Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics Land Use...

Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics

Land Use Economics Lecture Notes: Land Rents, Accessibility

and Urban Form

Based on Urban Economics by Arthur O’Sullivan

Notes by Austin Troy


Land Rent vs. Market Value

• Market value: the present value of the stream of rental income generated by land

• Rental Income: the amount the landowner charges to use land; equal to income from land minus costs


What is Present Value?

• It is the maximum amount an investor would be willing to pay for something, given that the investor could safely make i percent returns on an alternative investment (for instance, a savings account, or T-bills).

• It equals, the stream of income, discounted over time


How is PV discounted?• PV takes into account the fact that a dollar

earned 5 years from now if worth less to us now than a dollar earned today

• This is because income put off until later has opportunity cost associated with it.

• A dollar invested in five years is worth less than a dollar invested today

• PV takes into account lost opportunity from that alternative investment


How is PV calculated?

• For $20 yearly stream for 5 years at 10% PV= $20 +$18.18 + $16.53 + $15.04 + $13.70 = $83.45

• For a constant stream of income into infinity, rule simplifies to PV= R/i = $20/.1= $200

• Non-constant income example:• PV= $20 + $24/1.1 + $29/1.21 + $34/1.33…etc.

n

tti

RPV

0 )1(


Market value of land

• Equals PV of annual maximum rental payments that the landowner can charge

• For market value to equal PV: given yearly income R and alternative ROR of i , investor is indifferent between buying the land and investing that money elsewhere

• From here out we talk of land rent in place of price, and assume users of land pay rent


Land Rent and Productivity

• Value of land, and hence land rent derives from productivity

• Earliest model of productivity comes from Ricardo (1821) who looked at land fertility

• Assumptions: fixed inputs/output prices (price takers), zero profit, 3 levels of fertility, land to highest bidder, location (transpo costs) can be ignored, owners are not farmers


Ricardo model

• On fertile land, a farmer can produce same amount of corn with fewer inputs

• The price of this type of land is bid up

• All profit accrues to the landowner in the form of rents

• Payment to farmer is considered a cost


Ricardo model

ATC

MC

Profit=rent>>to landowner

ATC

MC

Profit=rent>>to landowner

160220

ATC

MC

$10

Q=amt of corn

$

“A” land “B” land “C” land

“A” land has lowest production costs= highest rents

“C” land’s rent is 0 because costs are greater than revenue

Price determined exogenously by supply and demand in market

$8

$4


Ricardo Model

• Competition among farmers for good land bids up rents on that land until economic profits* =0 for farmer. All profits on land go to owner.

• Economic profits: greater than “normal” profits required to pay for time of those doing the work

• Rent for A land= TR-TC= $2200-$880=$1320


Leftover principle• In equilibrium, Rent= profits, or revenue over

total nonland costs

• Rent eats up whatever is “left over” because competition for land bids away any excess

• That is, competition among farmers for land bids away excess profits until they are zero and landowner gets all surplus value


Exceptions to leftover principle

• If there is restrictions on entry or on competition– E.g. if farmer (non-owners) owns patent to

farming techniques that reduce costs, landlord cannot charge additional rents reflecting those additional profits because noone else would be willing to pay such high rents


Who benefits from improvement?

• Example: irrigation project• If price of corn is fixed (exogenous) the landlord

benefits because competition among farmers for land will bid away profit

• Winner: land owner; loser: farmer• However, if the project affects the price of corn

(price is endogenous), consumers gain with lower prices, while farmer pre rent profits are reduced, lowering land rents

• Winner: consumer; loser; land owner


Scale of improvement

• Who benefits is determined by scale of improvement

• Smaller the area, the more the benefit goes to landowner; larger the area, more goes to consumers because of price endogeneity

• Benefits from any improvement are capitalized into the value of land; a positive capitalization increases rents, which increases market value

• Negative factors can be capitalized too


Accessibility

• Now replace fertility of land with location as the prime determinant of land value--Von Thunen model (1826)

• No longer assume that transportation is costless

• This model explains why more “central” locations command higher rents and have higher market values than fringe areas


The Carrot Farmer

• Assume: land is equally fertile, profits are zero, there is one central market, p is fixed and farmers use fixed factor production

• Cost is now fn of distance – Transport Cost= cost/ton/mile*dist*Q– Profit= P*Q-PC-TC-Rent = 0 – Rent= P*Q-PC-TC


Carrot Farmer’s bid rent function

Bid rent/acre

$50

$300

Close Distance to market Far

Total Cost

Land rents

Total revenue per acre (P*Q; Q/acre does not vary)

$190

$110

$250


Carrot farmer’s decision

• Now, market-proximate land replaces fertile land as the most valuable type

• However, competition for close land bids away surplus profit so, assuming farmers are identical, they are indifferent among all locations, as long as total revenue exceeds total cost


The farmer and factor substitution

• What if farmers can be different? Then the bid-rent function becomes convex.

• Under linear function, fixed amount of land and non-land inputs, no matter where

• Under convex function, farmers engage in factor substitution: they increase non-land inputs (equipment, labor, technology) as land gets more central and expensive


Bid Rent fn for both farmers

Bid rent for flexible farmer

Bid rent for fixed-factor farmer

Rent/ acre

Distance to market U*


Bid rent of flexible farmer

• Flexible farmer will outbid the inflexible farmer in all locations but u

• That is, land will be used more intensively and, hence, more efficiently at central locations, and non-land inputs will be fewer far away

• With inflexible farmers, land is used more inefficiently

• Rents will still equal profits of highest bidder


Two competing land uses• Different land uses (e.g. SPAM factory and grain

farm) may have different bid rent functions. The shapes of those functions will determine who will locate where

• Steepness of fn determined per unit transport costs relative to per unit price

• As usual, land goes to highest bidder• Market allocates land efficiently to usage with the

most to gain from being close to the market


Determinants of bid rent slope

1. Per acre transportation costs. The more weight you produce/acre, the more transport will cost per acre cultivated. E.g. potatoes vs. cotton

2. Unit transport costs. The more a given unit weight costs to ship, the higher the transport costs. E.g. eggs vs. turnips


Bid Rent fn for both farmers

Rent/ acre

U’

Heavy good

Light good

U’= where heavy use transitions to light use


Multiple land uses 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

Date post:	21-Dec-2015
Category:	Documents
View:	220 times
Download:	0 times

Lecture by Austin Troy University of Vermont, based on Arthur O’Sullivan, Urban Economics Land Use...

Documents