Thursday, January 16, 2020

The utility of directly regulating Floor Area Ratio

In my last post on the obesity of midrise apartments, I mentioned that one possible solution to what I perceive as a problem is to restrict FAR (Floor-Area Ratio) tighter and loosen setback and height limits so that buildings' density be more limited by FAR regulations than geometric regulations. I got a bit of pushback on Twitter for that, and it's quite understandable, as it seems unintuitive and even counter-productive.

Unintuitive because whatever we might think of them, setback regulations and height limits can be justified, convincingly or not, by the idea of externalities. Buildings that are too high or too close to property limits are viewed as intruding visually (if nothing else) on neighboring properties, arguably justifying regulations to reduce these impacts on other properties or on the street. FAR regulations don't really have this argument though, not in a direct way anyway.

Counter-productive because, well, FAR is the best metric for built density. So by arguing for stricter FAR regulation, that means a restriction of density... when I've been arguing (and still do) for more density usually. Isn't that the opposite of what we should want?

Well, give me some time and I'll explain why I'm arguing for this.

The role of FAR in determining land value

One thing that's important to understand is that URBAN LAND HAS LITTLE TO NO VALUE IN ITSELF.

But urban lots are very valuable, so how can I say that?

Simple. Urban land has no value, it is the building allowance tied to that lot that has value. Developers buy land in order to build valuable buildings on them and reselling them. Speculators buy land they think is underpriced or will increase in value to sell to a developer down the line. So urban land's value is ultimately determined by what developers are willing to pay for it, and what is a developer willing to pay for a lot?

There's essentially three variables that help determine what a developer will be ready to pay for an urban lot.

  1. The market value of a square meter of floor area in the neighborhood (P)
  2. The construction cost of building that square meter of floor area (C)
  3. The amount of square meters of floor area that the developer can build on that lot (A)
 So you can sum up the value of an urban lot, regardless of its actual size, by the formula:


Okay, profit margin should be included there as well, but for simplicity's sake, let's set it aside since it would only complicate explanations and anyway, it's pretty much a constant.

You'll notice I put "less than or equal to" in there rather than an equal sign. That's because lot value can be less than the formula, if speculators face a lot of competition and pressure to sell, they can choose to sell for less. But a developer cannot pay a lot more than he can hope to get as income from it, he would go in the red if he did that, whereas the speculator is, usually, just cashing in his profits. Sacrificing a bit of your profits is easier to do than committing to your own personal bankruptcy...

Looking at a micro view, meaning from the point of view of one economic actor (the developer), two things are essentially independent variables, the market value of housing per square meter and the construction cost of housing, which are determined by market conditions in that neighborhood and the construction industry. The one variable that can change most is the amount of square meters of floor area they can build, because it is an outcome of municipal regulation and the developer can even ask for zoning variances or changes to increase it (thus increasing the value of the lot).

The area that can be built ties directly to FAR. So, if my understanding is correct, FAR is directly proportional to the value of urban lots.


So, the conclusions of this reasoning are the following:

  1. Lot value is directly proportional to the FAR developers expect to be able to build on it
  2. When FAR is not regulated, or when cities are open to spot zoning or FAR-raising variances, then this creates uncertainty about the ultimate FAR allowance of a lot, and thus, its value
  3. Speculators will tend to estimate optimistically the FAR that will be ultimately allowed on their lot (because they want to maximize profit), developers will tend to estimate pessimistically the FAR (because they want to minimize risk)
  4. It is crucial for reducing uncertainty and allowing speculators and developers to come to terms more readily to stabilize FAR with rigorous regulations, this helps stabilize land prices and helps the liquidity of lots
Therefore, FAR regulation, though it doesn't reduce externalities, does reduce economic uncertainty and helps facilitate deals between speculators and developers to allow the development of land.
I'll point out that FAR limits are a major part of Japanese zoning, the description of which I'm most well known. And if you agree with my assessment that the Japanese zoning system works uncommonly well for a zoning system, I don't think you can discount the role that FAR regulation plays in it.

Furthermore, it's important to understand that FAR is essentially always regulated by urban regulation and zoning.

The de facto FAR regulation of geometric regulations

Let's take a lot, 60 meters wide and 35 meters deep:

Let's suppose there are front and back setback regulations of 6 meters, and let's draw them on the lot:

Let's also suppose that there are side margin requirements of at least 3 meters on each side:

And then let's suppose there's a 6-story height limit:

The result of all these regulations is a box within which it is allowed to build, and outside of which it is illegal to build.

De facto, these geometric rules represent both:
  • A lot coverage maximum (how much of the lot can be built over)
  • A FAR maximum (representing lot coverage times the number of stories that can be built)
So there's no reason why you need an actual FAR maximum then, because it's already provided for by other rules, correct?

No, not correct.

The problem

The issue is that the lot's value is proportional to FAR, and if your allowed FAR is determined by geometric regulations, then developers willing to build up to the limit in every way will easily outbid anyone trying any other design. So basically, without an actual FAR restriction that is lower than the de facto FAR restriction of geometric rules, by setting those geometric limits, you already imposed on a developer the envelop of the building he will build. Notice how the last image's red block is nearly identical to those obese midrises I described? That is not a coincidence.

Let's continue on the previous example, the de facto regulations of the building are the following:
  • Maximum lot coverage: 54 meters wide by 23 meters deep, 1 242 square meters on a 2 100 square-meter lot, so 59% (let's round that up to 60%).
  • Maximum FAR: 60% times 6 stories equals 360% FAR
What happens if a developer who read my previous blog decided to make a 16-meter deep building only to maximize exterior walls and provide for more bedrooms per floor area? Well, his maximum FAR would be just about 40% by story, so 240% total.

That means that the FAR optimizing developer building obese midrises is going to massively outbid the slim building developer, his bid would be 50% higher because lot value is proportional to FAR. 

Alternatively, that would mean the thinner building would need to be able to sustain a much higher price per square meter to be viable. How much higher? That depends on how expensive the land is, so I'll answer by a table:

So, as we can see from this table, the more expensive land is, the more the premium that will have to be paid to afford the thinner midrise and its units with more bedrooms. Which means in suburban areas, building less than the maximum FAR is actually doable, it will increase prices by only 10% or so by square meter... but for areas with high land costs, the difference becomes incredibly high, making the thinner option completely non-viable.

So, to sum up, by restricting FAR through geometric regulations rather than directly, you:
  1. Essentially impose thick, deep buildings that fill up this entire space in urban areas.
  2. Where land prices are high, you get almost exclusively 1-bedroom apartments as a result (except where lots are smaller and have detached buildings only), anything else becomes much too expensive to build and buy because it would require to cut down the FAR and thus have much higher prices per square meter
  3. In suburban areas, this problem is much reduced, and so you'll get more flexibility on building shape and size.
Note that other regulations can also affect what is built. For example, minimum parking requirements famously restrict the amount of units that can be built by the amount of parking that can be provided for them on the lot. So in areas with little FAR restriction and high parking requirements, you're likely to get extremely big units, as it's the most profitable form of building that can be built... which likely explains the insane housing consumption of most of America.

A proposal

So my proposal after this reflection is the following:
  1. FAR needs to be regulated directly, and it needs to be done in a strict manner, not easily modifiable by zoning variances or spot zoning, in order to create certainty with regards to land valuation
  2. Maximum FAR ought to be at most 70 or 80% of "de facto maximum FAR", which is the FAR calculated as the maximum allowed if all geometric dimensions were pushed to the limits allowed by geometric regulations (height limits, setbacks, margins), so that developers are more free to adopt building shapes adapted to people's needs rather than just build thick boxes.
  3. Geometric regulations can be kept to consider externalities, and should still be modifiable with variance demands, flexibility on geometry, inflexibility on FAR
  4. Overall, allowed FAR should be increased by right in all neighborhoods to flood the market with available, untapped FAR, which should reduce the land value costs per square meter of floor area.
  5. In this regulation, there is one exception, there should be a low-rise zone with a 4-story limit that should be strictly respected and FAR designed accordingly, because low-rises are much, much cheaper to build than midrises and high-rises. Once a zone is upzoned from low-rise to mid-rise, the jump in FAR allowed should be significant to compensate that increase in construction costs.


  1. There's a problem here: developers maximize FAR because it maximizes value (as you noted, your model assumes no profit margin).

    If, as in your model, your externalities are caused purely by buildings sticking out of your red box, then maxing out FAR given the volume of the box is actually the best use of the land.

    In out model, developed value = land value - externalities cost. Since land value is directly proportional to FAR, you should (assuming fixed externalities cost) maximize FAR - that is, your size limits should be set to allow the maximum FAR that doesn't cause more externalities than you can tolerate. Unless externalities scale directly in proportion to FAR and are completely independent of building shape, this means you should never set this by FAR limitations.

    You have a good point about liquidity, but you shouldn't need FAR limitations for that - assuming the geometric rules are clear, the FAR should be predictable and shouldnt be a big source of uncertainty.

    1. The reality is that these geometrical limitations are quite arbitrary, justified by some "externalities" that are not quantified nor evaluated. Furthermore, they are often set at ridiculously low levels that require zoning changes for redevelopment in urban areas to be viable. So developers often have to seek or get zoning changes or variances for their development to see the light of day. This is what creates the uncertainty, because speculators know this and set their expectations at the actual form the development will take rather than the one established by the current regulations. But it's not a given that developers will get it.

      Now, if geometric regulations allowed for development and were strictly applied, then yes, there would be no uncertainty. But it would still not be good.

      There are strong negative consequences to this FAR-limiting by geometric regulations as well. I described some of them, maximizing FAR within an envelop is not necessarily good, in fact, it often results in poor design with a bias for studios and 1-BR units that deprive family units of units that would satisfy their needs.

      Courtyard apartments? C-,L-,T-shaped buildings? All of them require developers to reduce the FAR of their building if they respect geometric requirements, and thus punish them for adopting building shapes that are better for residents. This is not a good outcome at all.

    2. IMHO, the problem with fixed FAR and almost no height limit is that height if a very problematic externality. So, some setbacks and specially height limits will exist.
      As much I find fixed FAR interesting, if you have some setback and height regulations, and consider the within area where is legal to build, you would not maximise area usage unless you set a FAR less than 100% inside that area OR eliminate those height or setback limits.
      Very intuitive case of choice: Improve design flexibity and deal with externalities, or reduce externalities by limiting design.

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  3. Très bon ton blog! Je viens de le trouver par hasard sur le subreddit r/slatestarcodex.

    Je suis un immigrant au Québec et je me cherchais des bonnes sources "locales" sur le sujet d'urbanisme.

    Hope you'll keep posting!

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