Upload
sixd-waznine
View
230
Download
0
Embed Size (px)
Citation preview
7/28/2019 Week 3 Lesson1
1/61
LECTURE WEEK 3:ECONOMIC
RETURNSOUTLINE OF LECTURE WEEK 3:
Ricardian rent theory Classical rent theory
Urban rent theory
7/28/2019 Week 3 Lesson1
2/61
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)
7/28/2019 Week 3 Lesson1
3/61
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.
7/28/2019 Week 3 Lesson1
4/61
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
7/28/2019 Week 3 Lesson1
5/61
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
7/28/2019 Week 3 Lesson1
6/61
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
7/28/2019 Week 3 Lesson1
7/61
7/28/2019 Week 3 Lesson1
8/61
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
7/28/2019 Week 3 Lesson1
9/61
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
7/28/2019 Week 3 Lesson1
10/61
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
7/28/2019 Week 3 Lesson1
11/61
Agricultural and land rent
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.
7/28/2019 Week 3 Lesson1
12/61
Agricultural and land rent
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.
7/28/2019 Week 3 Lesson1
13/61
Agricultural and land rent
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.
7/28/2019 Week 3 Lesson1
14/61
Agricultural and land rent
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)
7/28/2019 Week 3 Lesson1
15/61
Agricultural and land rent
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.
7/28/2019 Week 3 Lesson1
16/61
Agricultural and land rent
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.
7/28/2019 Week 3 Lesson1
17/61
Agricultural and land rent
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.
7/28/2019 Week 3 Lesson1
18/61
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 )
7/28/2019 Week 3 Lesson1
19/61
Neoclassical rent theory
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
7/28/2019 Week 3 Lesson1
20/61
Neoclassical rent theory
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
7/28/2019 Week 3 Lesson1
21/61
Neoclassical rent theory
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)
7/28/2019 Week 3 Lesson1
22/61
Neoclassical rent theory
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
7/28/2019 Week 3 Lesson1
23/61
Neoclassical rent theory
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
7/28/2019 Week 3 Lesson1
24/61
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
7/28/2019 Week 3 Lesson1
25/61
Planning controls and rent theory
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
7/28/2019 Week 3 Lesson1
26/61
Planning controls and rent theory
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
7/28/2019 Week 3 Lesson1
27/61
7/28/2019 Week 3 Lesson1
28/61
Planning controls and rent theory
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
7/28/2019 Week 3 Lesson1
29/61
Planning controls and rent theory
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.
7/28/2019 Week 3 Lesson1
30/61
Planning controls and rent theory
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
7/28/2019 Week 3 Lesson1
31/61
Planning controls and rent theory
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
7/28/2019 Week 3 Lesson1
32/61
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.
7/28/2019 Week 3 Lesson1
33/61
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.
7/28/2019 Week 3 Lesson1
34/61
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.
7/28/2019 Week 3 Lesson1
35/61
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
7/28/2019 Week 3 Lesson1
36/61
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.
7/28/2019 Week 3 Lesson1
37/61
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
7/28/2019 Week 3 Lesson1
38/61
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?
7/28/2019 Week 3 Lesson1
39/61
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)
7/28/2019 Week 3 Lesson1
40/61
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.
7/28/2019 Week 3 Lesson1
41/61
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
7/28/2019 Week 3 Lesson1
42/61
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
7/28/2019 Week 3 Lesson1
43/61
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.
7/28/2019 Week 3 Lesson1
44/61
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.
7/28/2019 Week 3 Lesson1
45/61
7/28/2019 Week 3 Lesson1
46/61
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
7/28/2019 Week 3 Lesson1
47/61
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.
7/28/2019 Week 3 Lesson1
48/61
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
7/28/2019 Week 3 Lesson1
49/61
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
7/28/2019 Week 3 Lesson1
50/61
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.
7/28/2019 Week 3 Lesson1
51/61
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
7/28/2019 Week 3 Lesson1
52/61
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)
7/28/2019 Week 3 Lesson1
53/61
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
7/28/2019 Week 3 Lesson1
54/61
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.
7/28/2019 Week 3 Lesson1
55/61
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)
7/28/2019 Week 3 Lesson1
56/61
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
7/28/2019 Week 3 Lesson1
57/61
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
7/28/2019 Week 3 Lesson1
58/61
7/28/2019 Week 3 Lesson1
59/61
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
7/28/2019 Week 3 Lesson1
60/61
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
7/28/2019 Week 3 Lesson1
61/61