ABOUT four years ago Michael Fox and two former law-school friends sniffed around for an unfilled market niche. Shoes of Prey was the result. Old-fashioned shoemakers in shops are disappearing in Australia. Internet shoesellers are replacing them. Mr Fox’s firm goes one step further: it allows customers to design and order their own bespoke shoes online.

It wastes no time wooing men. “We figured women are more passionate about shoes,” says Mr Fox. Investors from America offered funds, some on condition that Shoes of Prey shift its base from Sydney to Silicon Valley. But Mr Fox and his friends refused to move. That decision appears to have done the firm no harm. It has sold more than 20,000 pairs of shoes, as far afield as France, Japan and America, and predicts that its revenue this year will be three times what it was in 2012.

A new report by PricewaterhouseCoopers (PWC), a professional-services firm, suggests that Australia could start a lot more businesses like Shoes of Prey. It predicts that online and high-tech start-ups could account for 4% of GDP and 540,000 jobs by 2033, up from 0.1% of GDP and 9,500 jobs today. The report is a reminder that Australia’s long boom selling minerals to China will not last for ever. It offers signposts as to how the country might shift from mining coal to mining data. Australia has about 1,500 tech start-ups, mostly in Sydney and Melbourne. About three-quarters are involved in media or telecoms, a small part of the economy. Yet vast untapped opportunities await in health care, an industry that will surge as the nation ages. And although there are only 23m Australians, communications technologies (such as Wi-Fi, which was partly invented in Australia) allow local firms to reach a global market. Australia’s regulatory environment for entrepreneurs is friendly, and the country is admirably open to skilled immigration. But PwC frets that “fear of failure” is more common in Australia than in America or Canada, and this could be holding it back. Some Australian entrepreneurs think the sky is bluer in California. Anthony Goldbloom founded Kaggle, a firm that matches data scientists with companies, in Melbourne in 2010. He moved it to Silicon Valley the next year. Mr Goldbloom felt “a vague sense of guilt” about staying in Australia when the odds were stacked against building a big tech business there. Other Australian start-ups want the best of both worlds. 99designs, a marketplace for designers that was also founded in Melbourne, opened a San Francisco office in 2010 to be closer to customers, marketing talent and venture capital. However, it keeps its developers in Melbourne, where they are less likely to be poached.

Shoes of Prey somehow manages to keep the Bay Area at bay. Mr Fox and his partners wanted to stay in Sydney to draw on familiar tech networks. China, where they make their shoes, and Japan, where some of their 35 employees work, lie in similar time zones to Sydney. Of the nine investors who put in $3m between them last year, the two from Silicon Valley imposed no pressure to relocate there. It perhaps helped that one of them, Bill Tai, a Valley-based tech investor, can keep an eye on things during his regular visits Down Under as a kite-surfer.