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Cities are vast, dynamic entities that are complex on a multitude of different scales. A visitor to any city can usually gauge within hours whether it “works” on a human level. But it is famously hard to quantify the factors that make one city better than another. 

Today, Luca D’Acci at the University of Strathclyde in Scotland suggests an interesting new way to visualize the benefits of certain factors in city living. 

Conventional thinking holds that an individual’s choice of where to live depends on factors such as the cost of housing, the quality of the area, the distance from the workplace, the proximity of friends and family, and local utilities such as schools, shops, and restaurants.

It’s hard to overstate the importance of this decision-making process. Many urban commentators argue that this decision is the single most important one determining the spatial structure of a city. 

If people decide to live elsewhere, a city dies. Exactly this has happened in America’s rust belt cities such as Detroit.

The standard model of a city is surprisingly simple. It consists of a central business district surrounded by concentric circles of progressively cheaper land. The assumption here is that being close to the central business district is the most important factor in anybody’s decision to move. 

But many cities, particularly in Europe, are much more complex than this. And in recent years, city planners have begun to place more emphasis on developing additional centers within cities. So it’s increasingly common for a city to have several centers performing different functions. 

D’Acci’s new model is designed to cope with this increased complexity. His idea is to calculate the benefit of a given location to a resident, taking into account the effect of all the city’s various amenities.Having done that, he calculates locations of equal benefit, connecting them with so-called “isobenefit lines”.

That gives a simple and immediate visual representation of the structure of the city in terms of the benefits it offers.

D’Acci’s approach is clearly a step forward. He points out that there is a strong correlation between isobenefit lines and property prices. That’s a good indication that the model captures some important elements of human behavior.

But this approach also has limitations. Chief among these is determining the benefit of various amenities in an objective and useful way. 

That’s particularly hard because a benefit for one person may be a disadvantage for another. Parents with young children need to live near good schools that young professionals might want to avoid like the plague. 

So more useful for individuals would be a way of rating the importance of amenities subjectively to produce a personalized isobenefit map of the city.   

Then there is the changing nature of work. With the increase in telecommuting, the need to be close to a central business district is changing. This has the potential to dramatically reshape isobenefit lines, perhaps on a monthly or even daily basis as an individual’s needs change.

So D’Acci has made a useful step forward, but clearly the process of modeling cities and their benefits is a work in progress.

Ref: arxiv.org/abs/1210.4461: Modeling Spatial Equilibrium in Cities: the Isobenefit Lines 

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