LAND USE in the

MONOCENTRIC CITY

• Monocentric city: Core dominated city• The key feature of the monocentric city: Heavy

concentration of employment in the central core area.

• Today’s most medium sized cities are monocentric.• However, in the typical modern city, employment is

not concentrated in the central area but instead distributed throughout the metropolitan area, with large fraction of employment in the suburban areas.

Our focus: Land use in the central business district (CBD).

We will consider, factories, offices and households.

We will work with the bid-rent functions: 1. Bid rent of factories (manufacturers)2. Bid rent of offices3. Bid rent of households

Bid-rent of manufacturers: 1. Fixed factor proportions:Assumption: Manufacturers produce doors and these firms have

the following properties:

i) Each firm uses one acre of land and $Cd worth of non-land inputs (Labor, capital and materials).

ii) Price of doors (Pd) is fixed.iii) Competitive markets.iv) Door freight costs from factory to the central terminal node:

$td.

Question: How much a door firm willing to pay for an acre of land?

Firms prefer to locate near the railroad terminal to increase their potential profit.

Hence, profit is a function of distance from the terminal (u).

d (u)= Pd. D-Cd-td.D.u-Rd(u)

Since door market is perfectly competitive, competition for land will drive up the price of land where economic profit =0.

This means, price of land is equal to: Pd. D-Cd-td.D.uAfter a firm uses its revenue to pay for its input suppliers, the landowner gets whatever is left. This is called the “left-over principle”.If a particular firm offers to pay a landowner less than the entire gap between total revenue and total non-land costs, the landowner could find another firm to outbid the first firm.

Left-over principle results form this competition between potential land occupants. If we set d (u)= 0, and solve for rent, we get the bid-rent for land by the door industry.

Rd(u)=Pd. D-Cd-td.D.u

Distance to terminal

Freight cost

Total revenue

Nonland Prod. Cost

Size of prod. site(acres)

Pre-rent profit

Bid rent for land

0 - 3000 1000 1 2000 2000

1 200 3000 1000 1 1800 1800

2 400 3000 1000 1 1600 1600

3 600 3000 1000 1 1400 1400

4 800 3000 1000 1 1200 1200

5 1000 3000 1000 1 1000 1000

6 1200 3000 1000 1 800 800

7 1400 3000 1000 1 600 600

8 1600 3000 1000 1 400 400

Bid rent for fixed input proportions technology

•E.g. Each firm produces 50 doors (D) using 1 acre of land and $1000 worth of non-land inputs. If price of doors is $60 per unit and unit freight cost (td) is $4 per unit, what is the bid rent for this firm?Rd(u)=(60)(50)-1000-(4)(50)(u)Bid rent depends on the distance from the terminal (u).Slope of the bid rent function: -td.D=-(4)(50)=-200.Under the assumption of fixed factor proportions, we obtain a linear bid-rent function.

2000

Distance from the central node

Bid rent with fixed factor substitution

Is fixed factor proportions assumption realistic? No…Most production processes are flexible, firms can substitute

nonland inputs for land. With variable factor proportions, firms can adjust their costs.

2. Flexible factor proportions:For such a firm, we should define the profit function as follows:

d (u)= Pd. D-Cd(u)-td.D.u-Rd(u).Td(u)Td(u)= Amount of land usedBid rent for land becomes:

Rd(u)=(Pd. D-Cd(u)-td.D.u)/Td(u)Factor substitution increases profits and according to the left-

over principle, higher profits translate into higher bid rents for land.

Distance to terminal

Freight cost

Total revenue

Nonland Prod. Cost

Nonland Prod. Cost

Size of prod. site(acres)

Size of prod. Site (acres)

Pre-rent profit

Pre-rent profit

Bid rent for land

Bid-rent for land

0 - 3000 1000 1560 1 0.3 2000 1440 2000 4800

1 200 3000 1000 1450 1 0.4 1800 1350 1800 3375

2 400 3000 1000 1350 1 0.5 1600 1250 1600 2500

3 600 3000 1000 1260 1 0.6 1400 1140 1400 1900

4 800 3000 1000 1180 1 0.7 1200 1020 1200 1457

5 1000 3000 1000 1110 1 0.8 1000 890 1000 1113

6 1200 3000 1000 1050 1 0.9 800 750 800 833

7 1400 3000 1000 1000 1 1 600 600 600 600

8 1600 3000 1000 950 1 1.1 400 450 400 409

Flexible bid-rent function lies above the inflexible bid rent function for all locations except u=7. At that distance same factor proportions are used.

Flexible bid-rent function is convex due to factor substitution. By factor substitution, the firms will generate savings in both transportation costs and production costs. As we approach to the export node, bid-rent curve becomes steeper.

Who will occupy the land? Flexible or inflexible firms?Since flexibility translates into lower production costs, higher profits and a higher bid rent for land which, flexible firms will occupy the land.Flexibility also brings efficiency.

Bid-rent of office firms: Office firms provide a variety of goods and services but they

share two important characteristics:

1. They gather and process information.2. Office firms rely on face-to-face contact in this process.

E.g. Loan officers of banks meet with their prospective borrowers to appraise their creditwothiness.Investment advisors of firms meet with their clients to assess their attitudes towards risk and their investment inclinations.

Suppose that office firms in the city provide financial services. The industry has the following characteristics:1.Each firm is based in an office. Output : Financial consultations, ech firm produces F consultations per month.2.Each consultation requires 1 trip from office to city center.3.Pf (consultation price)is fixed.4.Nonland production cost of the office = Cf(u). It varies with the price of land and u (distance to the city center).5.Travel cost of a finance firm: Opportunity cost of workers’ travel between office and clients in the city center.tf.W.F.u= Travel cost for a location u blocks away from the city center.tf: Minutes to walk 1 round-trip block, W: wage/minute

f (u)= Pf. F-Cf(u)-tf.W.F.u-Rf(u).Tf(u)Using the zero profit condition, bid rent for land becomes:

Rf(u)=(Pf. F-Cf(u)-tf.W.F.u-Rf(u))/Tf(u)Only difference from the door company is about the

transportation technology. Transport cost per mile of finance firm depends on the opportunity cost of the firm’s workers (wage).

Convex and negatively sloped bid rent function.

Residential Land UseAssumptions: 1. One member of each hh commutes to a job in the CBD.2. Noncommuting travel is insignificant.3. Public services and taxes are the same at all locations.4. Air quality is the same at all locations.5. All households have the same income and tastes for housing.6. There is a monetary cost of commuting but no time cost; the

opportunity cost of commuting time is zero.

• According to the left-over principle , the bid rent for residential land equals the excess of total revenue of housing producers over total cost.

• Hence, we can first talk about the revenue side of the housing market.

• Price of housing decreases as we move away from the city center.• We will consider two cases: No consumer substitution for housing

and consumer substitution for housing.(i) No consumer substitution for housing: P(h)= Price per square foot of housing per monthThe housing price function indicates how much a hh is willing to pay

per square foot for dwellings at different locations in the city.

• Assume that this hh has a fixed budget of $300 per month to spend on housing and commuting. Monthly cost of commuting is $ 20 per mile per month. How much is the hh willing to pay for dwellings at different locations in the city?

$

Miles to city center

0.30

15

Housing-price function

The linear housing-price function indicates that city’s dwellings are identical; everyone lives in a 1000 sq-foot house regardless of the price of the housing. Only distance form the center matters.

• The equilibrium housing-price function makes residents indifferent among all locations because differences in commuting costs are exactly offset by differences in housing costs. A move of u miles toward the city center generates benefits and costs:

• Benefits: Commuting costs decrease by the change in the distance times the commuting cost: -th. u

• Costs: Housing costs increase by the change in the price of housing consumption: Ph. H

• Household will be indifferent if:-th. u= Ph. H

(ii) Consumer substitution for housing: If the housing consumption depends on price (more realistic);

hhs will consume smaller houses when price is higher.As consumer moves toward the city center, it pays a higher price

for housing and it occupies a smaller dwelling. As relative price of housing increases, hhs substitute nonhousing goods for housing (e.g. Entertainment, restaurant food, etc.).

Assumed consumption pattern:

Distance to city center (miles) 3 6 9 12

Housing consumption (sq. feet) 400 600 750 1000

Ph/sq mile

Miles to city center12

0.06

Now, the trade off between commuting and housing costs becomes: -th. u= Ph. H(u)

Slope of the housing function becomes:)(uH

th

u

Ph

Price function with consumer substitution

Price function without consumer substitution

Residential bid-rent: Residential bid rent indicates how much housing producers are

willing to pay for land at different locations in the city.

According to the left-over principle, housing producers will pay land rent equal to the excess of total revenue over total costs.

Assume that housing is produced with fixed proportions.

Each firm produces Q sq. feet of housing using 1 acre of land and $K worth of capital. When the building is complete, it can be used as either a single dwelling or divided into x units , with each living space equal to Q/x.

h (u)= Ph(u).Q-K-Rh(u)Rh(u)= Ph(u).Q-K

u*

TR=Ph(u).Q

Bid rent function

Miles to city center

$Cost of non-land inputs (K)

Since, price of housing declines as distance increases, TR is downward sloping.

• What happens if we relax the fixed factor proportions assumption?

• This means housing producers substitute K for land through building houses closer together or taller apartment complexes. E.g. Mavişehir, Güzelyalı.

• This decreases production costs and allows housing firms to pay more for land.

• Result: Bid rent function becomes more convex.• Population density becomes higher in the central city.

Land Use in the Central Business District

Income and Location:In many developed countries, recently, the wealthy tend to locate in the suburbs and the poor tend to locate near the city center. Average household income increases as we move away from the city center.

However, the most expensive land is near the city center.

Is this location pattern puzzling? Why should poor occupy the most expensive land?

• The answer lies in the “theory of income segregation” developed by Alonso (1964) and Muth (1969).

• This theory suggests that: “Central locations provide the best trade-off for the poor, while suburban locations provide the best trade-off for the wealthy”.

• E.g.Distance Slope of

housing price function

MB of high income HH

MC of high income HH

MB of low income HH

MC of low income HH

1 0.12 240 40 24 20

2 0.10 200 40 20 20

3 0.08 160 40 16 20

4 0.06 120 40 12 20

5 0.04 80 40 8 20

6 0.02 40 40 4 20

7 0.01 20 40 2 20

Distance from the city center

Housing price function

If a high income hh consumes 2000 square feet of housing, a move from city center to 1 mile out saves $ 240 (0.12 x 2000=240)

MB of moving decreases as distance increases.

Commuting cost of moving 1 mile from the center: $ 40.

Optimum location: MB=MC: 6 miles from the city

If low income hh consumes 200 sq feet of housing, MB=MC occurs 2 miles away from the city center.

Why is this difference between the optimum location of wealthy and poor?If wealthy hh receives an income four times the poor and if the wealthy has a house consumption 10 times the poor ( 2000 sq feet and 200 sq feet); if commuting costs of wealthy is two times the poor (40 vs. 20)…

These indicate that income elasticity for housing is greater than income elasticity of commuting cost. This means, the gap between the benefit curves is greater than the gap between the cost curves.

26

MBw

MCw

MBp

MCp

Distance

Wealthy hhs live farther from the city center.This is the traditional explanation for the pattern of income segregation.

Income and Residential Bid Rent FunctionIncome segregation can also be explained with the housing price

function and the residential bid rent function.

We know that the activity with the steeper bid rent function occupies the land closer to the city center.

Slope of the housing price function in the simple monocentric model:

)(uH

th

u

Ph

An increase in income increases both oppotunity cost of commuting (th) and housing consumption (H). Hence, increase in income has an ambiguous effect on the slope of housing-price function.

If income elasticity of housing is greater than income elasticity of commuting cost, then rich will have a flatter houing price function and a flatter bid-rent function.

Bid rent function of the poor

Bid rent function of the rich

Distance from the cityu*

Poor occupy the land less than u* miles away from the center.

An alternative explanation of income segregation suggests that the slope of the residential bid rent function is affected by other factors:

Problems of the central city (pollution, crime, inferior education, etc.) decrease the slope of the bid rent function. If the income elasticities of demand for safety, clean air, eduction are relatively large, bid rent function of wealthy hhs will be flatter than the bid rent function of poor hhs. In other words, if wealthy are willing to pay much more than poor for safety, clean air, superior education, welathy will outbid poor hhs for land in such areas.

Policy implications for income segregation:• A housing policy that encourages renovation of the

central city housing stock may cause some high-income hh to return to center.

• Polices that decrease poverty decrease crime rate, reduce fiscal problems, etc. Which encourage high-income hh to live in central city.

• Policies that control exclusionary zoning allow poor to move to suburbs.