Land Use Regulation and Municipal Utility

The bid-rent curve assumes competitive free market bidding, unfettered by government regulation: users locate where it is in their best interests to be, based solely on their individual profitability calculus. Such cases are rare in practice. Rather, significant regulation of land use is observed. Regulation comes at a cost. When measured at the municipal level, utility, the economic notion of well-being or improvement in circumstance, is lost when economic agents are constrained by regulation.
The model uses a variant on the Stone–Geary utility function for optimization and comparative statics. In it utility is defined as , where α is the proportion of utility arising from citizens' preference for environmental regulation, ; β is the intensity with which citizens derive negative utility from the appearance of advertising; is the productivity or efficiency of advertising, presumed to be related to the size of commercial signage; and is the tax rate levied on sales which depend on advertising. The controversy surrounds the remaining terms, specifically the difference between the maximum amount of advertising, , and that which is allowed, . Merchants want to be as high as possible, as close to full saturation, , as they can get. This makes the term approach zero. Residents want to be as low as possible, making the difference between the maximum and the allowed advertising as large as possible. The condition may be viewed as "full regulation", the case of no advertising allowed. The conflict is resolved by finding the optimum utility.
The illustration is the culmination of a complete analysis (an additional illustration of part of which is in the source code) that includes showing how maximum utility (the area under the green line) falls to a lesser amount (the area under the red line) as advertising efficiency is reduced by regulation. The arrow points to the difference, utility lost, as the area between these two lines.
  • Contributed by: Roger J. Brown
  • Reproduced by permission of Academic Press from Private Real Estate Investment ©2005


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The plot describes how an aesthetic regulation, modeled here as an ordinance regulating commercial signage, imposes uneconomic constraints on land users, restricting the efficiency of their activities on the land. Most models of social behavior are highly stylized and depend on a set of assumptions. This example is no different. The concept of utility resists quantification in that its cardinal value is unimportant, only its ordinal value matters. The Demonstration illustrates the power of using symbolic logic software to model complex concepts. There is an inherent conflict in property rights over providing municipal services (police and fire protection paid for with sales taxes) and a pleasant environment (absence of large, intrusive signs that generate sales to be taxed). To appreciate the Demonstration you must agree with the notion that the process of optimization in the presence of constraints is an accepted method of resolving conflicts in a civil society based on secular norms.
More information is available in Chapter Two of Private Real Estate Investment and at mathestate.com.
R. J. Brown, Private Real Estate Investment: Data Analysis and Decision Making, Burlington, MA: Elsevier Academic Press, 2005.


Contributed by: Roger J. Brown
Reproduced by permission of Academic Press from Private Real Estate Investment ©2005
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+