FIN 351 · Real Estate Principles

Bid-Rent Curves and Urban Land Use

See how households and firms turn access costs into location bids—and how the highest bid at each location becomes the final land-rent curve.

Created by Desen Lin · California State University, Fullerton

Learning map

One economic rule, four applications

Move any slider or use an animation button. The calculations, switching locations, and final envelopes update immediately.

1 · Households

Higher commuting cost creates a steeper bid curve and a stronger incentive to locate near the CBD.

2 · City system

A transport improvement changes central rent in a closed city but population and the boundary in an open city.

3 · Production

Revenue net of nonland cost sets the intercept; freight cost sets the slope.

4 · Development

The landowner chooses the building that supports the highest bid per hectare at that location.

Residential setting

1. A linear city with two household types

Walkers face a larger opportunity cost per mile than drivers. Competitive bidding sorts the steeper curve closer to the CBD and joins the two curves into one equilibrium envelope.

Rj(d) = anchor rent − cj × distancecj = hourly wage ÷ travel speed × 2 trips × workdays
City-size assumptions
City boundarysame density on two street sides
Type switchwalkers inside, drivers outside
CBD bidequilibrium envelope
Equilibrium residential bid-rent curveDashed: individual bids · Solid: winning envelope

The number of each household type determines how much of the city it occupies. Bid curves meet at the sorting boundary so households remain indifferent at the margin.

Migration assumption

2. Closed city versus open city

When travel becomes faster, a closed city keeps its households and boundary fixed. An open city instead holds the CBD bid at the outside-market level and adjusts through migration.

Closed: D fixed ⇒ R(0) changes   |   Open: R(0) fixed ⇒ D and population change
Monthly cost/mileinitial → improved
Closed-city CBD bidpopulation and radius fixed
Open-city radius
Adjustment to a transportation changeSame shock, different equilibrium condition

In the open-city comparison, the initial CBD bid is the utility-equivalent rent available in the wider system. Migration expands or contracts the city until that bid is restored.

Production setting

3. Competing producers and the land-rent envelope

Under zero economic profit, each producer can pay its revenue minus nonland and transportation costs. The activity offering more at a location wins the land.

R(d) = (PQ − w − i) − tQ × dIntercept = net revenue before freight · Slope = freight cost per mile
Wheat curve
Peas curve
Switching location
Production bid-rent curvesHighest nonnegative bid determines land use

A steeper curve does not necessarily imply a larger bid everywhere. Land use changes where the two offers intersect; beyond the zero-bid point, that activity cannot profitably occupy land.

Chapter 5 · Example 3

4. Which building should be built?

All three designs provide one hectare of office space. A taller building uses less land but costs more capital. The winning design is the one that supports the highest bid rent per hectare.

Bid rent/hectare = [revenue − nonland cost − capital cost − travel cost] ÷ lot hectares
Building design assumptions
Travel cost
Winning building
Land bid/hectaremaximum across designs
DesignLot haFloorsCapitalTotal land bidBid/ha
Bid rent per hectare by building typeOrange marker: selected distance

The tall design capitalizes scarce central land through more floors. Farther out, lower-density designs can win because saving capital matters more than saving land.

Interpretation

Three ideas to retain

Access is capitalized

A larger cost of distance produces a steeper bid-rent gradient because central locations save more travel resources.

The envelope is the market

Individual curves describe willingness to pay. The highest feasible bid at each location determines rent and land use.

Equilibrium depends on closure

Fixing population versus allowing migration changes which outcome—rent, population, or the city boundary—absorbs a shock.