This document discusses residential land use in a monocentric city with three key points: 1. It analyzes residential land rent through a housing price function and residential bid-rent function under assumptions of no consumer substitution and consumer substitution. 2. It examines two types of residential bid-rent functions - one with fixed factor proportions and one with factor substitution between land and non-land inputs. 3. It describes characteristics of a monocentric city where employment is concentrated in the central business district, resulting in gradients of land rent, residential density, and transport costs from the city center outward.

1. Residential Use of Land
in a Monocentric City
Hannah Faith Enriquez

2. 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

3. 
Assumptions in Residential Land Use:

4. 
HOUSING-PRICE FUNCTION

Price of housing – price per square foot of
housing per month

Ex.
1,000 square-foot house
Household rent – $250 per month
Price of housing – 25 cents/square foot
($250 divided by 1,000 sq. foot)

5. 
2 Types of Housing-Price Function:
a.
Linear Housing Price Function:
No Consumer Substitution
a.
Convex Housing Price Function:
Consumer Substitution

6. 

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

7. Housing-Price Function for a City with Identical Dwellings
(1,000 square-foot): No Consumer Substitution (LINEAR)
$
0.30
Price of
housing per
square foot
A  $300 - housing
 $120 – commuting
B  $180 - housing
0.18
Housing-price function
0.06
6
City center
Miles to city center
12
15

8. 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:
t – commuting cost/mile
H – housing consumption/sq. foot
P – change in price/sq. foot
If:
t = $20
H = 1,000 sq. foot
P=
0.02/sq.foot

9. 
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

10. 
As the relative price of housing increases,
the household substitutes nonhousing
goods

11. Housing-Price Function for a City with Identical Dwellings
: With Consumer Substitution (CONVEX)
$
Housing-price function: no
consumer substitution
0.30
Price of
housing per
square foot
Housing-price
function: with
consumer
substitution
0.12
Distance
to city
center
(miles)
Housing
consumpti
on (sq.
3
400
6
600
9
750
12
1,000
0.06
foot)
3
6
9
Miles to city center
City center
12
15

12. 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:
t
H
P
u
– commuting cost/mile
– housing consumption/sq. foot
– change in price of housing
– distance to city center
If:
u = 9 miles
t = $20
H(u) = 750 sq. foot
Slope =
0.0267/sq.foot

13. 
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

14. 
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 Proportions
b. Housing Firms engage in Factor Substitution

15. 
Residential Bid-Rent Function Equation:
Given:
P – price of housing
u – distance to city center
Q – square feet of housing
T – acres of land
K –nonland cost
u – 6 miles
T – 50
K - 50
consumption
3
R(u) = 1.98
Distance to
city center
(miles)
Housing
400
0.24
6
600
0.18
9
750
0.12
12
1,000
0.06
(sq. foot)
Price of
Housing

16. 
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.

17. 
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.

18. Residential Bid-Rent Function: Fixed Factor Proportions
$
Total Revenue = P(u) times Q
Cost of nonland inputs
Bid-rent Function
City center
u*
Miles to city center

19. 
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.

20. 
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.

21. Residential Bid-Rent Function: Factor Substitution
$
Bid Rent without factor
substitution
Bid Rent without factor
substitution
Bid rent
(per acre)
City center
3
6
9
Miles to city center
12

22. 
Residential Density- population density at
different locations in the city
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
a.

23. 
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

24. Land rent
per acre
Distance from city
center

25. 
Why do all manufacturers and office firms
locate at the CBD?

There are trade-offs:
1. Higher freight costs (transportation
costs)
 2. Lower wages


26. Suburbs
City Center
Low wages
Higher transportation
costs
High wages
Lower transportation
costs
Why?
- Horse-drawn wagons
are slower and more
expensive
Why?
- Workers commute
by streetcar and they
are faster and more
efficient

27. Residential Bid
Rent Functions
Manufacturer
Bid Rent
Functions
Office Bid Rent
Functions
Lowest
transport costs
Higher
transport costs
Highest
transport costs
Slope of Bidrent Function
Flat
Steeper
Steepest
Distance from
City Center
Farthest
Closer
Closest
Transport Costs

28. END