Affordaville: Understanding when to build which kind of building

Before reading this, you should have a good understanding of the construction types we’re considering. In this example, we’re going to take those construction costs and combine them with land costs to understand why people choose to build different kinds of housing in different places.

So let’s imagine a small town of about 100 acres and 300 households, where there’s no shortage of land to choose from. We’ll call it Affordaville. We’ll assume land costs are about $20,000 per acre in Affordaville; perhaps this is the value of the land if it were used for agriculture instead of housing. We’ll also assume some reasonably accurate construction costs to construct approximately equally-desirable homes of different construction types.

Rural Small-Town Affordaville

 Units per acreLand costsConstruction costsTotal cost per unit
Single-family 4$5,000$150,000$155,000
Low-rise apts12$1,667$150,000$151,667
Mid-rise apts36$556$250,000$250,556
High-rise apts288$69$500,000$500,069

High-rise is really expensive in Affordaville! Mid-rise apartments also cost way more than low-rise apartments, which cost about the same as a single-family home. If people like to have houses close together so they can talk to their neighbors and kids can play together, they may construct homes close together. But if somebody wants a house on an acre or more of land, the cost wouldn’t be unreasonable. More likely, you would see a mix of low-rise housing types and finish qualities that represent the preferences of the residents and potential residents. Some people will want bigger houses and some will want smaller, while others may prefer a townhouse because they really don’t want to maintain a large yard.

But it’s very unlikely that somebody would build a mid-rise or high-rise apartment building! A developer who bought a one-acre parcel and tried to put up a 36-unit midrise apartment complex could easily find themselves bankrupted! It costs them about $250K to build an apartment, but anybody who wants to live next door could easily build a house for $150K, so they’d have trouble selling them for anything close to cost!

Growing City Affordaville

Now imagine Affordaville has gone through a boom. We keep building new single-family houses further and further out until some people don’t like the commute. Some people really want to be able to live in the center-city so they can walk to work or be within a five minute drive of all the town’s stores. This competition for center-city land increases its price: now our land costs for the center-city are $400,000 per acre. Let’s look at what this does to our cost matrix:

 Units per acreLand costsConstruction costsTotal costs per unit
Single-family4$100,000$150,000$250,000
Low-rise apts12$33,333$150,000$183,333
Mid-rise apts36$11,111$250,000$261,111
High-rise apts288$1,388$500,000$501,388

The higher land prices encourage developers to switch to a more expensive construction technique to reduce the amount of land needed per new home — i.e., to substitute expensive capital for even more expensive land. Low-rise apartments may be duplexes or triplexes or quadplexes or any other constellation of low-rise wood-frame housing. Of course, just because the apartments are cheapest doesn’t mean that’s what will get built! Some people will still be willing to pay more for a single-family house because it’s worth it to them. Also, this is only the cost matrix for the center of Affordaville. Affordaville has spread out beyond its original 100 acres and other parts of it are less desirable, so they will have their own lower land price and their own cost matrix. Something else to note is that, even though low-rise apartments are now the least expensive option, they’re still more expensive than single-family houses were previously. If you aren’t paying close attention to the housing market and seeing that the cost of land rose before the apartments appeared, you may think that the apartments caused the increase in prices rather than the other way around.

Even though low-rise apartments are now the least expensive option, they’re still more expensive than single-family houses were previously. If you aren’t paying close attention to the housing market and seeing that the cost of land rose before the apartments appeared, you may think that the apartments caused the increase in prices rather than the other way around.

Burgeoning Metropolis Affordaville

Let’s bump land costs up to $2m per acre.

 Units per acreLand costsConstruction costsTotal costs per unit
Single-family4$500,000$150,000$650,000
Low-rise apts12$166,667$150,000$316,667
Mid-rise apts36$55,556$250,000$300,556
High-rise apts288$6,944$500,000$506,944

Now we start to see our city really grow! Instead of low-slung apartments, we see our expensive land lined with mid-rise apartments!

Metropolitan Affordaville

As Affordaville gets bigger and bigger and new industries move in, the competition for center-city land becomes intense. We’ll now assume land prices of about $12m per acre and see what this does to our cost matrix:

 Units per acreLand costsConstruction costsTotal costs per unit
Single-family4$3,000,000$150,000$3,150,000
Low-rise apts12$1,000,000$150,000$1,150,000
Mid-rise apts36$333,333$250,000$583,333
High-rise apts288$41,666$500,000$541,666

In center-city Affordaville, housing is now perpetually expensive, no matter what construction technique is used. This is a reflection of the enormous number of people all wishing they could live in the same place in the central city and all competing for the same scarce land resource. Again, a casual observer could look at a city and see expensive high-rise apartments and conclude that it’s the construction technique that caused the expense, rather than the truer relationship: the very high cost of land made it worthwhile to substitute expensive construction techniques for expensive land. There may still be individuals who want to pay high costs for a single-family house, but the savvy developer is willing to shell out for expensive construction techniques in order to save money on even more expensive land.

Further outside the central city, the demand for and price of land will be lower, changing the economics of which construction techniques are most cost-effective.

Again, a casual observer could look at a city and see expensive high-rise apartments and conclude that it’s the construction technique that caused the expense, rather than the truer relationship: the very high cost of land made it worthwhile to substitute expensive construction techniques for expensive land.

Review

To review, even before we’ve gotten to more complicated subjects like the effects of zoning or how to calculate land values, we can already answer a lot of questions about cities just by understanding the cost structure of various construction techniques and how they interact with land values:

  • High-rises, mid-rises, and low-rises tend to get built in different places because varying demand for locations makes different construction techniques economically viable.
  • Switching to denser construction techniques can prevent exorbitant price increases in popular locations but won’t return prices to the low levels before that land was popular.

Charts

This is a supply-and demand chart using our simplified model. The blue line represents, how many units developers are able to produce as the price goes up, without losing money. The red lines represent how many units homebuyers are willing to buy at a given price. Each red line represents a different scenario above. Where these two lines intersect is how many homes will get built in that particular scenario. There are many red lines but only one blue line because we are assuming fixed costs for different kinds of construction, but we are allowing variable demand for each different scenario.

The blue line is stair-stepped because developers are only able to supply so many single-family homes before they run out of land to do so. Then, for a while, prices rise but developers don’t build any more homes. That’s because even though they’re able to sell low-rise homes for more than it costs to build them, they wouldn’t be able to sell homes for as much as it costs to build mid-rise. Once it becomes profitable, that new construction type rapidly takes over until the next price break. This is that period everybody who lives in a growing city has experienced when suddenly new development feels like it’s happening everywhere.

And so this chart goes on: first one kind of development is feasible, then prices rise, then a denser kind of development is feasible for a while, then prices rise, then another kind of development is feasible once again.

Limitations of this chart

  • In real-life, most cities don’t have a “central city” with 400 acres of land with exactly identical desirability. That’s why you can see rings of different housing types where the central city has high-rise buildings, followed by mid-rise a bit further out, than low-rise further out than that.
  • Housing is built for the long-term. Just because the demand level in a neighborhood would mean that a new mid-rise apartment building can deliver a better price point for consumers and better profits for a developer doesn’t mean that it’s worth buying out an existing, well-performing low-rise apartment building and demolishing it.
  • We’ve constructed our model with the cost of building a mid-rise apartment building and a single-family house so that they’re perfect substitutes. And real people really do choose between single-family houses and an apartment in a mid-rise apartment building. But different people have different needs and desires, so it could easily be that some people are willing to pay much more for a single family house than a similar apartment, while others would only be willing to pay the same price. This would result in a greater mix of housing types, some with higher prices than others.

Next posts:

  • Restrictia: another model city, but with a zoning code.