5_Intercepts in the Monocentric model Flashcards
What does the slope of the bid-rent curve represent?
It represents how rent changes with distance from the central business district (CBD), but not the actual rent levels.
What determines the height of the bid-rent function?
The height is influenced by commuting costs, the number of households, building technology, and the value of land under its next best use.
Rent levels are reflected in the height of the bid rent curve
How does land rent change with distance from the CBD?
Land rent decreases as distance from the CBD increases, eventually reaching an alternative value like agricultural rent.
What happens to land rent at the urban boundary?
It equals the agricultural rent (or some alternative land use rent).
What factors determine land rent at the CBD?
Land rent at the CBD is a function of agricultural rent, commuting costs, and the number of people (R(0) = rₐ + tN).
How is the residential bid-rent function related to land rent?
The height of the residential bid-rent function is determined by the land rent function: P(x) = c(R(x)).
How does residential bid-rent change with distance from the CBD?
It declines, similar to land rent, reflecting decreasing willingness to pay for central locations.
What does the function P(0) = c(rₐ + tN) represent?
It expresses the bid-rent at the city center as a function of agricultural land value, commuting costs, and population.
What are the two main predictions of the monocentric model regarding development?
As distance to the CBD increases, (1) price per square foot for land falls, and (2) building height decreases.
Why is population density higher in central cities?
Central-city buildings are taller with smaller units, while suburban buildings are shorter with larger units.
In the context of the monocentric model, the height of the bid-rent function 𝑃(𝑥) is determined by:
Commuting costs
* The number of households
* Building technology
* The value of land under the next best use (i.e. the agricultural rent)
What determines this intercept of the agricultural rent?
The land rent exactly at the central business district will be a function of : the agricultural rent 𝑟 ,
𝑎 commuting costs 𝑡, and the number of people N
The height of the developer’s land-rent is:
𝑅 0 = 𝑟𝑎 + tN
Increasing in population (𝑁), value of agricultural land (𝑟a ), and commuting costs
(𝑡)
What does the bid-rent function describe?
The bid-rent function describes how land prices decrease as distance from the central business district (CBD) increases.
What determines the height of the bid-rent function P(x)?
The height of P(x) is determined by commuting costs, number of households, building technology, and the value of land under alternative uses (e.g., agricultural rent).
What equation expresses the developer’s land-rent at the CBD?
R(0)=r_a + tN, where r_a is agricultural rent, t is commuting cost, and N is the number of people.
How does the height of the residential bid-rent function relate to developer land rent?
P(0)=c(R(0))=c(r_a + tN), where c(⋅) is the unit cost function.
Why does bid-rent decline with distance from the CBD?
As distance from the CBD increases, commuting costs rise, leading to lower land values and rent.
What happens to land rent at the urban boundary x̄?
It equals the agricultural rent: R(x̄)=r_a.
What factors determine the intercept (height) of the bid-rent curve?
The intercept depends on agricultural rent r_a, commuting costs t, and population size N.
What does the function c(⋅) represent in the bid-rent function equation?
It represents the unit cost function that translates developer land rent into residential bid-rent.
How does population growth affect land rent in the CBD?
Higher population increases demand for central land, raising R(0) and P(0).
What does the downward slope of the bid-rent function represent?
It indicates that land rent decreases with increasing distance from the CBD due to declining accessibility and higher commuting costs.
residential bid rent in the mono centric model
residential bid-rent
(𝑃 (0) )
* Let us define a function c(.), which we will call the “unit cost function” is
some montone function
* We required that developers earn zero profits, which we can express as
*𝑃(𝑥)=𝑐(𝑅(𝑥))
* Now we can express 𝑃 0 = 𝑐 (𝑅 (0)) = 𝑐(𝑟𝑎 + tN)
