8_Comparative Statistics Flashcards
What is a Closed City model?
A model where the number of residents or firms is fixed, with no migration in or out.
What is an Open City model?
A model where the number of residents or firms adjusts to keep utility levels constant.
What is the main difference between Open and Closed City models?
The Closed City model assumes a fixed population, while the Open City model allows migration to maintain equilibrium.
What are some key parameters in the monocentric city model?
Commuting costs (t), agricultural rent (rₐ), population (N, only in Closed City), and income (y).
What is the purpose of comparative statics in urban economics?
To analyze how changes in parameters affect equilibrium results in the model.
How do we contrast exogenous and endogenous parameters in the monocentric model?
Exogenous parameters (e.g., commuting costs, income) are given outside the model, while endogenous features (e.g., P(x), R(x), h(x)) are determined within the model.
How does utility function in a Closed City model?
Utility is constant within the metropolitan area, but it can rise or fall for everyone.
How does utility function in an Open City model?
Migration keeps citywide utility levels constant, ensuring equilibrium.
Which model is better for understanding land use patterns: Open or Closed City?
It depends—Closed City is better for short-run changes, while Open City is better for long-run consequences.
Why is the Open City model useful in the long run?
Because labor supply to a city tends to be very elastic in the long run.
What does the monocentric model describe?
It describes how land use and real estate prices change with distance from the central business district (CBD), assuming all economic activity is concentrated at one point.
What is the bid-rent curve?
A graph showing how much different groups are willing to pay for land as a function of distance from the city center.
How is the height of the residential bid-rent curve determined?
It is given by P(0)=c(r_a+tN), where c(⋅) is the unit cost function, r_a is agricultural rent, t is commuting cost, and N is population.
What determines whether the rich or poor live in the central city?
The group with the steeper bid-rent curve occupies the central city.
What condition leads to the poor living in central cities?
When t_L/h_L > t_H/h_H, meaning low-income households spend a larger proportion of income on commuting relative to housing.
What condition leads to the rich living in central cities?
When t_L/h_L < t_H/h_H, meaning high-income households prioritize reducing commuting costs over increasing housing consumption.
How does equal commuting cost affect location choice?
If t_H=t_L=t, housing preferences drive location, and the poor remain in central cities.
What is the income elasticity of housing?
ε_hy = dy/y / dh/h, the percentage change in housing consumption due to a percentage change in income.
What is the income elasticity of commuting costs?
ε_ty = dy/y / dt/t, the percentage change in commuting costs due to a percentage change in income.
What happens if ε_ty < ε_hy?
Households prioritize larger homes over reducing commuting costs, leading the poor to live in central cities and the rich in suburbs.
What happens if ε_ty > ε_hy?
Households prioritize reducing commuting costs, leading the rich to live in central cities and the poor in the suburbs.
What is the difference between an open and closed city?
- Closed City: Population is fixed, and changes affect all residents.
Open City: Migration adjusts population to keep utility constant.
When is the closed city model useful?
For short-run analysis of income, commuting technology, or government policy.
When is the open city model better?
For long-run effects, as migration keeps the city in equilibrium.
What happens when transportation costs fall in a closed city?
- The bid-rent curve flattens.
Demand for central city housing falls.
Developers pay more for land farther out.
The urban fringe expands.
What happens inside and outside a threshold x_a when transportation costs fall?
- For x<x_a: Housing price & land rent fall, building height decreases.
For x>x_a: Housing price & land rent increase, building height rises.
What is the overall effect of declining commuting costs?
- People move further out.
They consume larger homes.
The urban area expands and overall utility rises.
What does the ‘If Rich Can Afford a Car, and Poor Cannot’ graph indicate?
- The poor, reliant on expensive public transport, live closer to CBD (steeper bid-rent curve).
The rich, who drive cars, live further out (flatter bid-rent curve).
What do the ‘Reduction in t’ graphs show?
They illustrate how falling transportation costs lead to a flatter bid-rent curve, urban expansion, and increased housing consumption.
What does the first graph illustrate about the effect of a reduction in commuting costs (𝑡)?
The graph shows the initial bid-rent curve under high commuting costs (𝑡₀). At this stage, people are willing to pay higher rents closer to the Central Business District (CBD) due to high commuting expenses.
How does a decrease in commuting costs (𝑡₁) affect bid-rent in a closed city?
As commuting costs fall (𝑡₁ < 𝑡₀), the bid-rent curve flattens, indicating a decreased willingness to pay high rents near the CBD. This leads to reduced housing demand in central locations and expansion of the urban fringe.
What happens to land rent and housing prices when commuting costs fall in areas closer to the CBD (𝑥 < 𝑥ₐ)?
Price of housing (𝑃ₕ) falls
Land rent (𝑅) decreases
Ratio of capital to land (𝐾/𝐿) decreases
Consumption of other goods (𝑐) falls
Building height decreases
What are the effects of falling transportation costs in areas farther from the CBD (𝑥 > 𝑥ₐ)?
Price of housing (𝑃ₕ) increases
Land rent (𝑅) increases
Ratio of capital to land (𝐾/𝐿) increases
Consumption of other goods (𝑐) increases
Building height increases
This shows how reduced commuting costs encourage people to move outward.
What is the overall impact of lower transportation costs in a closed city?
People relocate farther from the CBD
Housing consumption increases (larger houses)
Urban fringe expands
Overall utility is higher
How do falling transportation costs affect the bid-rent curve in an open city?
Falling transportation costs cause the bid-rent curve to flatten, but new households move in due to higher utility, shifting the bid-rent curve upward.
What happens to population density when transportation costs fall in an open city?
Population density increases as more people move into the city, leading to higher rents and an expanded urban fringe.
How does an open city respond differently to falling transportation costs compared to a closed city?
In an open city, population increases offset the falling transportation costs, leading to higher rents, whereas in a closed city, people spread out and consume larger homes.
How does an increase in agricultural rent affect urban land use?
Higher agricultural rent pushes the urban boundary inward, reducing the land available for residential and commercial use.
How does an increase in agricultural rent affect land use patterns in a city?
