On May 5th he revealed what he wants to do about it: he plans to add 200,000 more affordable housing units over the coming decade by preserving existing ones and encouraging the construction of more.

New York has certainly become less affordable. Between 2005 and 2012, the median inflation-adjusted rent in the city rose 11%, while the median renter’s income rose only 2%, according to the Furman Centre at New York University. It reckons that 54% of New York tenants spent more than 30% of their income on rent (the usual cutoff for “affordable”), up from 40% in 2000.

Plutocrats bear some of the blame. Like London, Miami and other desirable cities, New York has become a playground for billionaires. Developers can earn more selling luxury flats to oligarchs than basic ones to firefighters. But as a driver of the housing shortage, inequality is less important than demand and supply. On the demand side, New York has an enviable problem: people desperately want to live there. After decades of decline, its population resumed growing in the 1990s, reaching a new high of 8m in 2000, 8.2m in 2010 and 8.4m last year. Neither the attack on the Twin Towers, nor Hurricane Sandy nor, it seems, even the financial crisis have put people off. Talented and ambitious folk have more fun, and make more money, when living close to each other.

New York’s housing supply has long struggled to match demand, but especially since 2008, when the recession and the freezing of mortgage markets caused the number of permits issued for new residential units to fall (see chart). Fewer permits have been issued since 2010 than in 2008, even as the number of households has grown by roughly 85,000.

Activity has started to recover, but supply is still constrained by a lack of land and Byzantine rules about what can be built. New York seems like a tall city, but building height is heavily restricted. On average, developers may erect six square feet of floor space per square foot of land, says Richard Green, an economist at the University of Southern California; in Hong Kong, another dense coastal city, it’s closer to 20. Nearly 5% of units are designated for historic preservation, mostly in Manhattan.

Mr de Blasio sensibly wants to boost supply through increased density, but the mechanism he has chosen is problematic. “Mandatory inclusionary zoning” would raise permissible density in some areas, but developers would have to ensure that a minimum proportion of units meets the city’s definition of affordable. Forcing developers to build less profitable units acts as a tax, which could discourage, rather than encourage, supply. Jenny Schuetz, also at USC, says similar schemes in San Francisco and Boston’s suburbs have produced fewer affordable units than hoped, either because developers chose to build elsewhere or because they struck deals that weakened the requirements.

It would be more effective to hack back the regulations that discourage supply and raise costs. These include rent controls and the indiscriminate award of historic designations—which preserve the view for those who live in pretty, low-rise neighbourhoods like Greenwich Village, but put them out of bounds for everyone else.