RE5004 Chap.7 Monocentric Cities and Rent Gradients
Monocentric Cities and Rent Gradients
Price distance through indifference
With employment in the CBD and one land unit per household, rent falls by commuting cost per distance unit. The intercept is wage minus required utility, and zero edge rent closes city size and population.
Relax the fixed-lot assumption
When households choose land consumption, lower suburban rent induces larger lots.
Rent remains decreasing but becomes convex, while density falls with distance because it is the reciprocal of lot size.
Close the fixed-land benchmark
The rent schedule keeps identical households indifferent across occupied locations: extra commuting at distance is offset by lower land rent. Outside land rent fixes the boundary, and symmetry plus one household per land unit converts that distance into population.
Wage, required utility, commuting cost and the boundary condition are inputs in this stripped model; rent and the city edge adjust jointly.
Keep model versions separate
Once households choose lot size, the same travel increment is spread across more land at distant locations. The rent curve still falls but becomes flatter outward, while larger lots imply lower density.
The straight-line formula and constant-density population rule no longer apply without the fixed-lot assumption. State the version first, then use algebra, curvature and density relationships that belong to that closure.
What this chapter covers
- 01
Spatial indifference
- 02
Linear rent gradient
- 03
CBD intercept
- 04
City edge and population
- 05
Endogenous lot size
- 06
Convex rent and density gradients
Worked example · free
Solving an illustrative linear city
- 2Find the intercept.
- 2Solve zero edge rent.
- 2Use symmetry for population.
Key terms
- Monocentric City
- A city model with employment concentrated in one CBD.
- Spatial Indifference
- Equal utility across occupied locations after rent and commuting adjust.
- Rent Gradient
- The decline of land rent with distance from the centre.
- City Edge
- The location where urban bid rent meets outside land rent.
- Density Gradient
- The decline in households per land unit with distance.
Monocentric Cities and Rent Gradients FAQ
Why does rent fall with distance?
A more distant household pays greater commuting cost. Rent must fall enough to preserve the required utility, so accessibility is capitalized into the spatial rent pattern. This is an equilibrium result from competition for locations, not an administrative rule that landlords subtract travel bills. Under the fixed-lot assumptions, the decline per distance unit equals the commuting cost parameter.
What determines the city edge?
Under zero outside land rent, the edge is where wage minus required utility is fully absorbed by commuting cost. Higher commuting cost contracts the edge under fixed wage and utility. If outside land rent is positive, the boundary occurs when urban bid rent meets that amount and moves inward. Always substitute the solved edge back into the boundary condition before using symmetry to infer population.
Why is the richer rent curve convex?
Distant households consume larger lots at lower rent. The slope equals commuting cost divided by lot size, so its absolute value becomes smaller outward and the decreasing curve flattens. The second derivative is therefore positive even though the first derivative remains negative. Density falls because it is the reciprocal of land consumption, linking curve shape and household choice in the same mechanism.
How does positive outside land rent change the city edge?
The boundary occurs where the urban bid-rent schedule meets outside land rent rather than zero. Because some wage-utility surplus must now cover the competing rural use, the one-sided edge lies closer to the CBD than under zero outside rent, holding other inputs fixed. Substitute the new boundary into the household budget before inferring occupied distance or population.
Assessment move
Derive the fixed-lot model from the household budget, verify two locations and only then relax lot size. Never use the straight-line edge formula after switching to the richer model. Begin each solution with a version ledger: one CBD, identical households, fixed or chosen land consumption, outside land rent and symmetry.
For a numerical benchmark, calculate the CBD intercept, solve the boundary, substitute it back and test spatial indifference at one interior location. Check units so commuting cost per distance produces a rent flow per land unit. For comparative statics, distinguish rotation from shift: a change in commuting cost changes the slope, while wage or required utility changes the intercept.
When lot size becomes endogenous, replace the constant slope with commuting cost divided by land consumption and link larger outer lots to lower density. Sketch rent and density together to catch reversed curvature. End by explaining how accessibility is capitalized into land value and by naming any planning or infrastructure constraint that the benchmark holds outside the model.
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