4_Monocentric Model: Housing Developers Flashcards
What does locational equilibrium imply about people’s utility?
People must receive the same utility at all locations, meaning they are indifferent between different locations.
How does housing price vary with distance from the central business district (CBD)?
Housing prices must be higher near the CBD in equilibrium.
Why do housing prices work with commuting costs in locational equilibrium?
Higher housing prices balance commuting costs to keep people on the same indifference curve.
What equation represents the locational indifference condition?
𝑑𝑃(𝑥)/𝑑𝑥 = −𝑡ℎ(𝑥)
What does the slope of bid-rent function represent?
It represents the rate at which rent decreases as distance from the CBD increases.
What two factors influence rent changes with distance?
Commuting costs (𝑡) and housing consumption (ℎ(𝑥)).
How do economists incorporate the cost of commuting into bid-rent?
They include both the pecuniary cost (bus fare, gas) and the time cost of commuting.
How do economists value time spent commuting?
They equate the opportunity cost of time with the hourly wage.
Why must rents fall as distance from the CBD increases?
To compensate for the increased commuting costs and keep people indifferent across locations.
How does housing consumption change with distance from the CBD?
It increases as land prices decline.
How does non-housing consumption change with distance from the CBD?
It decreases as more income is spent on transportation.
What is the key trade-off in the monocentric city model?
A trade-off between commuting costs and housing costs.
What is the profit function for housing developers?
𝜋 = 𝑃ℎ(𝑥)ℎ(𝐾,𝐿) − 𝑝𝐾𝐾 − 𝑅(𝑥)L(𝑥)
How do developers determine the bid-rent function for land?
By solving for 𝑅(𝑥), which is given by: 𝑅(𝑥) = 𝑃ℎ(𝑥)ℎ(𝐾,𝐿) − 𝑝𝐾𝐾𝐿(𝑥)
Why don’t developers only build near the CBD?
If they all did, prices would increase, making it less profitable.
What happens to land rents in the suburbs compared to the central city?
Land rents are lower in the suburbs to compensate for lower revenues.
How do developers adjust their input use based on location?
In the city, developers use more capital and less land, while in the suburbs, they substitute toward more land.
Why are buildings taller in the city than in the suburbs?
High land prices in the city encourage developers to use more capital (taller buildings) instead of land.
How does population density compare between the city and suburbs?
The city has a higher population density due to more people per square foot.
What is the primary reason for higher density in central cities?
More capital-intensive development (taller buildings with smaller dwellings).
What is locational equilibrium?
A state where people receive the same utility at all locations, making them indifferent between different locations.
What must happen to housing prices near the Central Business District (CBD) in equilibrium?
They must be higher to compensate for lower commuting costs.
How do housing prices and commuting costs interact to maintain locational equilibrium?
Higher housing prices work with commuting costs to keep people on the same indifference curve.
What condition must hold for locational indifference?
The marginal benefit of a shorter commute must equal the marginal cost of higher rents.
What is the key equation for the bid-rent function?
𝑑P(x)/𝑑x = −𝑡ℎ(x)
What happens to prices as we move further from the CBD?
Prices must fall to compensate for increased commuting costs.
What is a compensating differential in this context?
A lower housing price at more distant locations that offsets the disadvantage of a longer commute.
What does the slope of the bid-rent function indicate?
How rents change with distance from the CBD.
What two factors influence the slope of bid-rent?
Commuting costs 𝑡 and housing consumption ℎ(x).
Why is the slope of bid-rent steeper near the CBD and flatter further away?
Near the CBD, people need a large rent reduction to move outward, while further away, a smaller reduction is sufficient.
Why is bid-rent higher with substitution?
When substitution is allowed, renters can adjust housing consumption, maintaining higher per-unit bid prices.
How does housing consumption change with distance from the CBD?
It increases as people move further away since land is cheaper.
How does non-housing consumption change with distance?
It decreases as people allocate more income to commuting costs.
What two factors combine to produce housing in the monocentric model?
Land (L) and capital (K).
What is ignored in the housing production function?
Labor.
What decision do producers make regarding land?
They decide where to build housing but do not occupy land themselves.
What is the formula for the bid-rent function for land?
𝑅(x) = 𝑃ℎ(x)h(K,L) − 𝑝K
What does 𝑅(x) represent?
The developer’s bid-rent for land.
Why must land rent decrease with distance from the CBD?
Because housing prices 𝑃ℎ(x) decline as distance increases.
Why don’t developers only build near the CBD?
If all developers built near the CBD, housing supply would increase, driving down prices.
What must happen to land prices for developers to be indifferent across locations?
They must be higher near the CBD to offset the higher revenue per square foot.
What happens to land prices relative to capital as distance to the CBD decreases?
Land becomes more expensive relative to capital.
How do developers respond to higher land rents in the city?
They substitute capital for land, building taller buildings.
What two main inputs do developers use in housing production?
Land (L) and capital (K).
What is an iso-cost curve?
A line showing all possible combinations of land and capital that result in the same total cost.
What is an iso-quant curve?
A curve showing different combinations of inputs that yield the same level of housing output.
What determines the slope of the iso-cost curve?
The relative prices of land and capital.
How does building height differ between the city and suburbs?
Central-city buildings are taller because developers substitute capital for expensive land.
What happens to price per square foot as distance from the CBD increases?
It falls.
Why is population density higher in the central city?
Tall buildings with smaller dwellings accommodate more people per square foot.
What is the relationship between building height and population density?
Taller buildings lead to higher population density.
How do developers adjust their use of land and capital between the city and the suburbs?
In the suburbs, developers substitute away from capital and toward land, as land is cheaper.
What happens to the slope of the iso-cost curve as we move from the city to the suburbs?
The slope becomes flatter in the suburbs, indicating lower land prices relative to capital.
How does capital intensity differ between city and suburban developers?
The central city developer is more capital-intensive (K0) than the suburban developer (K1).
Why do city developers use more capital than suburban developers?
Because land is more expensive in the city, developers substitute toward capital, leading to taller buildings.
What is the implication of higher capital intensity in city development?
Buildings in the city are taller compared to suburban developments.
How do developers adjust their use of land and capital in the city versus the suburbs?
Developers in the city face higher land rents, so they substitute towards more capital and less land, resulting in taller buildings. In the suburbs, where land is cheaper, developers use more land and less capital, leading to shorter buildings.
Why does the central-city developer use more capital than the suburban developer?
Since land is more expensive in the city, developers compensate by using more capital, which allows for taller buildings.
What does the slope of the iso-cost curve represent in this context?
The slope represents the ratio of land rent to capital cost (−Rp/K), showing that in the city, land is more expensive relative to capital, while in the suburbs, land is cheaper, leading to different building heights.
What two inputs are combined to produce housing in the monocentric model?
Land (L) and Capital (K).
Who owns the land in the monocentric model?
Out-of-town property owners.
Do producers occupy land in this model?
No, they decide where (x) to build housing.
How is the bid-rent function for land expressed mathematically?
R(x)=P h(x)h(K,L)−p K K L(x)
What does R(x) represent?
The developer’s bid rent for land.
How does the slope of the bid-rent function behave?
dR(x)/dx=h(K/L) dP h(x)/dx<0, meaning it decreases with distance from the CBD.
Why don’t developers only build near the Central Business District (CBD)?
Prices near the CBD would increase, making developers indifferent across locations.
How does land price change with distance from the CBD?
Land prices need to be higher near the CBD to make developers indifferent across locations.
Why must land rents be lower in suburban locations?
Suburban locations offer lower revenue per square foot compared to central-city locations.
What offsets the disadvantage of lower revenue in the suburbs?
The decline in P h(x) (price per square foot of housing) as distance increases.
How does land rent change with distance from the CBD?
It declines as distance from the CBD increases.
What happens to land input costs as distance from the CBD decreases?
Land becomes more expensive relative to capital.
How does this affect developers’ production decisions?
Developers substitute capital for land by constructing taller buildings in central areas.
What is an iso-cost curve?
A line representing different combinations of land and capital that result in the same cost.
What does an iso-quant represent?
Different combinations of inputs (K and L) that yield the same level of housing production.
How do developers’ capital and land usage differ between central cities and suburbs?
City developers use more capital and less land; suburban developers use more land and less capital.
Why are buildings taller in central cities?
Higher land costs force developers to build upward using more capital.
What happens to the price per square foot of land as distance from the CBD increases?
It falls.
What happens to building height as distance from the CBD increases?
It decreases.
How is population density measured?
As the number of people per square foot.
How does housing differ between central-city and suburban locations?
Central-city locations have taller buildings with smaller dwellings, while suburbs have shorter buildings with larger dwellings.
Where is population density higher?
In the central city.
