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Tuesday, January 3, 2017

Live Work Commute 2

Housing Costs and Density

Executive Summary:

The problem of rising rents has many people arguing for building many more apartments in order to lower rents.  They are thinking "the law of supply and demand" (LoSaD) says supply will increase indefinitely until everyone can afford the product.

That isn't what the LoSaD says, but in any case it is not relevant because the supply in the case of housing is land and they stopped making it.  As demand increases for a limited supply of land, the price will increase as long as there is anyone anywhere that can pay the price.  We show this with data and economics.

Key points:
  1. Econ 101's "Price Theory" - Law of Supply and Demand - is true for some things such as manufactured goods, commodities (like wood and grain), and for land but it is not true for housing because...
  2. ...Real estate involves a fixed amount of land within city boundaries.  Increasing demand for this land will not increase the supply, so the price must rise with demand.
  3. Construction costs for different densities are greater per square foot as the height and density increases past a certain point.
  4. People pay more to lessen their commute time.  Therefore centers of cities will cost more because living there makes commuting easier.
  5. The value of the land is determined by the income it will generate.  Higher density housing means each acre of land generates more rent.  This increases the value of the land and drives up the rental income required to generate a profit.
Separately, there is a set of falsehoods referred to as "Econ 101-ism".  I address it elsewhere:

In sum - Increased density means increased housing costs.  Therefore, adding housing to a dense city makes it more expensive.  This has been known and seen to be true everywhere since the 1800's.  Here's the academic way of saying it:

"Population Density is Higher near the City Center (where housing costs are high) than at the city outskirts (where housing costs are low)."

"...density as well as the land rent fall as the distance to the city center rises. This provides an explanation for the fairly general empirical fact that the population density is higher near the city center (where housing costs are high) than at the city outskirts (where housing costs are low). In addition, the size of the residential area depends on the opportunity cost of land but also on the number of consumerstheir income, and the value of their commuting costs to the CBD (Central Business District).
(From: "Economics of Agglomeration" by Dr. Fujita, & Dr. Thisse, page 83)

1.  Basic Supply Demand Curves - AKA "Price Theory"

The classic supply-demand graph.  If you think you understand "increased supply lowers price" you can skip this but note that it doesn't apply to real estate.

People are referring to the following graph and theory when they say "...basic Econ 101" (click graph to enlarge).

The blue "Supply" curve is how many "widgets" suppliers will make for a given price.

It is saying that as the price increases (on the vertical axis), makers of the product will be motivated to increase the quantity (horizontal axis = supply) since they can get more money by producing more.  Moving to the right up along the blue line implies the price keeps increasing.  This price increase  induces ever more supply.

The red "Demand" curve  is how many "widgets" consumers will buy for a given price.

It says that if the quantity available is very small for the fixed demand then the price will be quite high.  As the quantity increases the implicit bidding for goods will result in a lower price for each of the more plentiful goods.  At the far left, the high unmet demand causes people to bid prices higher.  At the far right, there is not enough demand (or too many products) so products will go unsold if the price is not lowered to that point.

The Equilibrium point (P*, Q*) is where the price bid by consumers = the ask price by suppliers.

This Price P* and Quantity Q* where supply meets demand is called the "clearing price".  If supply increases past the equilibrium point, demand by buyers is insufficient resulting in a lower price and an "over-supply".  Then goods are left unsold - shelves don't "clear".

2.  The Supply-Demand Graph Succeeds...

...when it is based on a model of manufacturing.  We'll call the manufactured product "widgets".  Assume there are fixed costs of $1 Million per year to build and maintain a factory.

Widget Factory - Costs $1 Million
Assume "fixed cost" $1 Million to build & maintain a widget factory
Further assume that each widget costs $100 in labor and materials.

Labor and Materials - $100 per Widget
Assume labor & material "variable cost" $100 for each widget
Building only 10 "widgets" per year means that each widget must sell for $100,100 to pay for the $1M fixed costs and the $100 for the (variable) costs of labor and material for the 10 widgets produced that year.  See table below:

But, suppose the factory makes 1,000 widgets in a year - line 2 in table above.  Then labor and material (variable) costs for those 1,000 widgets = $100,000.  Add the $1 Million (fixed) costs for the factory and you have a total cost of $1,100,000 for the 1,000 widgets.  That works out to $1,100 per widget - much cheaper than the cost per widget of $100,100 for making only ten widgets.

If we make even more widgets, say 100,000, we get line 3 in the above table and our unit cost per widget is now only $110.  And so on...

This is what people are thinking of when they say increased supply lowers costs.

The problem is this doesn't work for housing because land costs vary and construction costs vary.  There is no "factory" of fixed costs, so the more housing units you make the more expensive it gets.  Double the number of housing units and everything doubles - the cost of land, the cost of materials, the cost of labor - so the cost per unit of housing stays the same or even increases - building higher can cost a LOT more per square foot.

3.  The Supply-Demand Graph Fails.. items like land.  In the case of real estate, the amount of land in a city is fixed so if demand increases, the price of the land increases but not the quantity.  Now the Demand curve is a vertical line.  See below:

In the above graph, it doesn't matter what the demand is, the quantity of land is fixed.  Increasing demand moves you up the line to a higher price.  Decreasing demand moves you down the red line to a lower price.  If you build more offices or housing you increase the demand for land and the price goes up because the quantity of land can't change.  That is one reason increased density increases housing prices.

4.  Construction Costs Increase with Height

The basic supply-demand graph fails in another way in building apartments and condos.  The basic supply-demand curve seen earlier only works if doubling the quantity doubles the cost of making the product - if 20 "widgets" cost twice as much to make as 10 "widgets".   The fixed costs of factory are then spread over more "widgets" = lower fixed costs per widget.  This is not true in building apartments when increasing above a certain height.

It is relatively cheap to build a 4-unit 2-story apartment with off-street parking behind the building.  Wood frame, simple labor.

Cheap Apartments - Wood Frame - Simple Labor
As cheap to build as possible
Going to 5-story apartments with ground-level parking underneath the living units costs more per square foot since you need a steel and concrete core and base.  An 8-story costs more per square foot to build than a 5-story apartment.  This is because you have to use more highly skilled labor, bring in cranes and heavy earth-moving equipment, install elevators, use more expensive material like concrete and steel, replace cheap off-street parking with expensive multi-level steel and concrete underground parking, and various other things.  

We can see this in the screen capture below from Zillow.  Two apartment buildings in the same city, one 4-story, one 8-story.  The 8-story apartment charges 64% more for a 2-bedroom apartment.  The higher priced one is a bit closer to downtown and so has to build higher to spread the higher cost of land over more apartments.  The more expensive apartment is also larger, but costs more per square foot.  That it costs more, not less is the key point.

Costs and therefore prices actually increase with housing density but in a step-wise or 'lumpy' fashion.  The blog "Market Urbanism" explains it well:

"Housing supply is “lumpy” because of these abrupt changes in construction costs as the market moves from one type of housing to the next. Because it is much more expensive, on a per square foot basis, to build mid-rise housing than single-family housing, and much more expensive to build high-rise housing than mid-rise housing, the supply curve for housing within a neighborhood looks something like the stair-stepped red line:

"(Note that not even vulgar Econ 101 predicts that housing prices will drop after a switch to a more expensive technology. The switch merely prevents prices from continuing to rise because new supply can continue to be added at the same cost.)"

Going from 2-story cheap wood frame housing to 4-story housing, or from 4-story housing to 8-story housing will not happen until rents climb high enough to justify the increase in costs for the increase in cost per square foot.  Higher density increases building costs because of increased construction costs per square foot.  This added construction cost is in addition to the increase in land costs due to higher demand.

5.  High Density Costs More

We see below a curve of price vs. distance from high density urban centers.  The greater demand for land in a high density urban environment results in higher costs for that land as competing buyers bid up the price of land.  The theoretical curve for this is shown below (click on graph to enlarge):
The above is from a paper (2015) "SPATIAL DISTRIBUTION OF LAND PRICES & DENSITIES - The Models Developed by Economists" by Alain Bertaud at the Marron Institute of Urban Management at NYU.  He previously held the position of principal urban planner at the World Bank. His paper is available at:

The above theoretical econometric profile of land prices assumes an urban core with a single industry to which people commute from the surrounding area.  The surrounding area is assumed to be flat and easily developed for housing at any distance.  This sounds a bit simplistic but we see that it closely matches reality looking at actual distributions in the next chart (click on graph to enlarge):

About this graph, Mr. Bertraud writes " increase in population, everything else being equal, would increase both land prices and densities."  The bidding for the purchase of land that goes on - implicit or otherwise - is part of the supply-demand vertical line graph shown earlier and raises land prices as density increases.  This will show in that prices per square foot increase for comparable living units near the core and further away from the core.  Smaller living units at the same price as the suburbs or much higher prices for the same-sized units in the Central Business District.

Note that in the first graph the vertical axis is price and in the second the vertical axis is density.  That is because they are equivalent.

This applies to most cities reasonably well as seen here (click on graph to enlarge):

It looks like LA and Atlanta violate the rule.  They don't.  It just looks that way because the density per sq. mile in the Central Business District is much lower in LA, NYC, and Atlanta compared to say Bangkok.  Using the same numbers on the vertical axis for LA and Beijing makes LA look flat but it is all relative.

5.  People Pay More to Be Closer to Work

Commuting takes time.  Someone earning $50/hour while commuting 1 hour per day, 20 days a month is "paying" $1,000 per month in time lost to commute.  They should be willing to pay $1,000 per month more in rent to be closer to work (assuming they have that money).  Apartment owners in the center city capture that extra commute cost by charging higher rents for lessened commutes.  Or looked at another way, the implicit bidding in real estate transactions bids up the price.  Regardless of your perspective,  this explains part of the higher cost of center cities.

Here are some real world examples of commute times vs. price from the Financial Times.  They show that as the length of commute time (horizontal axis) decreases, rents (vertical axis) increase.  People are willing to pay more money to spend less time commuting and more time for themselves.  (click on charts to enlarge):

Graphs from:

Same thing only different:

Commute times are typically a bit over 30 minutes each way = 1 hour or more total every day.  Longer commutes typically are on public transit.  People are willing to spend more time commuting if they can read a paper or chat with a friend - see below (click graph to enlarge):

The three worst commutes in the US are in the NYC metro area.

This increased value in being close to a commute line is explicitly described in a recent NY Times article about the completion of a new subway line providing subway access where there was none before.  The principal fear by residents near the new subway entrance is that rents will rise so high they will be priced out of the city.  People pay more to lessen their commute time driving out those who can't keep up in the bidding war.

“Displacement is a real concern,” said Thomas K. Wright, the president of the Regional Plan Association, an urban policy group. “When you increase the values in areas like this, you need to do things to protect affordable housing and retail.”

6.  Higher Density = More Rental Income = Higher Land Costs

The price of the land is dependent on the income derivable from it.  Land with potential to produce $20,000/month income is worth twice as much as land producing $10,000/month income.  This is one of the most important ways to value that land which can produce rents and is more fully discussed here:

Land that can feed only 5 sheep is worth half as much as land that can feed 10 sheep
Land that can feed 10 sheep is worth twice as much as land that can feed only 5 sheep
If land is rezoned for higher density it will be able to realize a higher rental income because more apartments will generate more rents.  The land will cost more immediately after the rezoning. The high rise apartments built on it will cost more because they have to pay for the higher land cost.  The fact that more apartments can be built does not translate into lower cost per apartment. The supposed economy of scale that "Econ-101-ists" expect is negated by the higher cost of the land due to that increased density.

This is again where the basic "Econ 101" model breaks down.  There is no way to get the economies of scale that arise in the "widget" factory.  This is because the fixed cost of the factory in that model is not matched by a fixed cost of land for housing.  The cost of land for housing is highly variable. The cost of land depends on the number of apartments and demand for those apartments (schools, commutes, income levels).  On the other hand, factory costs are relatively stable regardless of the number of 'widgets' produced or the demand for those 'widgets'.

Compare the rents for two average priced 1-bedroom apartments - one in Manhattan, and the other in suburban Nassau County, Long Island.  $3200 for a 1 bedroom in Manhattan vs. $1400 for an average apartment in Nassau as seen below:

Manhattan prices 2016
Below is the house hold data for suburban Nassau County on Long Island, just outside NYC.
Suburban Nassau County, NY rents 2016

Here is an average 1 bedroom apartment for $3,200/month in Manhattan.

Here is an average 1 bedroom apartment in suburban Long Island (Nassau County) costing between $1500 and $1700 per month (half as much):

Neither of the two apartments are particularly luxurious, but to afford the Manhattan apt. at 33% of income you need $10,000/month = $120,000 per year income.  For the Nassau County apartment you need $4500/month or $54,000 per year income, if rent takes 33% of income.  People without sufficient income "pay" for the apartment in terms of commute time since they don't have the extra dollars for higher rent.

What can happen to lower rents a little is that a slew of new apartments come on-line all at once. This may result in a temporary over-supply.  Some older apartments will then back off some of the rent increases from the early boom years.before the new apartments were finished.   The newer apartments will not lower rents, though they may offer free gym memberships or two months free rent to new renters.

This may now be happening in NYC and after a few months delay in San Francisco as well.  There seems to be a small but noticeable affect on rents.  (That small decline may also be seasonal since in Winter, when the screen shots were taken, is not a popular time to change apartments.)  But this small rent decrease comes after huge increases which spurred the building.  A 100% increase followed by 5% decrease doesn't mean rents become more "affordable".  More on this in another post.


The net effect of increased density is increased rents.
  1. As density increases land becomes ever more valuable resulting in ever higher costs per acre of land.
  2. The higher cost for land implies greater height for apartment/condo buildings to pay for the costlier land.  An apartment building with more stories costs more than lower height apartments.
  3. Attempting to lower the land cost per apartment by increasing height/density increases the rent per acre which makes the land even more costly and raising the rent required.
  4. This continues on and on in an upward spiral of ever increasing costs resulting in the high cost of housing in New York City.

Someone suggested I add a solution to this problem.  I was surprised because I didn't know it was a problem.  Presumably people who live in Manhattan like living there and are willing to pay the high rents.  People who live in Paterson, NJ and commute to NYC are presumably happy with the commute.  If they didn't like their situation they could move to some place cheaper (and many do) so where's the problem?  There are, of course, trade offs which need to be articulated, and understood.  Higher density will raise rents and those currently in low cost housing will have to be accommodated for.

(Addendum 1/6/2017:  It may appear there is over-emphasis on the additional cost of building higher.  The dominant factor is demand for land.  Even if buildings were super cheap, new buildings would charge higher rent because they can - "new" commands a premium.  And they won't build at all if rents start to decline - what for?  Rents can go down - look at Detroit: economic collapse and grotesque corruption & mismanagement will lower rents.)

There is much more to say on this but it is already too long, and I have covered the basics.

This is Part 1 on the subject.
Part 2 is here:
Part 3 is here:

For now, this is ...