> In a market where supply is constantly being added to meet demand, you would expect costs to go down in cities where people are leaving.

Sufficient supply is not being added to meet demand -- that's why prices keep going up.

> For example, NYC's population has remained relatively static or even gone down, but the rent prices sharply go up, far more than inflation.

NYC's population grows by about 0.3% every year:

https://www.macrotrends.net/cities/23083/new-york-city/popul...

COVID was an outlier for the obvious reason, during which it dropped by <0.1%/year, and is already back up to the high water mark.

Meanwhile the city has added less than that amount of net housing with the obvious result.

The housing market is also in a very weird state right now, because the fed raised interest rates, which long-term lowers housing prices by making it harder to borrow for a mortgage. But because the lesson people took from 2008 was to get a fixed-rate mortgage, now most existing owners have below-market mortgage rates and can't move without taking out a new mortgage at the higher rate, so they stay put, which means there is no inventory on the market and anyone trying to buy has to be desperate enough to outbid anyone else for the scarce inventory. But that can't last forever because eventually people will either be forced to move for any of the usual reasons or will have paid off enough of their existing mortgage for this to be less relevant -- or interest rates will go back down. Which, counter-intuitively, could actually lower housing prices by increasing inventory, especially because by then there would be pent-up demand for sellers to be able to move.

There is also some uncertainty in the stock market -- it had pretty much been on a bull run since right after the crash in 2008 until COVID but post-COVID has been a rollercoaster -- so you have a lot of investors looking to diversify and buying up real estate. Which they might be stupid to do because housing prices are crazy -- look at this graph and realize that 2007 was a massive housing bubble:

https://fred.stlouisfed.org/graph/?g=kYEb

> Keep in mind the majority of the value is in the property too, not the amount made from rent.

They still get that whether they rent it out or not. It's like saying well, I could get a 9% return from this investment, but if I refuse to rent it out then I'd still get a 5% return, so let me do that and set the rest of this money on fire for no personal benefit.

> then withhold apartments in order to either force legislative changes or force rent to go up.

But this is the part that makes no sense. To be profitable, you not renting out a subset of your units would have to make the rents on the other units (i.e. rents city-wide) go up by more than the entire amount of the rent on the units you withheld. How are they going to do that? The largest real estate investor in NYC owns far less than 1% of the real estate.

For that to make sense would require some enormous disadvantage to actually renting out those units, like rent control or laws that make it hard to evict destructive or non-paying tenants. Because that would make renting the units a significant risk to your investment, since a buyer wouldn't pay full price for a building full of tenants paying below-market rent or trashing the building who can't be removed.

But then the cause of the rent-increasing behavior is the inept laws that increase the cost of providing rental units by so much that it's not even profitable to do it when they're already built, and the solution is to remove the laws creating the perverse incentives.

Self-serving politicians like to take offense when investors respond in predictable ways to toxic laws, but umbrage doesn't lower the rent.