What’s the “Sweet Spot” For Building Housing Inexpensively?

(Source: Unsplash/Bethany Opler.)

I recently shared a graph on Twitter and got a whole bunch of varied reactions. Twitter is a good place for quickly road-testing ideas and framings to see how they’re understood and what people push back against.

The point I was trying to make was a simple one about the costs of building new housing. Countless American cities are in need of much more housing for their residents, and a reasonable question to ask is, “What’s the cheapest way to produce it?” To answer that, we need to understand how development costs work.

I have a rough conceptual diagram, without hard numbers attached to it, that I use to illustrate the way the height and complexity of a residential building intersects with the cost of building it. We’ll get to the version I shared on Twitter, but first, let me actually break it up into two separate diagrams: one that shows how the cost of land for new housing changes with density, the other that shows how the cost of construction itself changes.

(For the purposes of this article, we’re going to ignore various forms of prefab or manufactured housing. They deserve a lot of consideration—just not here and not now.)

Land Cost vs. Density

This graph is simple math. If you have a piece of land that is on the market for $K, and you build n units of housing (apartments, condos, townhomes, detached homes, etc.) on it, then the cost of land per unit will be K/n. This is the meaning behind the observation that density is how the poor are able to (sometimes) outbid the rich for urban land: by sharing the cost of that land among many households.

Notice that the slope of this inverse function curve starts out very steep and then moderates. Most of the gains come early. If you build six units where you could have built one unit, then you have saved 83% of the land cost per unit. If you build 60 units instead, you’ve only saved another 15%. If you go from 60 to 300, the savings are minimal.

The important caveat to this, of course, is that land cost in reality depends on a lot of things, and one of them is how much housing is allowed by the zoning code. A plot of land where you can legally build 300 homes is going to cost much, much more than an identically-sized plot of land where you can legally build six.

Still, what this implies is that ultra-high-density construction is not going to net you some sort of magically inexpensive new housing. On the most expensive urban land, it’s still what makes the most sense. But on cheap land, there aren’t miraculous gains to be had from, for example, having a public housing developer come in and build a tower in a low-rise neighborhood. Maybe this is obvious, but I’ve seen people talk about density as though it’s a Magical Affordability Button, and it isn’t. Here’s the other reason why:

Construction Cost vs. Density

The cost of construction itself follows a stair-step pattern. It’s not smooth or linear. This is something local planners and officials need to understand, but often don’t.

The “steps” reflect thresholds in the size and complexity of a building where different, more expensive materials or technologies become required. Some of these thresholds are a matter of physics and technology. Above about six stories, for example, you need steel-frame construction. Below that, you can use wood (often on top of a concrete podium for mid-rise buildings—the classic “5 over 1” that is ubiquitous in U.S. cities).

Some of the cost thresholds are also determined by regulation. Parking mandates are, as always, the elephant in the room. The U.S. Americans With Disabilities Act (ADA) generally requires an elevator in a building of six or more stories, unless each floor is smaller than 3,000 square feet. Also, under most U.S. building codes, most apartment buildings must have two stairwells. In practice, this leads to buildings with far more inefficient floor plans, with less rentable space and more space devoted to corridors and stairs. (The prohibition on “single-stair” buildings has a bunch of other negative consequences for energy efficiency and the ability to build apartments on small lots.)

All of these types of requirements result in stair-step thresholds where adding units to a building requires a jump in the cost of constructing that building—often enough of a jump to make creating the additional housing not worth it to the developer.

Where local regulation really runs afoul of the goal of abundant and affordable housing is where there is a glaring mismatch between the physical requirements of construction and the regulatory requirements.

One of the most common examples of this—a problem in almost every city, large and small—is the requirement that three-unit buildings be built under the international commercial building code (IBC) and have costly features such as sprinklers, while one- and two-unit buildings (i.e., duplexes) can be built under the simpler residential building code (IRC). This very often renders three- through about six-plexes a non-starter on residential lots where they would otherwise be the optimal way to deliver a cheap-to-construct building that spreads its land cost across multiple households. (For an example of a city taking the lead on fixing this issue, look at Memphis.) 

There are similar mismatches for higher-density and taller forms of construction. Payton Chung makes this point in a 2014 article for Greater Greater Washington about the height limits in Washington, DC:

Yet here in DC, the 90-foot height limit on residential areas, and commercial streets outside the core, tightly caps the additional building area that could pay for the substantial cost premium of building a high-rise.

For many areas in DC, land is expensive enough to fall into a Twilight Zone. These areas are expensive enough to require high-rise densities, but the local rents are too cheap to justify high rises’ high per-foot construction prices.

In areas that are in-between, a lot of landowners are biding their time, waiting until the moment when land prices will justify a 90-foot high-rise — a situation which explains many of the vacant lots in what might seem like prime locations.

Putting It Together

The quickly-thrown-together graph I shared on Twitter layered the two cost curves—land and construction—on top of each other. This creates the potential for confusion, because it’s not actually obvious where they should sit relative to each other. It’s going to vary a lot depending on where you are. I have tweaked the graph to offer some clarification, though.

A lot of commenters said, “You should put real numbers on this.” I disagree. Real numbers are open to all sorts of nitpicky scrutiny and turn a conceptual lesson into an empirical case study. Empirical case studies are great and important, but that’s not what I’m trying to offer here.

Below, in a rough conceptual sense, is the most common scenario for North American metro areas, by far. It’s one in which land cost is not exorbitantly high, and the dominant development pattern is low-rise, single-family homes. I’ve added a line (in yellow) which shows the added costs of land plus construction.

There are several “sweet spots” where development cost per unit of housing is minimized, and they occur right before each “stair step” where adding more units requires a different type of construction or design:

Of those “sweet spots,” the leftmost one, when land cost is reasonably low, reflects the absolute lowest cost for building a single housing unit. It’s represented by the gold star on this graph:

What that sweet spot corresponds to in real terms is the maximum density of housing you can build while still using the cheapest construction techniques, basically the same ones you would use for a single-family house.

In other words, it corresponds to the missing middle.

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The missing middle refers to the range of small-scale apartment housing, from duplexes all the way up to small apartment buildings (as well as other arrangements like cottage courts) that:

1. Can fit on a regular urban lot, without the developer needing to buy up many lots and combine them.

2. Can be done by a relatively small-scale, semi-amateur developer without a huge amount of capital.

3. Uses basic construction techniques and doesn’t require features like elevators, steel-frame construction, or structured parking that add expense and complexity.

The missing middle is the dominant urban form in large U.S. cities built before the mid-20th century. It’s the triple-deckers of Boston, the row houses of Philly and San Francisco, the brownstones of New York, the various larger (but still generally walk-up) apartment buildings interspersed into that fabric.

There’s a very good reason for that. It’s the “sweet spot” on the construction-cost curve. The missing middle was the cheapest way to build a pretty high density of housing on relatively affordable land. Almost anybody could learn to do it. (And did.)

Today, of course, somewhere between 70% and 90% of the residential land area of most U.S. cities is reserved for one thing and only one thing: single-family homes. Single-family zoning, in effect, is a legal requirement to waste land. It requires a household to buy more land than they might otherwise want to, for the privilege of being able to own a home in a given neighborhood. Its primary function is to make housing more expensive.

Allowing households to pay for less land—either by broadly allowing missing middle housing, accessory dwelling units (ADUs), or reducing or eliminating minimum lot sizes and allowing larger lots to be split up—is the single best thing most cities, in most neighborhoods, can do to make it possible to build housing at a lower floor price.

If you’re a city official, and you claim to be serious about affordability in your local housing market, but you haven’t worked toward eliminating single-family zoning, I have a tough message for you: you’re not serious about affordability.

This Isn’t an Argument Against Large Buildings

The most common negative reaction my graph received on Twitter came from people who seemed to think I was making an argument against allowing mid-rise and high-rise buildings. I’m not, and the math we’re talking about doesn’t support that. Quite the contrary. Developers build tall buildings for a reason: because they’re profitable in the locations that support them. They hit their own “sweet spot” in terms of cost.

Here’s what the combined land + construction graph looks like (again, in an abstract sense, without hard numbers) in a situation where land is extremely expensive:

Here, the minimum combined cost of land plus construction is found not at the “missing middle” low-rise sweet spot, but just below one of the higher thresholds for development cost and complexity.

There’s also a point to be made here that I’ve made many times before: the majority of housing is not new construction. Most people live in “used” homes, and the market price of a pre-existing home or apartment has nothing to do with construction cost. It is simply set by what buyers and renters are willing to pay. If there’s a lot of available supply on the market—almost any supply, really—it will help moderate the costs of existing housing, because home seekers will have more options and rents will be bid down.

If one way to get a lot more housing in your city is in towers, and you have developers who want to build towers, fine. I’m not against letting them build towers where the market supports it.

Here’s the nuance, though. We should recognize that very often, where we’re seeing that happen today, it’s because of an overall, artificial scarcity of developable sites. Most cities lock down most of their urban land under single-family zoning or otherwise extremely restrictive rules on what can be built. And then funnel a whole city’s worth of demand to a tiny minority of neighborhoods.

This is what is affordable in most towns. pic.twitter.com/kqzdyq5eDW

— Aaron Lubeck (@aaron_lubeck) June 19, 2023

In that small number of places, we upzone to allow very high densities, and land prices shoot through the roof. The housing built in those neighborhoods is going to be comparatively dense. But it’s also likely to be very expensive.

It’s still supply, and supply helps moderate rents region-wide. I’m not disputing that. But we can do better.

Some cities, in the name of “solving” the affordability crisis, have tried to artificially induce very high densities in very constrained areas. (I’m looking at you, Seattle, with your “urban village” strategy.) What this does is send land values sky high and requires more expensive forms of construction. You still get apartments out of the deal, often perfectly nice apartments in nice buildings, which people are happy to live in. But there’s ultimately going to be a cap on how much of that sort of development the market can sustain. There are only so many cranes. Only so many big development firms, capable of building large mid-rises and high-rises.

If developable land is not scarce—if there are lots of sites in lots of neighborhoods where it is legal to house more people than are housed today—then land values will likely moderate. They won’t be so spiky. And there will be a whole lot of places where that missing middle sweet spot becomes attainable.

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