# Modeling the relation between income and commuting distance

## Author Info

Listed author(s):
• Giulia Carra

(IPHT - Institut de Physique Théorique - UMR CNRS 3681 - CNRS - Centre National de la Recherche Scientifique - Université Paris-Saclay - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

• Ismir Mulalic

(DTU - Technical University of Denmark [Lyngby])

• Mogens Fosgerau

(DTU - Technical University of Denmark [Lyngby])

• Marc Barthelemy

(CAMS - Centre d'analyse et de mathématique sociale - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, IPHT - Institut de Physique Théorique - UMR CNRS 3681 - CNRS - Centre National de la Recherche Scientifique - Université Paris-Saclay - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

Registered author(s):

## Abstract

We discuss the distribution of commuting distances and its relation to income. Using data from Denmark, the UK, and the US, we show that the commuting distance is (i) broadly distributed with a slow decaying tail that can be fitted by a power law with exponent $\gamma \approx 3$ and (ii) an average growing slowly as a power law with an exponent less than one that depends on the country considered. The classical theory for job search is based on the idea that workers evaluate the wage of potential jobs as they arrive sequentially through time, and extending this model with space, we obtain predictions that are strongly contradicted by our empirical findings. We propose an alternative model that is based on the idea that workers evaluate potential jobs based on a quality aspect and that workers search for jobs sequentially across space. We also assume that the density of potential jobs depends on the skills of the worker and decreases with the wage. The predicted distribution of commuting distances decays as $1/r^{3}$ and is independent of the distribution of the quality of jobs. We find our alternative model to be in agreement with our data. This type of approach opens new perspectives for the modeling of mobility.

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File URL: https://hal-cea.archives-ouvertes.fr/cea-01568435/document

## Bibliographic Info

Paper provided by HAL in its series Post-Print with number cea-01568435.

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 Length: Date of creation: 08 Jun 2017 Publication status: Published in Interface, Royal Society, The, 2017, 13 (119), pp.20160306. 〈10.1098/rsif.2016.0306〉 Handle: RePEc:hal:journl:cea-01568435 DOI: 10.1098/rsif.2016.0306 Note: View the original document on HAL open archive server: https://hal-cea.archives-ouvertes.fr/cea-01568435 Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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