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Rational expressions are algebraic fractions in which both the numerator and the denominator are polynomials. These expressions follow the arithmetic rules of numerical fractions but require extra care due to the presence of variables. A fundamental part of working with rational expressions is identifying values that make the expression undefined, typically those that result in division by zero or undefined radicals.Determining the DomainThe domain of a rational expression includes all real...
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Related Experiment Video

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Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street
14:55

Evaluating the Effect of Roadside Parking on a Dual-Direction Urban Street

Published on: January 20, 2023

Urban scaling and the production function for cities.

José Lobo1, Luís M A Bettencourt, Deborah Strumsky

  • 1School of Sustainability, Arizona State University, Tempe, Arizona, United States of America. jose.lobo@asu.edu

Plos One
|April 2, 2013
PubMed
Summary

Urban economic productivity scales with population size, increasing 11% per population doubling in US cities. This finding stems from a new model explaining Total Factor Productivity (TFP) based on social and infrastructural factors.

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Design and Construction of an Urban Runoff Research Facility
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Design and Construction of an Urban Runoff Research Facility

Published on: August 8, 2014

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Last Updated: May 12, 2026

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Design and Construction of an Urban Runoff Research Facility
13:48

Design and Construction of an Urban Runoff Research Facility

Published on: August 8, 2014

Area of Science:

  • Urban economics
  • Economic geography
  • Complexity science

Background:

  • Economic productivity differences in urban areas are challenging to quantify.
  • Existing models struggle to unambiguously identify factors influencing urban economic output.

Purpose of the Study:

  • To derive a microscopic model of urban scaling relations for economic quantities versus population.
  • To develop a new expression for Total Factor Productivity (TFP) in urban areas.
  • To empirically demonstrate the relationship between urban productivity and city population size.

Main Methods:

  • Microscopic derivation of urban scaling relations.
  • Consideration of social and infrastructural properties common to cities.
  • Development of a Cobb-Douglas type production function for economic output.
  • Empirical analysis of contemporary US cities.

Main Results:

  • Urban economic output follows a Cobb-Douglas production function.
  • Total Factor Productivity (TFP) shows a systematic dependence on city population size.
  • Urban productivity increases by approximately 11% with each population doubling in US cities.
  • Deviations from average scaling reveal regularities related to local factors.

Conclusions:

  • Urban productivity is influenced by the interplay of wages and labor, which scale differently with population.
  • High-productivity cities exhibit high wages and high employment relative to their size.
  • The study provides insights into microscopic processes driving urban economic productivity and informs economic growth theory.