If planning constrains housing supply, how does it do it?

I’ve long puzzled over the exact mechanism by which planning regulations are supposed to constrain the rate of new housing supply. Sure, they constrain the locations at which different types and densities of uses can occur. That’s their purpose.

But density (dwellings per land area) and the rate of supply (new dwellings per period across all sites in a region) are very different.

It seems logical to me that landowners maximise their economic returns from two choosing

1. a density of development that maximises the residual (i.e. their revenue minus the cost of development), and
2. a rate of sales (and hence development) per period of time.

It is not at all clear that if more dwellings can be built on one site that this changes the optimal rate of sales per period for that site.

It is also the case that only landowners can choose to make planning applications, and that a huge majority of approvals are for projects that exceed coded density limits. We have a property market after all.

What I am puzzled about is that when someone claims that planning reduces housing supply, what sort of counterfactual pattern of supply do they have in mind?

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