Location Theory - Is the Bid Rent Curve Linear?
The bid rent curve for a single user is often modeled as linear. An aggregate of users discloses that the curve is actually convex to the origin because only the portion above any particular crosspoint matters, making the bid rent curve at least piecewise linear. In the limit when the number of users is extremely large, the curve becomes a smooth exponential decay.
The graphics show five different types of users and how they self-select into different areas based on their transportation costs. Moving the sliders changes the transportation costs and the shape of the bid rent surface composed of the upper portions of a number of bid rent curves. Note how small differences in transportation costs result in subtle changes in the bid rent surface. Also, some combinations of changes will completely eliminate differences between some user types as their transportation costs merge.
R. J. Brown, Private Real Estate Investment: Data Analysis and Decision Making, Burlington, MA: Elsevier Academic Press, 2005.