The 21st century will be the urban century. It has been several millennia in the making, but we recently crossed an important threshold: For the first time, more than half of the human population lives in cities. And the proportion will only keep increasing.

This will have countless implications for innovation, culture, politics, society, and life in general. But right now, it's mostly an emergency: The people flocking to cities aren't just going to Paris and Houston — they are flooding developing world cities that cannot house them, and often end up in shantytowns.

The world needs more cities. It needs a lot of them. And it needs cities that are equipped with infrastructure suited for the 21st century and beyond.

In The New York Times, the academics Alex Tabarrok and Shruti Rajagopalan point to an innovative solution: cities that are privately owned and privately run.

Depending on where you are on the political spectrum, this sounds like either a utopia or a dystopia. But Tabarrok and Rajagopalan are pragmatic. According to their research, cities need a "Goldilocks" level of central planning. Cities with too much central planning are unlivable (think Brasilia); so are cities with no central planning (think Calcutta or Lagos).

Private ownership and management of cities might be a more effective way of reaching this happy medium, since they offer the possibility of central planning (unlike anarchic cities with ineffective governments), as well as the competition and the profit motive that might protect cities from grandiose, quasi-utopian planning schemes.

They point out that private cities in some form or another already exist, and have been working just fine for many years. Company towns were a feature of the Industrial Age, and they often left behind fond memories. Today the city of Gurgaon, in India, houses two million people and is known as "the Singapore of India." There are still some company towns in the U.S., and they are typically ranked among the best places to live.

There are two more very interesting examples of private cities that these authors don't mention.

The first — and it is too bad that it is almost exclusively mentioned as a punchline — is seasteading, or the idea of building self-sustaining communities at sea. The main problem is that it is very challenging from an engineering perspective, and would doubtless be very expensive. The cost for building a real city at sea has been estimated at around $50 billion — a number that sounds astonishing until you remember that the total capital held under management by the private equity industry globally is $3 trillion, or that the world's billionaires are worth $7 trillion, according to Forbes. In this era of zero interest rates and capital gluts, the fact that there is no money for truly ambitious projects points to a deep cultural malady.

The second is charter cities, the brilliant idea by the development economist Paul Romer to create new "Hong Kongs" in the world's poorest areas. Just as British governance in Hong Kong enabled millions of Chinese to escape Communist poverty — and eventually helped lead the Chinese Communist regime to reform, lifting hundreds of millions more out of poverty — this could be repeated across the world's poorest areas. The charter cities project doesn't envision private cities, but rather government-to-government partnerships. But there is no intrinsic reason that this should be so. If we're talking about, say, Burkina Faso granting New Zealand the right to administer 1,000 square kilometers of its territory for 50 years, why couldn't it grant that right to Goldman Sachs instead? (If there ever was a job for Mitt Romney...)

As I noted in a previous column, the world needs more city-states. The city-state is a perfectly sized political entity; city-states and competition between city-states is what enabled the flowering of the Renaissance. And some of these cities were more or less private: Venice was a plutocracy, and Genoa's city government was owned by its central bank, which in turn was owned by the country's wealthiest families. It worked.

Private cities aren't the answer to everything. There should be lots of different kinds of polities, and lots of different kinds of city-states — including private cities.