Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport...
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Transcript of Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport...
![Page 1: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/1.jpg)
Fun with Rent Functions!
![Page 2: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/2.jpg)
We derived a rent gradient
Remember, slope was related to mgl transport cost.
Let’s assume that we have an open city.
What does that mean?
A> People can migrate from elsewhere. Utility can’t increase.
Rent
Distance
Ag.Rent
u
![Page 3: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/3.jpg)
We derived a rent gradient
Suppose, everywhere that transportation costs decrease.
Open city!
What happens at u = 0.
A> Nothing
What happens elsewhere?
Rent
Distance
Ag.Rent
u 'u
Why?
![Page 4: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/4.jpg)
We derived a rent gradient
Suppose, everywhere that transportation costs decrease.
Closed city!
What happens at u = 0.
A> Rent falls
Why?
What happens elsewhere?
Rent
Distance
Ag.Rent
u 'u
Why?
![Page 5: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/5.jpg)
Let’s get more analytical (Brueckner Handbook)
Two Eq’m conditions
ARutWkR ),,,( (18)
k
NuWtkkD0
),,,(
K = distanceW = incomet = mgl. Transp. Costu = utilityN = population
(19)
![Page 6: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/6.jpg)
Land price rises
ARutWkR ),,,( (18)
k = distanceW = incomet = mgl. Transp. Costu = utilityN = population
If RA , since W, t, and u are fixed,the only thing that can change is
k
If land price rises, then people are worseoff, so they move. City contracts until enough move out. Utility is constant.
![Page 7: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/7.jpg)
Income rises
ARutWkR ),,,( (18)
k = distanceW = incomet = mgl. Transp. Costu = utilityN = population
What if W ?
k
u can’t increase, so price of land(housing) must rise, as people move in to take advantage of increased W.
At there is excess demand so thecity must expand.Higher rents smaller housinghigher density.
![Page 8: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/8.jpg)
Mgl. Transport cost rises
ARutWkR ),,,( (18)
k = distanceW = incomet = mgl. Transp. Costu = utilityN = population
What if t ?
k
u can’t decrease, so price of land(housing) must fall, as people move out.
At there is insufficient demand so thecity must contract.Lower rents bigger housinglower density.
![Page 9: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/9.jpg)
Closed city
ARutWkR ),,,( (18)
k = distanceW = incomet = mgl. Transp. Costu = utilityN = population
Assume that N is constant.
If RA , with N constant,
k
If land price rises, less land for samenumber of people. Rents rise,housing prices rise.
![Page 10: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/10.jpg)
Closed city (2)k = distanceW = incomet = mgl. Transp. Costu = utilityN = population
What about a change in income W?
Let p = price of housing
)())((W
p
W
u
u
p
dW
dp
- + +As W , people demand more housing, more land, and utility .Since you have the same number of people, if demand furtherout, some of it must decrease further in.
KEY: What happens at k = 0?
Increase in t does the reverse.
![Page 11: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/11.jpg)
Open v. closed?
• Costs of migrating may be high so utility differences may persist over time.
• BUT, migration flows ultimately must eliminate differentials.
• In real world, there is positive correlation between income and city population predicted by OC model.
• Within a city you almost always want to do “open” analysis. Suppose you build a small park. Who will benefit? Why?
![Page 12: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/12.jpg)
Land andLabor Mkt. Eq’a
![Page 13: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/13.jpg)
Revisiting Model
• We had business more centrally located.
• Then residential.
• At edge of the city, we get farmland.
Distance
Lan
d R
ent
Business
Residential Agric.
City limits
![Page 14: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/14.jpg)
What is Zoning?
• Zoning involves a set of restrictions on what people can do with their land.
• Generally imposes the restriction with some sorts of public good in mind.
• Discuss
![Page 15: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/15.jpg)
Revisiting Model
• Suppose we forbid land development past a certain distance. What will the impacts be?
• Immediate impact?
• City ends at boundary! Distance
Lan
d R
ent
Business
Residential Agric.
City limits
Service boundary
![Page 16: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/16.jpg)
More general effects ...• Limiting size of city reduces labor supply
– Wages rise, but,– This induces immigration from outside.
• Since we have a smaller city, rents and density MUST RISE
• Business sector bids less for land, because nonland costs have risen ...
• Residential sector bids land away from the business sector. So we will see ...
![Page 17: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/17.jpg)
Revisiting Model
• Ultimate impact depends on whether change is “small” or “large.”
• If it is “small” residents can’t be better off, because others would migrate in.
Distance
Lan
d R
ent
Business
Residential Agric.
City limits
Service boundary
![Page 18: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/18.jpg)
Ultimate winners and losers
• In an open city, residents neither win nor lose. Migration keeps their utility constant.
• Landlords outside the service boundary lose.
• Residential landlords win.
• Business landlords lose.
• Zoning is about land.
![Page 19: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/19.jpg)
Labor Market
• We’ve talked about the land market.
• If people come in, what is likely to happen in the labor market?
• Wages will fall.
• Rents will rise and wages will fall.
DL SL
L0
w0
wage
Labor
S'L
L1
w1
![Page 20: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/20.jpg)
Eq’m in Land and Labor
Two sectors – Business, Consumers
Business = (w, R) U = U (w, R)
0d dw dRw R
- -
0dR wdw
R
0U U
dU dw dRw R
+ -
0
UdR w
UdwR
![Page 21: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/21.jpg)
U > u* < 0
U < u* > 0
Equilibrium in the Land and Labor Markets
Among urban areas, what must happen for business profits to be constant?
Wage, w
Ren
t, R
Why?
= 0
Among urban areas, what must happen for consumer utility to be constant?
Why?
U = u*
Eq’m where 2 curves cross! Why?
Re
we
Increased R off-sets decreased w
Increased R off-sets increased w
U < u* < 0
U > u* > 0
![Page 22: Fun with Rent Functions! We derived a rent gradient Remember, slope was related to mgl transport cost. Let’s assume that we have an open city. What does.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649d5d5503460f94a3b52d/html5/thumbnails/22.jpg)
U > u* < 0
U < u* > 0
Equilibrium in the Land and Labor Markets
Suppose profits rise? From previous eq’m, is now greater than 0.
Wage, w
Ren
t, R
= 0
In new eq’m, w'e > we ;
R'e > Re
U = u*
Re
we
Increased R off-sets decreased w
Increased R off-sets increased w
U < u* < 0
U > u* > 0
Other firms come in, demand land, bid up wages.
>0