Quiz1.
md 2025-03-03
Hengyu Fu: I'm taking a course about urban economics. In this slides, we talk about the relationship
between the housing prices and the distance from CBD. Please using the knowledge of urban economics to
prove housing prices would decrease with distances from CBD.
Deepseek: In urban economics, the monocentric city model explains why housing prices decrease with
distance from the Central Business District (CBD) through the interplay of commuting costs, spatial
equilibrium, and housing consumption trade-offs. Hereʼs a step-by-step proof:
1. Key Assumptions of the Monocentric Model
All jobs are concentrated in the CBD.
Households are identical in income and preferences.
Commuting costs increase linearly with distance from the CBD.
Spatial equilibrium: Utility is equal across locations (no household gains by relocating).
2. Budget Constraint and Trade-offs
A householdʼs disposable income is allocated to: $$ \text{Income} = \text{Composite Goods} +
(\text{Housing Price} \times \text{Housing Quantity}) + \text{Commuting Cost} $$
Commuting cost rises with distance $x$: Commuting Cost $ = t \cdot x $.
To maintain spatial equilibrium, households farther from the CBD must compensate for higher
commuting costs by spending less on housing per unit area.
3. Spatial Equilibrium and Housing Prices
If housing prices ((p)) were constant across locations, households closer to the CBD would have
higher disposable income (due to lower commuting costs), enabling them to consume more housing
and composite goods. This violates spatial equilibrium.
Result: Housing prices must decrease with distance ((x)) to offset rising commuting costs.
Households farther from the CBD pay less per square meter but consume larger dwellings, ensuring
utility remains equal everywhere.
4. Bid-Rent Theory
Proximity to the CBD is valuable because it reduces commuting costs. Households bid more for
central locations, driving up land and housing prices near the CBD.
As distance increases, the willingness to pay for housing declines, lowering prices.
5. Housing Production
Developers maximize profits by building taller (higher floor-area ratios) on expensive central land.
This increases housing supply per unit land area but raises prices per square meter.
In peripheral areas, lower land prices allow for less dense (shorter) buildings, reducing housing prices
per square meter.
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Quiz1.md 2025-03-03
6. Empirical Regularities
The model predicts (and data confirm):
Higher housing prices near the CBD (e.g., Beijingʼs Ring One vs. Ring Five).
Larger dwellings in suburbs (lower (p) offsets higher (x)).
Declining building heights and population density with distance.
Conclusion
The inverse relationship between housing prices and distance from the CBD arises from:
. Commuting cost compensation: Lower (p) offsets higher $t \cdot x$.
. Spatial equilibrium: Equal utility across locations.
. Bid-rent dynamics: Proximity commands premium pricing.
Thus, housing prices decrease with distance from the CBD to maintain equilibrium in household utility and
market incentives.
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