They'd make less money [1]. Demand for shelter is close to inelastic, but demand for shelter in Atlanta is not.
Consider the extreme: they mandate rents of $1mm a month. Assuming no government interference, they might land a couple tenants at that price. But the vast majority would balk, thereby leaving them with less profit.
You can realistically use something like this to maybe bump rents a bit, but you cannot use it to radically alter markets, because it is supply and demand that set market prices.
Price fixing doesn't eliminate supply and demand entirely or make demand elasticity vanish.
What it eliminates is real competition among sellers ("fixing" the supply curve).
It raises prices - it doesn't magically make any asking price feasible.
Not finding demand to suddenly ask for $2M for a two bedroom house in Kirkwood is not some proof "hey, supply and demand is working just fine".
You're correct in one technical sense and wrong in another. (Either way, a good discussion.)
In a competitive market, price and quantity are set by the marginal incremental cost (MIC) and average total cost (components of the supply curve) and the demand curve.
Monopolists, however, ignore the demand curve. Their quantity produced is entirely set by MIC and marginal incremental revenue (MIR) [1]. In a very real sense, the market is no longer about supply and demand--it's about the producer's costs and revenue. (Your technical win is in the MIR being related to the demand curve.)
[1] https://en.wikipedia.org/wiki/Monopoly_price#/media/File:Mon...
And I that’s also a possible answer your question, on why they are leaving money on the table. To avoid inviting political action.
The monopolist doesn't have to follow this rule: they set the price to whatever makes the most profits and leave the price there regardless of fluctuations in housing supply.
Which would be illegal.
That's basically what I wrote in my original comment. They're far from a real monopoly, but they can probably gouge people a few % points, which isn't great.
You can price-fix and collude with other big home-owning landlords to milk your buyers, but to a point. Beyond that people just wont rent and move away, downscale as much as they can to smaller appartment, find roomates, or try to move back to their parents.
