in "fin tech" firms between 2010 and 2014, said a member of Stockholm's business-development council.

Games firms do well, too. Microsoft bought Mojang (creator of Minecraft) for $2.5 billion, two years ago. In February, Activision Blizzard, a California firm, snaffled up King Digital (maker of Candy Crush and other games) for $5.9 billion. Communication is another strength. Microsoft bought Skype for $8.5 billion, five years ago.

Then there is Spotify, which streams music, sells advertising and has persuaded 30 million users — at the latest count — to pay for tracks. Last year it was valued at $8.4 billion. In March it raised $1 billion, in consolidated debt, from a single round of financing.

Spotify is in "a hyper growth stage," said an employee. It has 1,000 staff at its operational headquarters in central Stockholm, though the firm is legally incorporated in Luxembourg. A team of 53 exists to recruit "super talent" globally; the firm expects to double the number of employees at its main offices by, or soon after, the turn of the decade. By then, it might count as Europe's first real example of a new tech giant. (SAP, an older software goliath in Germany, is worth some $83 billion.)

As the industry leader in music-streaming, Spotify will expand as long as most musicians continue to cooperate with it. Taylor Swift and certain other artists refuse to do so, but they are exceptions. More in doubt is whether Spotify will grow in Stockholm or shift elsewhere.

Last month its co-founders, Daniel Ek and Martin Lorentzon, wrote a public letter about Sweden's business climate. They raised three concerns. Employees who get stock options face whopping tax bills. Renting a home in central Stockholm has become eye-poppingly expensive. Both problems worry foreigners especially. Third, too few Swedish schoolchildren are learning to code: needlework and carpentry are compulsory, not programming. Unless politicians act, say Ek and Lorentzon, the firm could choose to grow somewhere else — Silicon Valley, perhaps.

That sounds a mite ungrateful. Stockholm has long promoted tech, and all but pampered those who exploit it.

A policy of welcoming foreigners also helps tech firms. Carl Bildt, an opposition politician, said "an open attitude to people coming from wherever to work" is hugely beneficial, as Sweden relies on imported talent. He wants the 100,000-odd refugees who arrived last year to be taught coding, so they can respond "to a huge demand for that sort of talent."

Spotify's complaints are not just self-interested, they are also carefully timed. Sweden is now debating a proposed legislative change to let employees in companies with fewer than 50 workers for a time enjoy lower taxes on stock options. Spotify and others are miffed that the reform would exclude bigger firms. Talk of growing elsewhere is obviously intended to spur a rethink. Damberg said the government will listen and consider a bolder reform, but said Sweden has fostered lots of big, non-tech firms before without dropping its egalitarian, high-tax approach.

Tackling pricey housing in Stockholm is harder. A banker with a young family, looking to buy, laments that prices have doubled in five years and properties sell in a frenzy of bidding.

As for schools, more teaching in tech is bound to come — the question is how fast. A pilot scheme of compulsory coding lessons is to start in some Stockholm schools. One goal is to get more young women to take it up: Spotify says its Saturday camps for preteen programmers often have more girls than boys; but by college age, male coders vastly outnumber female ones.

Even if it got all its wishes, Spotify might end up growing faster abroad in any case. What really matters, said Jessica Stark, who leads SUP46, a lobby for Swedish tech firms, is the broader signal to many other start-ups as they grow — who voice the same complaints as the music-streaming company. "Stockholm should definitely not aspire to be Silicon Valley, but that doesn't mean we can't compete with it," she said.

Copyright 2013 The Economist Newspaper Limited, London. All Rights Reserved. Reprinted with permission.