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Residential Use of Land in a Monocentric City
Hannah Faith Enriquez
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Two steps in the analysis of residential land rent:
Housing-Price Function- indicates how much a household is willing to
pay for dwellings at different locations in the city
Residential Bid-Rent Function- indicates how much housing producers are willing to pay per acre of land at various locations in the city
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Assumptions in Residential Land Use:
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HOUSING-PRICE FUNCTION
Price of housing – price per square foot of housing per month
Ex. 1,000 square-foot houseHousehold rent – $250 per month
Price of housing – 25 cents/square foot ($250 divided by 1,000 sq. foot)
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2 Types of Housing-Price Function:
a. Linear Housing Price Function: No Consumer Substitution
b. Convex Housing Price Function: Consumer Substitution
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Linear-Housing Price Function: No Consumer Substitution
Assumptions:
1. Identical dwellings – every dwelling in the city has 1,000 square feet or living space
2. Fixed budget – the household has a fixed budget of $300 per month ( on commuting and housing costs)
3. Commuting cost – monthly commuting costs are $20 per mile/month
1 mile - $20 2 miles - $40
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Miles to city center
Price of housing per square foot
6
0.06
0.30
0.18
12 15
City center
Housing-price function
Housing-Price Function for a City with Identical Dwellings (1,000 square-foot): No Consumer Substitution (LINEAR)
A
B
$
$300 - housing
$120 – commuting $180 - housing
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Linear Housing Price Function: No Consumer Substitution
a. Households are indifferent among all locations within the city
Why? Because differences in commuting costs are offset by differences in housing costs
Slope: If: t = $20H = 1,000 sq. foot P = 0.02/sq.foott – commuting cost/mile
H – housing consumption/sq. foot P – change in price/sq. foot
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Convex Housing Price Function: Consumer Substitution
A more realistic assumption:◦Household obeys the law of demand:
decreases the quantity demanded as price increases
As a household moves toward the city center, it pays a higher price for housing, so it occupies a smaller dwelling
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As the relative price of housing increases, the household substitutes nonhousing goods
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Miles to city center
Price of housing per square foot
6
0.06
0.30
0.12
12 15
City center
Housing-Price Function for a City with Identical Dwellings : With Consumer Substitution (CONVEX)
$Housing-price function: no
consumer substitution
Housing-price function: with
consumer substitution
93
Distance to city center (miles)
Housing consumpti
on (sq. foot)
3 400
6 600
9 750
12 1,000
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Convex Housing Price Function: Consumer Substitution
a. As the household moves toward the city center, housing consumption decreases, thus increasing the slope of the housing price-function.
Slope:
If: u = 9 milest = $20H(u) = 750 sq. foot Slope = 0.0267/sq.foot
t – commuting cost/mileH – housing consumption/sq. foot P – change in price of housingu – distance to city center
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How rapid does the price of housing decrease as distance to the city center increases?
Housing-Price Gradient: percentage change in the price of housing per mile
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Residential Bid-Rent Function- indicates how much housing producers are willing to pay per acre of land at various locations in the city
2 Types of Residential Bid-Rent Functions:
a. Housing with Fixed-Factor Proportionsb. Housing Firms engage in Factor Substitution
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Residential Bid-Rent Function Equation:
P – price of housingu – distance to city centerQ – square feet of housingT – acres of landK –nonland cost
Given:
u – 6 milesT – 50K - 50
Distance to city center
(miles)
Housing consumption (sq. foot)
Price of Housing
3 400 0.24
6 600 0.18
9 750 0.12
12 1,000 0.06
R(u) = 1.98
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Since P(u) decreases as u increases, R(u) declines as u increases. The bid rent function is convex since the housing price function is convex.
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Bid-Rent Function: Fixed Factor Proportions
The characteristics of the housing industry are as follows:
1. Production - each firm produces Q square feet of housing using land and non-land inputs.Once the firm erects a building, it can be used as a single dwelling (with Q square feet of space) or divided into x units each of which has (Q/x) square feet of living space.
2. Non-land Cost - Firms use (K) worth of non-land inputs for each building.
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Miles to city center
u*
Residential Bid-Rent Function: Fixed Factor Proportions
$Total Revenue = P(u) times Q
Cost of nonland inputs
Bid-rent Function
City center
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3. Fixed Factor Proportions - Each firm produces its house, regardless of the price of land.
4. Housing Prices - the housing price function is negatively sloped and convex (i.e. slope gets steeper as location approaches city center)
5. Perfect Competition - the housing industry is perfectly competitive so each house builder makes zero economic profits in long run equilibrium.
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Bid-Rent Function: Factor Substitution
Involves substituting non-land inputs for land as the price of land increases which means building progressively taller buildings as location approaches city center.
The flexible firm (with factor substitution) is able to produce housing more cheaply than the inflexible firm since the flexible firm uses less of the more expensive input at each location. Thus the flexible firm can always outbid the inflexible firm for land.
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Miles to city center
6
Residential Bid-Rent Function: Factor Substitution
$
Bid Rent without factor substitution
City center3 9 12
Bid rent (per acre)
Bid Rent without factor substitution
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Residential Density- population density at different locations in the city
a. Consumer substitution – price of housing decreases as distance to the city center increases
b. Factor substitution – price of land decreases as the distance to the city center increases
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Monocentric City
2 features:
1. Office firms occupy the central area of CBD (central business district)
2. Employment is concentrated in the CBD, not distributed throughout the city
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Land rent per acre
Distance from city center
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Why do all manufacturers and office firms locate at the CBD?
There are trade-offs:
1. Higher freight costs (transportation costs)
2. Lower wages
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SuburbsCity Center
Low wagesHigher transportation costs
Why? - Horse-drawn wagons are slower and more expensive
High wagesLower transportation costs
Why?- Workers commute by streetcar and they are faster and more efficient
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Residential Bid Rent Functions
Manufacturer Bid Rent Functions
Office Bid Rent Functions
Transport Costs Lowest transport costs
Higher transport costs
Highest transport costs
Slope of Bid-rent Function
Flat Steeper Steepest
Distance from City Center
Farthest Closer Closest
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