New York is building like it has not in years. It is still undersupplied.

Construction spending in the city is on track for $80 billion this year, up 16 percent on the three-year average, with permits for more than 31,000 new homes against a five-year average of about 20,000. The Building Congress expects another 70,000 units over the next three years. Set against a rental vacancy rate of 1.4 percent, the lowest since 1968, that is about 23,000 homes a year for a city that has been short of them for decades. The cranes are welcome. They do not change the math.

I have felt it directly. Over the past few weeks I have been in multiple bidding wars, on the buy side and the sell side. Well-priced homes still draw several offers within days, even at current interest rates, because there is simply not enough to buy: Manhattan has 11 percent fewer listings than a year ago.

This week’s ten run from a $995,000 prewar one-bedroom on East 65th Street to a $19,995,000 new townhouse in Brooklyn Heights. Seven are in Manhattan and three in Brooklyn. If one pulls at you, reply and we’ll set up a private tour.