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.