I think this is wrong.
The main reason I think this is because there are a finite number of new buyers per period, and residential developers are not in the business of competing with themselves on price. No sane developer floods the market with new housing just because the regulations are changed to allow them to build 100, rather than 50, homes on their lot. In fact, they might just build at the same rate on that lot for twice as long before moving to the next location.
A key confusion in housing supply and zoning discussions is that density limits per lot are interpreted incorrectly as a constraint the rate of new housing supply per period. New homes per lot is not the variable of interest in city housing supply. New homes per year across all lots in a city is the critical variable.
Zoning constrains the location of different densities of housing, but not the total rate of supply across all lots in a city. 
In the past, I have tried to dispel some of the key problems with the standard static economic models that conflate the allowable density per lot with the rate of supply. This is what I said then about these models
The only problem is this. When you convert the model to English you realise it has little basis in reality. The only real pattern that is consistent with the model is that higher buildings are near the city centre. But I could come up with a million other models that are consistent with that pattern.
One of the main flaws in the AMM model is that there is no possibility for development of sites within the city into new buildings. Every site is already used at its optimal level. There are no vacant sites or sites with old buildings ready for knock-down and reuse. There is no development industry. There are no landowners.
Also because of the comparative-static nature of how the model is used, every time there is a marginal change in any of the parameters of the model — a new person moves to the city, the rental price of the second best land use increases, or the efficiency of construction methods change — the whole city is wiped clean of homes and buildings. The single social planner who controls everything in the city then dictates that the whole city will be rebuilt with a new optimal allocation of housing and commercial buildings under new conditions, and this whole new stock of buildings rebuilt in an instant to that new specification.
In that blogpost I introduced some new ideas about how to conceptualise regulatory constraints using this diagram.
I want to now offer a simple “bathtub” analogy that demonstrates why our thinking about housing supply and zoning is often misguided.
Imagine a city region is like a bathtub. The limit on total development, if every location was used to its highest-value use, is the depth of the tub. This is affected by geographic, regulatory, and economic constraints. The water level is the current total stock of housing across the city. Lastly, the dripping water from the tap is how fast new development is occurring across the total city to increase the total stock of housing.
The question is, what part of this bathtub situation would you address with policy changes to increase the depth of the water? The depth of the bathtub, or the rate of water flow from the tap?
Changing the depth of the tub is a bit like rezoning the whole city for higher density. It seems intuitively like a good idea, but if the city is nowhere near its bathtub capacity, what mechanism is there for this to affect the rate at which the tub gets filled?
The more effective approach is the look at the tap, and the rate at which new housing is developed. This can involve a few things, like making it more costly for landowners to delay converting land into higher-value residential uses. Or, it can mean redirecting credit flows into new, rather than existing housing, to encourage new supply. Regardless, when you start to look at the tap you see that the key variable that needs to be tweaked by policy are the dynamic incentives of landowners—delaying, or slowing, development needs to be made relatively more costly.
In Australia, for example, our housing tap drips at a rate that is around 2% of the total stock, and it requires something like 5-7% of the workforce to build at this rate (and more in some cities with high rates of housing construction).
To have a meaningful effect on the total stock housing, and therefore the price, requires an economically significant long-term construction boom. For example, increasing the rate of new supply by 50% for a decade—employing more than 7.5% of the total workforce instead of about 5%—will increase the total stock by just 9.8%. By any metric, this will have a price effect in the range of 5-15%. The point being, the large changes in the rate of supply have small effects on the total stock and these require a large share of economic resources shifted away from current uses and towards housing construction over a long period, particularly in boom cities.
Now, I am totally supportive of a sustained effort to build more housing to provide more options for households. But I am against pretending that rezoning means that developers voluntarily, and dramatically, increase the rate that they supply new housing to such a degree that they subsume a substantial portion of the workforce while at the same time reducing the price of the asset that earns them a living.
To change the rate of supply requires changing the dynamic incentives of landowners by making it relatively more costly to delay new housing development. This cost to delay means that bringing forward development, even if a lower price must be accepted, becomes viable. These types of changes will be labelled as punitive by landowners, but that’s how you know they are effective—it forces them to build housing when they prefer not to.
Finally, we can always create non-market housing institutions that build new housing regardless of market conditions, allowing this organisation to actually build at a rate that will depress prices, or offer housing to residents at below market prices.
With a bit of luck I hope that in future conversations about housing supply and zoning that the rate of new housing supply per period across all lots is no longer conflated with the allowable density of housing per lot.
fn.  I do note that some cities may very well have planning regulations that are so poorly designed that they do in fact constrain the rate of supply.
Update: Total employment in housing construction reduced to remove the engineering construction workforce.