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

2. 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

3. 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)

4. 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

5. 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

6. 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

7. Monocentric city firms’ bid rent function
flexible producer
The flexible firm outbids the fixed factor firm everywhere but point u’’. At u’, the fixed factor producer uses too much land
Bid Rent B
Fixed-factor producer A u’
u’’
Distance from export hub

8. Nonland versus land inputs for the Flexible producer
Non-land inputs B
flexible producer A
Land Amount

9. 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

10. 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.

11. 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).

12. Multiple land use rent gradient
Office Bid rent
Manufacturing
zone
Residential
zone
Bid Rent
Manuf. Bid rent
Residential bid rent
Office zone U’
U’’
Distance to center

13. Locational choices Residential Zone Manufacturing Zone Office Zone U’

14. Locational choices
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
Residential Zone
Manufacturing Zone
Office Zone U’
U’’

15. 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

16. 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.

17. Housing price fuction
$.3
D for housing near center pushes up price until rent= budget-CC.
P housing/ sq ft
Residents now indifferent among all locations in city
$.18
$.06
6 mi
12 mi

18. 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)

19. Residential housing price function with consumer substitution
$.3
Price w consumer sub
P housing/ sq ft
$.18
$.06
6 mi
12 mi

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. Income segregation-High IEDH relative to IECC
MB(rich)
MC(rich)
$40
MC(poor)
$20
MB(poor) U’
U’’

28. Income segregation- similar IEDH relative to IECC
MB(rich)
MC(rich)
$40
MC(poor)
$20
MB(poor)
U’’

29. 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

30. 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

31. Income Segregation and Bid Rents
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
BR-rich
BR-poor u*

32. 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).

33. 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??

34. 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

35. 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

36. 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

37. Relative Locations before streetcar
Business bid rent fn
Bid rents
Residential bid rent fn
Agricultural rent
Distance
9 mi
2 mi
Residential zone
ag zone
Business zone

38. 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

39. Relative Locations before streetcar
Business zone
ag zone
Business bid rent fn
Residential bid rent fn
Agricultural rent
Residential zone
Bid rents
Distance
2 mi
9 mi

40. Effect of reduced commute cost
Business bid rent fn
Bid rents
Residential bid rent fn
Agricultural rent
2 mi
17 mi
Residential zone
ag zone
Business zone

41. Effect of reduced wage on residential bid rents
Business bid rent fn
Bid rents
Residential bid rent fn
Agricultural rent
~2.5 mi
13.5 mi
Residential zone
ag zone
Business zone

42. Effect of reduced wage on residential bid rents
Business bid rent fn
Bid rents
Residential bid rent fn
Agricultural rent
3 mi
13.5 mi
Residential zone
ag zone
Business zone

43. 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

44. 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).

45. 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

46. 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

47. 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

48. 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

49. Suburban manufacturing without truck
Total cost $
i=ideal location w/out truck
labor cost
Freight cost
Firm locates at city center
Distance

50. Suburban manufacturing with truck$
j=ideal location with truck
Total cost
labor cost
Freight cost
Firm locates at city center
Distance

51. Manufacturing bid rent and beltways

52. 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.

53. Offices drawn to suburbs by
-Decoupling of operations: increase in splitting offices into front and back offices
Better communication and connectivity: , 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