<p>Try <a href="https://www.mheducation.com/highered/product/urban-economics-o-sullivan/M9780078021787.html" rel="nofollow noreferrer">Urban Economics by Arthur O'Sullivan</a>, it covers a large number of location-related topics and the pricing of land.  There are also spatial equilibrium models that find the locations of firms, but not necessarily the locations of cities.</p>

CC BY-SA 4.0
2021-09-12T02:38:52.940Z
2021-09-12T02:38:52.940Z
RegressForward
<p>Most organic population center growth is due to maximization of utility on an individual scale under imperfect information. The confounding factors to such growth generally center around taxation (particularly property taxes and local-based income/sales taxes) and zoning ordinances passed by local municipalities.</p>
<p>If each dollar spent on housing returned equal value before utility(ceteris paribus), an individual would prefer to be as close to work as they could to minimize time and other resources spent on commuting. Now, generally utility functions dictate that there are factors other than work that impact utility return from location only, and how other people in the aggregate perceive the housing in that location influences cost per utility benefit.</p>
<p>People will tend to live in the closest residential zone to their work that is within their price range. In a normal city setup with no outstanding geographical or social features, this ends up looking like a ring surrounding the centroid of employment (the Cartesian point that approximates the center of employment spread). Features such as a lake or a casino will tend to distort this ring based on perception. Lakes will raise property values, which would tend to distort pricing utility and cause a &quot;bunching&quot; effect on the ring shape, with less population density toward the center of that distortion spot (as the perceived value increase will price out a non-insignificant number of buyers).</p>
<p>A negative perception of an area will have a similar effect to some degree, such as having a casino nearby. You will see an increase in population density and a reduction in housing pricing in the vicinity, which may also be offset by things like hotels and businesses displacing housing due to lower residential land values. This will make a similar 'bunching' effect on the ring with the caveat of a different density for the center of the distortion.</p>
<p>If much of the housing exists in suburbs rather than inside the city limits, you will start to see population displacement effects from taxation. A locally higher property tax will reduce housing value, where a local sales tax (such as a lump tax levied per gallon of gas sold, or per unit of tobacco product sold) will have a muted but similar effect. Many communities will also dictate zones for specific housing. As an anecdote, the suburb of Wyoming, Michigan has parceled out lots in sizes by band, where lots farther from the Grand Rapids city center tend to be larger, thereby artificially altering population density in a specific shape.</p>
<p>Some cities and suburbs also impose an independent income tax from the state and federal income taxes. This can be seen in Michigan in both Detroit and Lansing, and has the effect of reducing property values in those locations marginally, with an uneven distribution of impact(if you earn income via business ownership or securities exchange, it won't affect your personal utility, but will affect the present value of the home, leading to a present, but still much smaller impact than what is seen with an individual who is actively earning a wage via employment).</p>

CC BY-SA 4.0
2021-08-16T15:29:36.897Z
Thanks for these thoughts. Can you provide any references?
afreelunch
CC BY-SA 4.0
2021-08-16T15:58:40.623Z
From my time at Wayne State University, one of my professors had written a book on the physical distribution of fast food, and had then related it in the course to a variety of different topics, including distribution of residencies. The book was unpublished at the time I took the course, and perusing through his CV, it looks like he never published it. https://clasprofiles.wayne.edu/profile/aa1313 is the link to his bio at WSU, and the timeframe would be circa 2012. Perhaps he is listed as a co-author under another authority.
GOATNine
CC BY-SA 4.0
2021-08-12T20:03:58.013Z
2021-08-12T20:03:58.013Z
GOATNine
<p>If you want a highbrow mathematical economics take on the topic, you can take a look at the 1977 book &quot;The Economics of Space and Time&quot; by Arnold M. Faden. You can find a review of the book by Hal Varian <a href="https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-1/issue-2/Review--Arnold-M-Faden-The-economics-of-space-and/bams/1183544087.full" rel="nofollow noreferrer">here</a>.</p>

CC BY-SA 4.0
2022-06-09T07:55:56.327Z
2022-06-09T07:55:56.327Z
Michael Greinecker
<p>I am interested in reading up on the geometry of cities: what explains their ‘shape’ (e.g. why is the population often distributed in a rough circle)? I imagine that this is a question with some literature. Does anyone know of the classic papers? Textbook recommendations also appreciated!</p>
<p>P.S. While I would be happy to read about empirical work on this, I am mainly interested in the topic from the theory side.</p>

CC BY-SA 4.0
2021-08-12T13:59:00.677Z
I would be genuinely and happily surprised (and happily corrected) if this fell under mathematical economics. Possibly some type of anthropology, sociology, town planning literature. Not sure if this is the type of thing you mean?https://discovery.ucl.ac.uk/id/eprint/1370661/6/1370661_Fractal%20Cities%20Chapter%201.pdf
EB3112
CC BY-SA 4.0
2021-08-12T14:07:42.187Z
No, that's not what I mean. As I say in the question, I am looking for mathematical models.
afreelunch
CC BY-SA 4.0
2021-08-12T14:18:16.643Z
I am struggling to see the link between economic activity and the shape of the cities borders. I mean, it's not that it's independent of economic activity; I just don't see economists seeking to explain those kinda questions in their mathematical modelling. Best of luck on your search
EB3112
CC BY-SA 4.0
2021-08-12T14:34:10.153Z
OK thanks. If you are interested in an (empirical) paper on this topic, by an economist and published in an economics journal (AER), you might want to look at this one: https://www.aeaweb.org/articles?id=10.1257/aer.20171673
afreelunch
CC BY-SA 4.0
2021-08-12T14:42:19.890Z
It's an interesting perspective. But you're interested from a slightly different motivation, no? You'd like to know what kinda economic/population behaviour explains their shape, rather than how shape/scale/density affects economic activity like the AER paper?
EB3112
CC BY-SA 4.0
2021-08-12T14:48:59.827Z
Yes, that's right (and I can understand how that second question might be deemed "not economics" on a rather narrow definition of the field).
afreelunch
<urban-economics><spatial-economics>
The geometry of cities (reference request)
afreelunch
# The geometry of cities (reference request)

(Asked by: username_0 on 2021-08-12)

I am interested in reading up on the geometry of cities: what explains their ‘shape’ (e.g. why is the population often distributed in a rough circle)? I imagine that this is a question with some literature. Does anyone know of the classic papers? Textbook recommendations also appreciated!

P.S. While I would be happy to read about empirical work on this, I am mainly interested in the topic from the theory side.

**Tags:** urban-economics, spatial-economics

> **Comments:**
> **username_1**: I would be genuinely and happily surprised (and happily corrected) if this fell under mathematical economics. Possibly some type of anthropology, sociology, town planning literature. Not sure if this is the type of thing you mean?https://discovery.ucl.ac.uk/id/eprint/1370661/6/1370661_Fractal%20Cities%20Chapter%201.pdf  
> **username_0**: No, that's not what I mean. As I say in the question, I am looking for mathematical models.  
> **username_1**: I am struggling to see the link between economic activity and the shape of the cities borders. I mean, it's not that it's independent of economic activity; I just don't see economists seeking to explain those kinda questions in their mathematical modelling. Best of luck on your search  
> **username_0**: OK thanks. If you are interested in an (empirical) paper on this topic, by an economist and published in an economics journal (AER), you might want to look at this one: https://www.aeaweb.org/articles?id=10.1257/aer.20171673  
> **username_1**: It's an interesting perspective. But you're interested from a slightly different motivation, no? You'd like to know what kinda economic/population behaviour explains their shape, rather than how shape/scale/density affects economic activity like the AER paper?  
> **username_0**: Yes, that's right (and I can understand how that second question might be deemed "not economics" on a rather narrow definition of the field).  

---

## 3 answers

### Answer by username_4 on 2022-06-09. Score: 4 | Accepted answer

If you want a highbrow mathematical economics take on the topic, you can take a look at the 1977 book "The Economics of Space and Time" by Arnold M. Faden. You can find a review of the book by Hal Varian [here](https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-1/issue-2/Review--Arnold-M-Faden-The-economics-of-space-and/bams/1183544087.full).


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### Answer by username_2 on 2021-09-12. Score: 2

Try [Urban Economics by Arthur O'Sullivan](https://www.mheducation.com/highered/product/urban-economics-o-sullivan/M9780078021787.html), it covers a large number of location-related topics and the pricing of land. There are also spatial equilibrium models that find the locations of firms, but not necessarily the locations of cities.


---

### Answer by username_3 on 2021-08-12. Score: 1

Most organic population center growth is due to maximization of utility on an individual scale under imperfect information. The confounding factors to such growth generally center around taxation (particularly property taxes and local-based income/sales taxes) and zoning ordinances passed by local municipalities.

If each dollar spent on housing returned equal value before utility(ceteris paribus), an individual would prefer to be as close to work as they could to minimize time and other resources spent on commuting. Now, generally utility functions dictate that there are factors other than work that impact utility return from location only, and how other people in the aggregate perceive the housing in that location influences cost per utility benefit.

People will tend to live in the closest residential zone to their work that is within their price range. In a normal city setup with no outstanding geographical or social features, this ends up looking like a ring surrounding the centroid of employment (the Cartesian point that approximates the center of employment spread). Features such as a lake or a casino will tend to distort this ring based on perception. Lakes will raise property values, which would tend to distort pricing utility and cause a "bunching" effect on the ring shape, with less population density toward the center of that distortion spot (as the perceived value increase will price out a non-insignificant number of buyers).

A negative perception of an area will have a similar effect to some degree, such as having a casino nearby. You will see an increase in population density and a reduction in housing pricing in the vicinity, which may also be offset by things like hotels and businesses displacing housing due to lower residential land values. This will make a similar 'bunching' effect on the ring with the caveat of a different density for the center of the distortion.

If much of the housing exists in suburbs rather than inside the city limits, you will start to see population displacement effects from taxation. A locally higher property tax will reduce housing value, where a local sales tax (such as a lump tax levied per gallon of gas sold, or per unit of tobacco product sold) will have a muted but similar effect. Many communities will also dictate zones for specific housing. As an anecdote, the suburb of Wyoming, Michigan has parceled out lots in sizes by band, where lots farther from the Grand Rapids city center tend to be larger, thereby artificially altering population density in a specific shape.

Some cities and suburbs also impose an independent income tax from the state and federal income taxes. This can be seen in Michigan in both Detroit and Lansing, and has the effect of reducing property values in those locations marginally, with an uneven distribution of impact(if you earn income via business ownership or securities exchange, it won't affect your personal utility, but will affect the present value of the home, leading to a present, but still much smaller impact than what is seen with an individual who is actively earning a wage via employment).

> **Comments:**
> **username_0**: Thanks for these thoughts. Can you provide any references?  
> **username_3**: From my time at Wayne State University, one of my professors had written a book on the physical distribution of fast food, and had then related it in the course to a variety of different topics, including distribution of residencies. The book was unpublished at the time I took the course, and perusing through his CV, it looks like he never published it. https://clasprofiles.wayne.edu/profile/aa1313 is the link to his bio at WSU, and the timeframe would be circa 2012. Perhaps he is listed as a co-author under another authority.  

---

