Of course, what really did it was steam, iron, and steel. Until the 1800s, economic growth in Europe was about half a percent a century. Didn't matter whether you had a king or a Parliament. A few coastal cities had figured out how to do shipping efficiently and were doing OK, but that had been happening on and off since Roman times. Those were sometimes city-states run by merchants, and were the closest thing to capitalist empires before the Industrial Revolution. That didn't scale; there wasn't much to ship yet.
Then came steam engines. It took a century to get that right. The first Newcomen steam engine, in 1712, was a dud, mostly because there was nothing to make a good boiler and cylinder with yet, so an extremely inefficient low pressure system had to be used. It took a century to get to Watt's engine. That was good enough for locomotives, and finally things started to spin.
The big moment was the opening of the Liverpool and Manchester Railway, in 1830. This was the moment when railroads got out of beta. People could, for the first time, buy a ticket and go someplace. Within a few decades, railroads were everywhere in Europe and growing in the US and India.
The Next Big Thing was steel. Steel has a long history, but until 1880, it was an expensive niche product, like titanium today. Then came the Bessemer process. Suddenly there was something strong and cheap from which you could make stuff.
None of this came out of the merchant city-states. The Hanseantic League didn't develop railroads. The Mediterranean maritime states didn't develop heavy industry. The most capitalist organizations on Earth at the time did a lot for art and architecture, but didn't start the Industrial Revolution early.
For a different view, learn how the East got rich. Read "How Asia Works". This is a good study of how some of the east Asian countries went from the 18th century to the 21st in a few decades. The early stages required some degree of central planning, and specific incentives.
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