8_Comparative Statistics

Question 2

What is a Closed City model?

Answer 2

A model where the number of residents or firms is fixed, with no migration in or out.

Question 3

What is an Open City model?

Answer 3

A model where the number of residents or firms adjusts to keep utility levels constant.

Question 4

What is the main difference between Open and Closed City models?

Answer 4

The Closed City model assumes a fixed population, while the Open City model allows migration to maintain equilibrium.

Question 5

What are some key parameters in the monocentric city model?

Answer 5

Commuting costs (t), agricultural rent (rₐ), population (N, only in Closed City), and income (y).

Question 6

What is the purpose of comparative statics in urban economics?

Answer 6

To analyze how changes in parameters affect equilibrium results in the model.

Question 7

How do we contrast exogenous and endogenous parameters in the monocentric model?

Answer 7

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.

Question 8

How does utility function in a Closed City model?

Answer 8

Utility is constant within the metropolitan area, but it can rise or fall for everyone.

Question 9

How does utility function in an Open City model?

Answer 9

Migration keeps citywide utility levels constant, ensuring equilibrium.

Question 10

Which model is better for understanding land use patterns: Open or Closed City?

Answer 10

It depends—Closed City is better for short-run changes, while Open City is better for long-run consequences.

Question 11

Why is the Open City model useful in the long run?

Answer 11

Because labor supply to a city tends to be very elastic in the long run.

Question 12

What does the monocentric model describe?

Answer 12

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.

Question 13

What is the bid-rent curve?

Answer 13

A graph showing how much different groups are willing to pay for land as a function of distance from the city center.

Question 14

How is the height of the residential bid-rent curve determined?

Answer 14

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.

Question 15

What determines whether the rich or poor live in the central city?

Answer 15

The group with the steeper bid-rent curve occupies the central city.

Question 16

What condition leads to the poor living in central cities?

Answer 16

When t_L/h_L > t_H/h_H, meaning low-income households spend a larger proportion of income on commuting relative to housing.

Question 17

What condition leads to the rich living in central cities?

Answer 17

When t_L/h_L < t_H/h_H, meaning high-income households prioritize reducing commuting costs over increasing housing consumption.

Question 18

How does equal commuting cost affect location choice?

Answer 18

If t_H=t_L=t, housing preferences drive location, and the poor remain in central cities.

Question 19

What is the income elasticity of housing?

Answer 19

ε_hy = dy/y / dh/h, the percentage change in housing consumption due to a percentage change in income.

Question 20

What is the income elasticity of commuting costs?

Answer 20

ε_ty = dy/y / dt/t, the percentage change in commuting costs due to a percentage change in income.

Question 21

What happens if ε_ty < ε_hy?

Answer 21

Households prioritize larger homes over reducing commuting costs, leading the poor to live in central cities and the rich in suburbs.

Question 22

What happens if ε_ty > ε_hy?

Answer 22

Households prioritize reducing commuting costs, leading the rich to live in central cities and the poor in the suburbs.

Question 23

What is the difference between an open and closed city?

Answer 23

• Closed City: Population is fixed, and changes affect all residents.
  Open City: Migration adjusts population to keep utility constant.

Question 24

When is the closed city model useful?

Answer 24

For short-run analysis of income, commuting technology, or government policy.

Question 25

When is the open city model better?

Answer 25

For long-run effects, as migration keeps the city in equilibrium.

Question 26

What happens when transportation costs fall in a closed city?

Answer 26

- The bid-rent curve flattens. Demand for central city housing falls. Developers pay more for land farther out. The urban fringe expands.

Question 27

What happens inside and outside a threshold x_a when transportation costs fall?

Answer 27

- For xx_a: Housing price & land rent increase, building height rises.

Question 28

What is the overall effect of declining commuting costs?

Answer 28

- People move further out. They consume larger homes. The urban area expands and overall utility rises.

Question 29

What does the 'If Rich Can Afford a Car, and Poor Cannot' graph indicate?

Answer 29

- 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).

Question 30

What do the 'Reduction in t' graphs show?

Answer 30

They illustrate how falling transportation costs lead to a flatter bid-rent curve, urban expansion, and increased housing consumption.

Question 31

What does the first graph illustrate about the effect of a reduction in commuting costs (𝑡)?

Answer 31

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.

Question 32

How does a decrease in commuting costs (𝑡₁) affect bid-rent in a closed city?

Answer 32

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.

Question 33

What happens to land rent and housing prices when commuting costs fall in areas closer to the CBD (𝑥 < 𝑥ₐ)?

Answer 33

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

Question 34

What are the effects of falling transportation costs in areas farther from the CBD (𝑥 > 𝑥ₐ)?

Answer 34

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 ## Footnote This shows how reduced commuting costs encourage people to move outward.

Question 35

What is the overall impact of lower transportation costs in a closed city?

Answer 35

People relocate farther from the CBD Housing consumption increases (larger houses) Urban fringe expands Overall utility is higher

Question 36

How do falling transportation costs affect the bid-rent curve in an open city?

Answer 36

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.

Question 37

What happens to population density when transportation costs fall in an open city?

Answer 37

Population density increases as more people move into the city, leading to higher rents and an expanded urban fringe.

Question 38

How does an open city respond differently to falling transportation costs compared to a closed city?

Answer 38

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.

Question 39

How does an increase in agricultural rent affect urban land use?

Answer 39

Higher agricultural rent pushes the urban boundary inward, reducing the land available for residential and commercial use.

Question 40

How does an increase in agricultural rent affect land use patterns in a city?

Answer 40