Week 3 Lesson1

7/28/2019 Week 3 Lesson1

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LECTURE WEEK 3:ECONOMIC

RETURNSOUTLINE OF LECTURE WEEK 3:

Ricardian rent theory Classical rent theory

Urban rent theory


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Ricardian land rent

Ricardo introduced the crucial concepts in the theoryof land rent:

1. Land varies in its natural endowment or advantagefor the user.

2. Land of a given level of natural endowment oradvantage is fixed in supply.

3. The land market is governed by competition amongland users.

4. Land rent is determined by the differences in naturalendowment or advantage of land.

5. Land has single use ( grow corn)


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Ricardian land rent

The supply of land at each location fixed perfectly price

inelastic.

The demand for a particular site quite sensitive, or elastic,

with respect to price.

Numerous competitive sites, or substitutes, exist at adjoining

locations

Determining Rent : Land must be priced at each site so that its

occupant is charged for the value of whatever locational

advantages exist at that site.

Understanding these advantages and how consumers

evaluate them is the key to understanding the usage pattern

of land and housing prices.


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Ricardian land rent

This is a theory of compensating differentials.

Only demand considerations determine the relative

value of land or housing at different locations.

The supply of land does play a role, but only insetting the overall level of prices.

The first theory of land rent by David Ricardo in his

1821 Ricardos focus was on agricultural land.

Useful to study it as a steppingstone to the modern

theory of urban land rent


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Ricardian land rent

The markets for land and housing: completely

productdifferentiated.

Each product sold in the market (every flat or

location) unique.

Urban land a completely differentiated

product.

Difficult to speak about the supply of land or

demand for sites at any particular location


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Ricardian land rent

Imposition of taxes on land will neither

increase rents nor alter the use of land

Price of land is high because the price of corn

is high and not vice versa

So price of land is high because the price (

housing) is high, and not vice versa ( refer

diagram 1 )

So Ricardian argued that price of land and

housing is wholly demand determined, so


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Ricardian land rent

a) rent of land is solely demand determined,

since supply is fixed, variations in rents can

only occur through shifts in the demand curve

DD, so the rent of land is HIGH because the

price of corn is high and not vice versa

b) taxes levied on rents will not alter either

the rent paid or the quantity of land supply


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Ricardian land rent

Supply of land is irrelevant, but supply of land

is under control of the planning authorities

and can be changed

So Ricardian argument is based on assumption

that the supply of land is fixed and

unchangeable. An increase in the amount of

land allowed by the planning system to beused for housing can therefore result in the

price of land & housing


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Agricultural and land rent

Ricardos fundamental insight was thatagricultural land is not all of the same level offertility.

There is a fixed supply of land of the bestfertility, called No. 1 land.

Land with a somewhat lower level of fertility

called No. 2 land, fixed in supply too. Land with even lower levels of fertility (No. 3,

No. 4, etc.) also fixed in supply


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Assume that with equal employment of capital andlabor, No. 1, No. 2, and No. 3 land would yield a netproduce of 100, 90, and 80 units of corn per acre.

The country under consideration young and has a smallpopulation.

A sufficient amount of No. 1 land exists to feed theentire population, with some No. 1 land left over.

The land rent is zero.

The most fertile land is a free good: supply exceedsdemand, even at a price of zero.


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Say rent for No. 1 land is not zero but somepositive number.

Only some of the land earns this rent.

Some of the land is left vacant, and the vacantland earns 0 rent.

Owners of vacant land are willing to rent out theirland for less than the assumed positive rentrather than earning nothing.

The competitive bidding process will continueuntil rent is down to zero.


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As Ricardo put it, when, in the progress of

society, land of the second degree of fertility is

taken into cultivation, rent immediately

commences on that of the first quality, andthe amount of that rent will depend on the

difference in the quality of these two portions

of land.


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Land rent exists because land varies in fertilityand land of a given fertility level is fixed inquantity

Further, progress of society will bring No. 3land into cultivation:

Rent for No.3 land = 0. (each acre produces 80units)

Rent for No.2 land = 10. (each acre produces 90units)

Rent for No. 1 land = 20. (each acre produces 100units)


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No. 2 land remains a free good, commanding

a zero rent, if not all of it is in use.

But now all no. 1 land is in use.

If it remains a free good, all farmers would try

to acquire no. 1 land, and none would be

interested in working on no. 2 land.

The demand for no. 1 land exceeds the

supply.


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This situation persists so long as farmer couldearn more working on no. 1 land than no. 2land.

No. 2 land produces 90 units of corn per acreand is a free good.

Equilibrium reached only if the rent for no. 1

land exceeds the rent for no. 2 land just by 10units of corn: the advantage of no. 1 landover no. 2 land.


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Competition among farmers generates the

result.

A farmer who is cultivating No. 3 land would

pay up to 20 units of corn to occupy No. 1

land.

The farmer who actually occupies No. 1 land

must pay 20 units or lose his lease.


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Neoclassical rent theory

Assumption :

a) Land had alternative uses like any other

factor of production

b) land supply is not fixed

c) each piece of land had an opportunity cost-

the rent that could be obtained in the most

profitable alternative use ( rent of land enter

into cost of production )


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Refer diagram 2 : The neoclassical approach is

represented by diagram 2.2.

Horizontal and vertical axis represent quantity

of land and rent. Total supply of land is OS.

Land now is assumed to be two uses, growing

potatoes and corn

Demand for potatoes is PP


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So the amount of land used for potatoes is

indicated along the horizontal axis from left to

right, starting from O. The remaining land can

be used for growing corn, so the demand forcorn is indicated in the reverse direction along

the horizontal axis from right to left, starting

at S. Demand for corn is CC Equilibrium in the land mkt is determined at ss

and dd intersect


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Rent is OR, OX is used for growing potatoes

and XS for growing corn

This diagram explanation is contrary to

ricardian theory, suppose there is an increase

in the demand for potatoes, with no change in

the demand for corn, demand for land for

potatoes will shift to P1P1, increased indemand for potatoes cause reduction in usage

of land for corn, from SX to SX1 ( diagram 2.3)


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Rent paid for all land increased from OR to

OR1 . Less corn is supplied to the market and

now rent price already increased, therefore

the price of corn will also rise, therefore theincrease in the rent of land is not caused by

the rise in corn price but vice versa.

So the Ricardian theory can be incorrect ifland has alternative uses and can be shifted

from one use to another


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Conclusion: rent of land for particular use is

not solely determined by the demand for the

product, land taxes can affect the use of land.

Land with higher taxes will result shift in theuse of land from the higher to the lower taxed

use with the tax being passed on in the form

of a higher price for the product of the landtaxed at the higher rate


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Planning controls and rent theory

Ricardian theory seem to be more relevant if

planning control is allowed ( if each piece of

land can be regarded as having a single use

which is allowed by the planning system)

Refer diagram 4 ( 2.4-handout): Supply of land

is OS. OX is allowed for housing and XS is

allowed for agricultural. Demand for housingis HH and demand for agricultural is

downward sloping from right to left


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Planning system separates the markets and

different rents are charged in each market, RH

and RA rent for housing and agricultural

respectively.

Supply is fixed by the planning system and

price of rent is determined by the demand

Thus the price of housing land is high because

the price of housing is high and not vice versa


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The argument that supply of land can be

changed does not affect the price of land can

be explain using diagram 5 ( 2.5- handout)

Initially land supply is fix at OX and demand

for housing is HH. The pricing of housing land

is OR. Let assume demand for housing shifts,

demand will cause the price of land to rise andvice-versa. So price of land is demand

determined


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affect house price and land prices more

quickly than shift in supply. A fall in interest

rates is likely to result in house price being

higher within few months, on the other handan increase in supply of land for housing may

take years to affect prices, especially large

development of the site will be phased overmany years. So increase in supply unlikely

affect price of housing in short-term


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If the land and property market were efficient

then announcement of an increased in land

supply would result in house buyers and

builders immediately lowering their prices inanticipation, but property market is not an

efficient.


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Example where Ricardian and Neoclassical

both are agree ( diagram 2.6 ): Land area OS.

DD demand for industry. Amount of land use

for industrial is OI. Price for industry use isOP1. HH demand for housing. Amount of land

available for housing is IS, price of land use for

housing is SPH

Both market appears representing Ricardian

Model


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Assume demand for housing and housing land

increases, demand shifted to H1H1, price of

housing land is higher than industrial land, so

now more profitable to develop industrial landfor residential use, new equilibrium at E.

This situation best represent neo-classical

model


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Urban Land Theory

As in agricultural land, a fundamental characteristics ofurban housing and land markets is that

housing and land are more expensive at betterlocations and cheaper at less advantageous sites.

This holds whether we consider

natural locational amenities, such as lakes or anocean, or

manmade locational advantages, such as distanceto employment

or cultural centers.


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Urban Land Theory

To study how rent and locational advantage

interact, we begin with a model of a very

simple city,

originally due to German geographer J.H.

von Thunen in his 1826 classic Isolated State,

the modern version of which appeared in

W. Alonsos Location and Land use in 1964.


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Urban Land Theory

In this city, commuting or access to place of

employment is the only locational advantage

that is considered.

The city is monocentric.

It has only one employment center.

Commuting to this center gives rise to what is

called (Ricardian) location rent.


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Urban Land Theory

Assume that the density of development is

fixed.

This absence of any factor substitution may

seem unrealistic, but we will be determining

density in the following


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Urban Land Theory

Households are identical, and the number of workers

(commuters) per household is fixed.

Household income (y) can be spent on commuting, housing,

and nonhousing consumption (x)

Employment is at a single center, called the Central Business

District (CBD), to which households commute along a direct

line from their place of residence.

Commuting costs k dollars annually per km.

The location of a household refers to its linear distance (d)

from the employment center.


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Urban Land Theory

Housing has fixed and uniform characteristics atall locations.

Housing rent is an annual amount R(d), whichvaries by location (commuting distance d)

Housing is provided by combining a fixed amountof land per unit of housing (acres, q) togetherwith a fixed amount of housing capital (materialsand labor) that costs C (no factor substitution) to

construct. Residential density, i.e. number of households

per acre is 1/q


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Urban Land Theory

Housing at any location is occupied byhouseholds who offer the highest rent; land isallocated to that use yielding the greatest rent.

Consider two locations: d1 and d2. Suppose

kd1 + R(d1) < kd2 + R(d2) .

The household, say household A, who occupieslocation d1 spends less on commuting and rentaltogether than the household, say household B,who occupies location d2.

Can this situation be equilibrium?


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Urban Land Theory

Seeing this difference in commuting and housingexpenditure, household B would want to move tolocation d1.

To compete for the lease at location d1,

household B can offer to pay a little bit more thanwhat household A currently pays.

So long as (1) remains, the process of thiscompetitive bidding continues.

In equilibruim we must have kd1 + R(d1) = kd2 + R(d2)


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Urban Land Theory

R(d1) R(d2) = kd2 kd1.

Think about d1 < d2, so that location d1 is a more

desirable location.

It costs less to commute from this site to jobs thanwhat it costs to commute from location d2.

The savings in commuting cost must be just offset by

the higher rent. When the housing market is in

equilibrium, increased rents as one moves towards

the CBD must exactly offset the lowered commuting

costs.


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Urban Land Theory

Since the quality and density of housing is assumedfixed across locations, the only variation possibleamong housing units is commuting distance.

If housing rents do not exactly offset commuting costs,

then consumers who live at farther locations wouldseek to move to closer ones.

They do so by offering greater housing rent thancurrent occupants.

Since housing is rented to the highest bidder, rents atthe closer locations would rise, while those at farthersites would fall


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Urban Land Theory

When rents exactly offset commuting costs,

households would no longer have an incentive

to move.

The market is then said to be in a equilibrium.

Mobility aims to increase welfare is not

possible when the housing market is in

equilibrium


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Urban Land Theory

Let the farthest location in the city be b and

write R(b) = .

For any d b, R(d) = R(b) + k (b d) = + k (b

d)

This is the bid rent function: the maximum

rent that households would be willing to bid

for each location d in city.


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Urban Land Theory

Suppose rents in all locations in city, except for

one, say location d1, follow the above

equation.

How much households would be willing to pay

to occupy housing in this location d1 ?

If at location d1 , R(d1 ) < + k (b d1 )

all households in the city would like to move

to just this location.


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Urban Land Theory

In many cities throughout the world, land

beyond the edge of development is used for

agriculture.

In this case, it earns some rural rent per acre

(ra).

In other situations, land is simply held vacant

with little or no meaningful rural rent


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Urban Land Theory

land owners seek the highest income from

their land, just as housing is rented to those

making the highest offer.

As long as urban housing yields a rent for a

site that exceeds that which the owner can

receive from farming, land will be rented to

urban households.


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Urban Land Theory

At the edge of the city (b) , then, urban landlordscan rent land for its

agricultural value (opportunity cost) of ra per

acre. With fixed density, a lot for each housing unit can

be rented for raq

The (annualized) cost for putting up a housing

unit at the edge of a city has two components:

the land rent raq


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Urban Land Theory

the structure rent, which is the annualizedcost of constructing a unit c = iC, where i is theinterest rate

This structure rent could be measured by theannual mortgage payment necessary to coverthe cost of constructing the unit.

If property development is perfectlycompetitive where firms earn zero profit,

R(b) = = raq + c


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Urban Land Theory

R(d) = raq + c + k (b d)

Housing rents at any location will equal the

sum of

construction cost

the opportunity cost of land plus

the difference between commuting costs atthe urban edge and those at the location in

question.


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Urban Land Theory

Moving from the edge of the city, rents must riseas commuting costs decrease.

To the extent that households maintain the samehousing and commuting expenditure :

R(d) + commuting exp. = raq + c + k (b d) + kd =raq + c + kb

Equilibrium housing rent at any interior siteabsorbs the savings in commuting that result by

moving in from the farthest location currentlydeveloped in the city


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Urban Land Theory

Only with these rents will households bewilling to live at any location within the city

There are three components to housing rent:

1. the rent necessary to convert a lot fromfarm land into urban land (raq)

2. the rent on the structure that sits on the

site 3. the location rent resulting from saved

commuting costs, k (b d)


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Urban Land Theory

Both the agricultural rent and the structure rentare constant across locations.

The slope of the housing rent function with

respect to distance, k, is due to the locationrent.

Rents fall away from the city center (per km) byexactly the amount of additional commuting

incurred by each household. This slope is known as the rent gradient in urban

economics


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Urban Land Theory

Those components of housing rent thatinvolves location and agricultural land areoften combined into

a hypothetical rent for just urban land r (d) .

Urban land rent can be thought of as aresidual:

the land rent that is left after subtractingthe rent for the housing structure from thetotal rent.


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Urban Land Theory

Housing rent is measured per housing unit,while land rent will be measured as rent peracre (unit of land).

To convert housing rent R(d) into land rent, r(d),subtract the structure rent and then divideby land per unit (q),

r (d) = ra+ k (b d)/q

This is the same as multiplying housing-minus-structure rent by residential density (1/q)


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Urban Land Theory

Urban land rent has two components.

1. The first is the rent (per acre) for its

alternative use (agricultural)

2. the second is the savings in commuting

costs per acre that result when housing is

placed on the land


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Urban Land Theory

At a density of 1/q, there are that many

households per acre, each of which is saving k

(b d) in commuting

The gradient for land rent with respect to

distance has a slope of k/q.

The rent per acre of land falls by the increased

total commuting of all who live in the 1/qunits built on the land


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Urban Land Theory

When commuting is more costly (per km),

interior housing and land rents will be higher

relative to edge rents because the commuting

cost savings at interior locations are higher

When urban land has a more productive

alternative use (higher ra), urban housing and

land rents will also be greater, because thisland rent component of housing rent is higher


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Urban Land Theory

When the density of urban housing is greater,

the gradient for urban land rents will become

steeper, with higher rents at the city center

relative to those near the edge.

The slope of the land rent gradient is k/q.

If the amount of land used per housing unit, q,

decreases, then the land rent gradientbecomes steeper


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