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.
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.
Try Urban Economics by Arthur O'Sullivan, 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.
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).
