Alonso and the Scaling of Urban Profiles

in Geographical Analysis (2019)

How urban characteristics change with total population, their scaling behavior, has become an important research field since one needs to better understand the challenges of urban densification. Yet urban ... [more ▼]

How urban characteristics change with total population, their scaling behavior, has become an important research field since one needs to better understand the challenges of urban densification. Yet urban scaling research is largely disconnected from intra-urban structure, and this seriously limits its operationalization. In contrast, the monocentric model of Alonso provides a residential choice-based theory to urban density profiles. However, dedicated comparative static analyses do not completely solve how the model scales with population. This article bridges this gap by simultaneously introducing power laws for land, income and transport cost in the Alonso model. We show that the equilibrium urban structure of this augmented model matches recent empirical findings about the scaling of European population density profiles and satisfactorily represents European cities. This result is however not compatible with the observed scaling power of housing land profiles, and challenges current empirical understanding of wage and transport cost elasticities with population. Our results call for revisiting theories about land development and housing processes as well as the empirics of agglomeration benefits and transport costs. [less ▲]

Alonso and the scaling of urban profiles

E-print/Working paper (2018)

Urban characteristics scaling with total population has become an important urban research field since one needs to better understand the benefits and disadvantages of urban growth and fur- ther ... [more ▼]

Urban characteristics scaling with total population has become an important urban research field since one needs to better understand the benefits and disadvantages of urban growth and fur- ther population concentration. Urban scaling research, however, is largely disconnected from the empirics and theory of intra-urban structure for it considers averaged attributes and ignores resi- dential choice trade-offs between transport and housing costs within cities. Using this fundamental trade-off, the monocentric model of Alonso provides theory to urban density profiles. However, it is silent about how these profiles scale with population, thus preventing empirical scaling studies to anchor in a strong micro-economic theory. This paper fixes this gap by introducing power laws for land and for population density in the Alonso model. From an augmented model with land use, we derive the conditions at which equilibrium profiles match recent empirical findings about the scaling of urban land and population density profiles in European cities. We find that the Alonso model is theoretically compatible with the observed scaling of population density profiles and leads to a satisfactory representation of European cities. The conditions for this compatibility refine current understanding of wage and transport costs elasticities with population. Although they require a scaling power of the profile of the share of urbanised land that is different from what is observed, it is argued that alternatives specifications of transport cost functions could solve this issue. Thus our results call for revisiting theories about land development and housing processes as well as the empirics of agglomeration benefits and transport costs. [less ▲]

Homothetic Scaling of Urban Land Use and Population Density Gradients in Monocentric Models

Scientific Conference (2017, November)

Homothetic Scaling of Urban Land Use and Population Density Gradients in Monocentric Models

Scientific Conference (2017, September)

Exploring the polycentric city with multi-worker households: An agent-based microeconomic model

in Computers, Environment and Urban Systems (2017), 62

We propose an agent-based dynamics which leads an urban system to the standard equilibrium of the Alonso, Muth, Mills (AMM) framework. Starting for instance from a random initialization, agents move and ... [more ▼]

We propose an agent-based dynamics which leads an urban system to the standard equilibrium of the Alonso, Muth, Mills (AMM) framework. Starting for instance from a random initialization, agents move and bid for land, performing a kind of local search and finally leading the system to equilibrium rent, density and land use. Agreement with continuous analytical results is limited only by the discreteness of simulations. We then study polycentrism in cities with this tool. Two job centers are introduced, and the economic, social and environmental outcomes of various polycentric spatial structures are presented. We also introduce two-worker households whose partners may work in different job centers. When various two-worker households are mixed, polycentrism is desirable, as long as the centers are not too distant from each other. The environmental outcome is also positive, but housing surfaces.increase. (C) 2016 Elsevier Ltd. All rights reserved. [less ▲]

Land use and density in the European city: monocentric analysis and scaling

Scientific Conference (2016, August)

In this work we study the evolution of land use and population density in European cities with respect to the distance to the city centre, and how land use and density curves scale with city population ... [more ▼]

In this work we study the evolution of land use and population density in European cities with respect to the distance to the city centre, and how land use and density curves scale with city population. The principal aim of this research is to provide stylized facts and generic formulas for the calibration of monocentric urban economic models to European cities. We use the GMES Urban Atlas database, providing a precise description of land use in the 305 major European larger urban zones (LUZ), which have more than 100.000 inhabitants. For the population density we use the Geostat population grid, which covers the whole of European Union (EU) with a 1km$^2$ grid dataset. We combine the land use and population datasets by attributing the population of the Geostat grid to the geographic units of the (much more precise) land use dataset. This attribution is proportional to the surface of each unit and weighted thanks to the nomenclature of the GMES Urban Atlas, which gives classes of soil sealing and density of urban fabric. Then we analyse the evolution with distance to the city centre, which we define for convenience as the location of the city hall, of population density and of the share of land used for different purposes: housing, roads, railways, urban green, water, agriculture, forest. To this end, we define concentric rings of fixed width around the city centre, in which we average land use and population. In order to compare results between different cities and to obtain a global picture ("average" or "standard" European city), we study simple scaling relationships for the obtained monocentric land use shares and density curves. We choose to study the scaling of these curves with respect to the city population, as has been done in the literature for different parameters (like income or road space). In our case city population is taken as the population of the LUZ, computed thanks to the population grid. It turns out that land use curves, in particular housing or roads shares, tend to scale like the square root of city population. Population curves have roughly exponential shapes, as widely modelled in the literature, and tend to scale like the city population to a power close to $1/3$. These results allow us to propose a simple monocentric description of land use shares and population curves in a representative European city, whose size can be chosen based on the scaling relationships we obtain. This result is especially interesting, and of practical use, for the purpose of calibration of monocentric urban models. [less ▲]

Land use and density in the European city: monocentric analysis and scaling

Scientific Conference (2016, May)

In this work we study the profile of land use and population density in European cities with respect to the distance to the city centre. More specifically we address the scaling of land use and density ... [more ▼]

In this work we study the profile of land use and population density in European cities with respect to the distance to the city centre. More specifically we address the scaling of land use and density curves with respect to city population and rely on fine grained land use data. Our main objective is to retrieve generic laws that can support the calibration of monocentric urban economic models for European cities. We use the GMES Urban Atlas database, providing a precise description of land use at 5m resolution in the 305 major European urban areas (more than 100.000 inhabitants). We combine this dataset with population density from the Geostat population grid, which covers the whole of European Union (EU) with a 1km2 resolution. Population is allocated proportionally to surface and weighted by soil sealing and density classes of the GMES data. We analyse the evolution with distance to the city centre, which we define for convenience as the location of the city hall, of population density and of the share of land used for different purposes: housing, roads, railways, urban green, water, agriculture, forest. To this end, we define concentric rings of fixed width around the city centre, in which we average each land use and population. In order to compare different cities and to identify a global picture, i.e. a standard representative European city, we study scaling relationships for the ob- tained monocentric land use shares and density curves. We analyse the scaling of these curves with respect to city population, following similar approaches con- ducted in the literature for different parameters (such as income or road space). The total population for each city is computed from the population grid. We find that land use curves, in particular housing and roads shares, tend to scale like the square root of city population. Population curves have roughly exponential shapes, as it has been widely modelled in the literature, although usually not based on land use and soil sealing data. Population curves tend to scale like the city population to a power close to 1/3. These results allow us to propose a simple monocentric description of land use shares and population curves in a representative European city, whose size can be chosen based on the scaling relationships we obtain. This result is especially interesting, and of practical use, for the purpose of calibration and validation of monocentric urban models, that can differentiate (or not) housing from land and include interactions between non-developed and developed land. [less ▲]

Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise

in Journal of Physics. A, Mathematical and Theoretical (2014), 47(10), 105001-11

Thermal noise in a cellular automaton (CA) refers to a random perturbation in its function which eventually leads the automaton to an equilibrium state controlled by a temperature parameter. We study the ... [more ▼]

Thermal noise in a cellular automaton (CA) refers to a random perturbation in its function which eventually leads the automaton to an equilibrium state controlled by a temperature parameter. We study the one-dimensional majority-3 CA under this model of noise. Without noise, each cell in the automaton decides its next state by majority voting among itself and its left and right neighbour cells. Transfer matrix analysis shows that the automaton always reaches a state in which every cell is in one of its two states with probability 1/2 and thus cannot remember even one bit of information. Numerical experiments, however, support the possibility of reliable computation for a long but finite time. [less ▲]

Dynamical fluctuations in a simple housing market model

in Journal of Statistical Mechanics: Theory and Experiment (2012)

We consider a simple stochastic model of an urban rental housing market, in which the interaction of tenants and landlords induces rent fluctuations. We simulate the model numerically and measure the ... [more ▼]

We consider a simple stochastic model of an urban rental housing market, in which the interaction of tenants and landlords induces rent fluctuations. We simulate the model numerically and measure the equilibrium rent distribution, which is found to be close to a lognormal law. We also study the influence of the density of agents (or equivalently, the vacancy rate) on the rent distribution. A simplified version of the model, amenable to analytical treatment, is studied and leads to a lognormal distribution of rents. The predicted equilibrium value agrees quantitatively with numerical simulations, while a qualitative agreement is obtained for the standard deviation. The connection with non-equilibrium statistical physics models such as ratchets is also emphasized. [less ▲]

Socio-economic utility and chemical potential

in Europhysics Letters (2011), 93(3), 38002-6

In statistical physics, the conservation of particle number results in the equalization of the chemical potential throughout a system at equilibrium. In contrast, the homogeneity of utility in socio ... [more ▼]

In statistical physics, the conservation of particle number results in the equalization of the chemical potential throughout a system at equilibrium. In contrast, the homogeneity of utility in socio-economic models is usually thought to rely on the competition between individuals, leading to Nash equilibrium. We show that both views can be reconciled by introducing a notion of chemical potential in a wide class of socio-economic models, and by relating it in a direct way to the equilibrium value of the utility. This approach also allows the dependence of utility across the system to be determined when agents take decisions in a probabilistic way. Numerical simulations of a urban economic model also suggest that our result is valid beyond the initially considered class of solvable models. Copyright (C) EPLA, 2011 [less ▲]