Land Use Planning Tools Lecture 2: Land use in the

Monocentric and Multicentric Cities

Adapted from Arthur O’Sullivan, Urban Economics, chapters 8-9

Notes by Austin Troy

Bid Rent of Firms in the CBD

• Let’s assume a traditional 19th Century city:– Central railroad freight terminal– Central market– Workers travel to center via streetcar– Goods go from factory to railroad via horse cart– Also assume fixed factor production

Bid Rent of Firms in the CBD

• Profit fn looks same as in chapter 7 = PQ-NC-TC(d)-R(d)

– Profit= price*quantity – nonland costs- transport costs (function of distance) – rents (function of distance);

– TC(d)= cost/ton/mile* distance*quantity

– Then R(d)= PQ-NC-TC(d)

Freight Costs and Rents

• Freight costs decrease with proximity to city center

• Through leftover principle, rents increase as transport costs decrease

• Hence, there will be a downward sloping bid rent function; it will be linear for fixed factor producers and convex for flexible producers

Flexible versus fixed producers

Fixed: R(d)= P*Q-NC-TC(d)Flexible: = P*Q-NC-TC(d)-R(d)*L(d),Where L(d) is amount of land used at

distance d; this results in rent function:R(d)= (P*Q-NC-TC(d))/L(d)Flexible farmer substitutes nonland for

land input: spends more on equipment and labor as land gets more expensive

Flexible versus fixed producers

Flexible produce = factor substitution = lower costs* = higher profits

By leftover principle, higher profits= higher bid rents

Close to city center, land costs are lower; at periphery, freight costs are lower

Monocentric city firms’ bid rent function

Distance from export hub

Bid Rent Fixed-factor

producer

flexible producer

A

B

The flexible firm outbids the fixed factor firm everywhere but point u’’. At u’, the fixed factor producer uses too much land

u’ u’’

Nonland versus land inputs for the Flexible producer

Land Amount

Non-land inputs

flexible producer

A

B

Most central firm type: offices

• Office firms: require 1) lots of meetings and face to face contact, 2)ability to gather, process and distribute information quickly and 3)access to services, like printing, lawyers, designers, accountants, etc.

• This type of firm will have a steep bid rent function because the travel cost of individuals is very high; travel cost is high because their pay rate is high, since it is generally skilled work

Land use in CBD

• All firms are attracted to center, but only some will be willing to bid enough

• Office firms have steepest bid rent fn, and will occupy the most central land

• Market allocation is efficient, because the office industry has the most to gain from being in the center; manufacturing could gain too, but not as much, so it’s willing to locate a little further out.

Office vs. manufacturing

• Suppose office firm 1 block from center and manufacturer 5 blocks. If they swapped locations, this would dramatically increase the office firm’s travel cost– Office firm TC= 3min/block*$4/min*200

meetings/month= $2400 per block/month

• So the swap increase TC for office by $9,600/mo, but only saves the manufacturer $800/month in transportation costs (50 tons * $4/ton/block= $200/block).

Multiple land use rent gradient

Office zone

Manufacturing

zone

Residential

zone

Distance to center

Bid Rent

Office Bid rent

Manuf. Bid rent

Residential bid rent

U’ U’’

Locational choices

Office Zone

Residential Zone

Manufacturing Zone

U’

U’’

Locational choices

Office Zone

Residential Zone

Manufacturing Zone

U’

U’’

So workers live on the periphery because they are cheap to transport (i.e. commuting costs are low) relative to cost of moving freight (for manufacturers). For offices, same problem, because of high price of moving executives around for meetings. If office is in suburbs, executive is constantly going to CBD

Who occupies what?

• Activities are arranged according to transport costs; those with the highest costs occupy the most central land

• Activity with the highest transport cost will have the highest bid rent curve

• All firms have tug-of-war between locating centrally to keep transport cheap, and locating in the suburbs to keep workers’ commute cost lower (and hence pay lower wages)

• CBD wins because cost of freight hauling greater than cost of moving workers

Housing price function

• In the monocentric model, residents will be attracted towards the center but be outbid by offices and manufacturing.

• Assume no factor substitution, identical 1000 sq ft houses, fixed budget of $300/mo for housing+commuting, commute cost (CC)= $20/mi.

• WTP for housing = $300- CC.

Housing price fuction

P housing/ sq ft

$.3

$.18

$.06

6 mi 12 mi

D for housing near center pushes up price until rent= budget-CC.

Residents now indifferent among all locations in city

Housing price function with consumer substitution

• With consumer substitution, residents consume less land as price of land goes up; instead consume more local amenities

• Hence, more central homes are smaller• Flexible residents will outbid fixed factor

residents everywhere but tangency point• Change in P due to distance= , or

negative of (tranpo cost/mi divided by amount of housing consumed)

)(uH

t

u

P hh

Residential housing price function with consumer

substitution

P housing/ sq ft

$.3

$.18

$.06

6 mi 12 mi

Price w consumer sub

Residential bid rent function and factor subsitution

• Residents’ housing price fn with consumer substitution drive producers’ factor substitution

• Factor Substitution: Housing producers substitute capital for land as move closer to center; higher density allows residential housing firms to pay the higher cost of land in more central locations. Different from consumer substitution

• Producers’ bid rent functions are convex because of consumer substitution in the housing price function

Density increases towards center because:

• Consumer substitution in housing pr fn. – P(housing) goes down away from center, so

households consume more housing (i.e. larger dwellings) towards periphery

• Factor substitution in producer bid fn– Price of land goes down as move away because

of housing price function; housing production firms respond by using more land per unit of housing (less density) towards periphery; towards center they respond with greater density

Changes to Residential Model

• All the following changes in assumptions make cost of commuting greater, and housing price fn/residential bid rent fn steeper:– No time cost to commuting (only monetary cost)>>

time cost to commuting (opportunity cost)– Amenities (shopping, recreation) etc. are evenly

distributed across city>> Amenities concentrated in the CBD

– All households one earner>>two earners commuting to center

Spatial heterogeneity

• In reality (we’ll get to this later) there is considerable variation in services and amenities throughout urban area

• Schools: suburban areas often have best schools and people will bid up price of housing to live in those districts.

• Same idea with environmental quality, scenic values and tax rates

Income segregation• Simple monocentric model would suggest that rich

occupy most valuable (central) land• Why is it the opposite?• Households find location providing best tradeoff

between land and commuting cost• Because the rich person consumes much more

housing, they save much more for each move out

Income segregation

• In other words, MB=MC at much closer point to CBD for the poor

• They have less to gain from moving outward because they can’t afford to consume nearly as much housing (that is, as big houses)

• But their commuting costs are not much less than that of the rich

• As income increases, housing consumption increases faster than commuting costs

Segregation and Income Elasticity

• Income elasticity of demand for housing is high; that is, housing consumption goes up significantly (is elastic) in response to income increase

• When IEDH is large relative to income elasticity of commuting cost, gap between MB curves will be much greater than gap between MC curves

Income segregation-High IEDH relative to IECC

MB(poor)

MB(rich)

MC(poor)

MC(rich)

U’ U’’

$20

$40

Income segregation- similar IEDH relative to IECC

MB(poor)

MB(rich)

MC(poor)

MC(rich)

U’’

$20

$40

Empirical Evidence

• One study (Wheaton 1977) has found that IEDH is roughly equal to IECC

• If this is the case, then different income groups should be living in the same places

• Other explanations needed

Other Explanations for Income Segregation

• Newer housing in suburbs: quality is higher, more modern, lower maintenance; poor get stuck with older central city housing

• “Urban flight:” crime, low school achievement, fiscal problems all more common in city centers. Rich can afford to leave

• Large-lot suburban zoning: very common, keeps price of housing high and poor out

Income Segregation and Bid Rents

u*

BR-rich

BR-poor

Rich BR is flatter:

1.If IEDH > IED of commuting costs or

2. because of the draw of suburban land and the negatives of central city living

Exceptions

• In some cities, especially in Europe, the opposite is true: rich live in center, which is prohibitively expensive for poor, who live out in suburbs.

• Has to do with level of amenities in the city center (e.g. Paris vs. Detroit).

Why do poor have steeper housing price functions?

• Slope function

• Increase in income both t and H(u)• If D for housing is more responsive to income than

commuting costs are to income (due to increase in opportunity cost), then rich have flatter curve;that is they have a powerful urge to consume land

• But if Wheaton’s results are correct, the slopes should be the same, so what’s up??

)(uH

t

u

P hh

Alternative Explanation

• Slope of housing price fn must be affected by other factors, such as:– Tax rates, school quality, pollution, crime

• Central city problems cause demand for suburban land to go up

• If IED for low pollution, low crime, good schools, etc. is high relative to IED for commuting, then wealthy will have flat fn

• That is, wealthy willing to pay more for these goods than the poor are and will outbid them on fringes

Policy Ramifications

• Policies that help rebuild the inner cities, bring amenities, decrease crime and pollution, improve schools, will bring some wealthy back from suburbs

• Policies that limit exclusionary (large-lot) zoning will help bring poor out to suburbs and allow for higher suburban densities

Policy Intervention: Labor and land markets

• What happens to business and residential location if we put in a streetcar system?

• Assumptions: no consumer or input substitution (fixed factor), population density the same at all residential locations, business density same in business locations, city is rectangular

Relative Locations before streetcar

Business bid rent fn

Residential bid rent fn

Agricultural rent

Business zone Residential zone ag zone

Bid rents

Distance2 mi 9 mi

Now add a streetcar system

• Streetcar decreases commuting costs, tilts residential bid rent fn outwards

• Residential area expands into ag land• Labor supply increases with S(housing)• Increase in labor S decreases wage• Wage decreases causes intercept of residential fn to

shift down, while business bid rent fn shifts up, because costs are lower

• Lower costs mean firms willing to pay more for CBD land, businesses occupy more land

Relative Locations before streetcar

Business zone ag zone

Business bid rent fn

Residential bid rent fn

Agricultural rent

Residential zone

Bid rents

Distance2 mi 9 mi

Effect of reduced commute cost

Business zone ag zone

Business bid rent fn

Residential bid rent fn

Agricultural rent

Residential zone

Bid rents

2 mi 17 mi

Effect of reduced wage on residential bid rents

Business zone ag zone

Business bid rent fn

Residential bid rent fn

Agricultural rent

Residential zone

Bid rents

~2.5 mi 13.5 mi

Effect of reduced wage on residential bid rents

Business zone ag zone

Business bid rent fn

Residential bid rent fn

Agricultural rent

Residential zone

Bid rents

3 mi 13.5 mi

Long term equilibrium effects

• Eventually, the shrinking of the residential area brought about by lower wages reduces labor supply, while demand for labor goes up in response to larger business district.

• End result: residential and business districts are now in between original size and largest size following short-term effects; land rent is higher everywhere

Are there any welfare benefits from streetcar in long term?

• No: commuting is more efficient, but wages are lower and rents are higher in response; this is because it is an “open city.” We assume that any advantages brought about by upgrade are quickly eliminated by in-migration; migration stops when there are benefits offset the costs (lower wages, higher rents).

Spatial distribution in modern, multicentric cities

• Jobs are generally far from city centers now

• 40% commute from suburban home to suburban job

• Cities are increasingly decentralizing with smaller portion of population in center

• As population shifts outward, density gradients have decreased significantly

Why are we decentralizing?

• Rising income? This will cause decentr. If IED for housing> IE of commuting. Some studies support this

• Lower commuting costs due to better roads, better cars, transit systems

• Urban problems: old housing, income/racial mix, fiscal problems, crime, education– There is considerable empirical support for this

Why decentralized manufacturing?

• Intracity truck: in tug of war between desiring to be near workers and be near central export node, the latter began to lose out as trucks reduced price of getting freight to and from the node. I.e. cost of moving freight high relative to moving people in old days; now the opposite

Why decentralized manufacturing?

• Intercity truck: truck is now competitive with trains and shipping, making central export node less relevant. This decreased freight costs associated with suburban settings. The biggest single factor increasing cost effectiveness of intercity truck was interstate highway system.

• Now manufacturers locate close to suburban highway interchanges. Beltways maximize access to interstates; result in manufacturing ring

Suburban manufacturing without truck

Freight cost

labor cost

Total cost

i=ideal location w/out truck

Distance

$

Firm locates at city center

Suburban manufacturing with truck

Freight cost

labor cost

Total cost

j=ideal location with truck

Distance

$

Firm locates at city center

Manufacturing bid rent and beltways

Additional factors pulling manufacturing towards suburbs

• Single story plants using assembly line production; require more land than traditional multi story plants

• Airports: require a lot of land and tend to be on fringes; many firms transport by air freight

• Cars: with demise of hub and spoke streetcar system, firms now locate where they are most reachable by car: highway exits.

Offices drawn to suburbs by

• -Decoupling of operations: increase in splitting offices into front and back offices

• Better communication and connectivity: email, phones, Internet, teleconferences

• Many businesses now are less reliant on face to face meetings

• However, there will always be advantage to downtown clustering for certain types of firms that require face to face contact