Transcript Housing_1

Housing
© Allen C. Goodman, 2000
Importance
• Necessity – We must have shelter.
• Importance – For most households, it is the single most
important item of consumption. It is also, particularly in
Western countries, the largest store of wealth.
• Durability – Housing lasts a long time. Most estimated
depreciation rates are no higher than about 1%, and in
many places houses last hundreds of years.
Importance, cont.
• Spatial Fixity – With only minor exceptions, housing
cannot be transported.
• Indivisibility – Households cannot mix units to get what
they want.
• Heterogeneity – Housing can have a great number of
characteristics. One can think of a large number, and
differential preferences over:
–
–
–
–
Quantity
Quality
Location
neighborhood
Importance, cont.
• Nonconvexities in production – Rehabilitation, conversion,
demolition, and reconstruction involve discontinuous
changes. Why? It is generally easier to change housing
quality discontinuously, rather than through continuous
upgrading.
• Informational asymmetries – Information is not perfect.
Potential occupants don’t know everything about dwelling
units. Landlords and tenants must interact without perfect
information
• Transactions costs – Can run to 10% or more of the cost of
the unit.
Two Other Terms
• Homogeneous – You can summarize housing in
one dimension, i.e. through expenditures. Speak
of housing as a number of units, possibly indexed
by location.
• Heterogeneous – Composed of many features.
Particularly important when considering
individual demand and supply features.
Homogeneous Analysis
• Rent Control –
• One market
S
D
p
Shortage
p*
pc
qc
q* q
Homogeneous Analysis
• Rent Control –
• Two Markets
Du
S
D
Uncontrolled
Su
p
Shortage
p*
pc
qc
D´u
q* q
pu*
Housing Policy
• Early U.S. policy involved building and/or renting
new units. Called public housing.
• (Parenthetically) U.S. has much smaller direct
government involvement than most other
countries.
• In 1960s (and possibly before), it became clear
that this was terribly expensive.
• Many economists lobbied for various types of
cash-based aid.
• What would
you like, $100
for housing,
or $X that you
could spend
any way you
want?
Other Goods
In-kind transfers
C
B
A
Housing
If we give money …
D´
S
Price
• What will happen
to demand?
• What will happen
to supply?
D
Quantity
Supplies of Land and Housing
LAND First
L = LA + LU
dL = dLA + dLU
dLU = - dLA
-csEd
Price
dLU p
dLA
p
LA

dp LU
dp ( L  LA ) LA
Es =
Es = -Ed (LA/LU)
LU
L
Land A
L
Muth
• Estimates agricultural demand elasticity  -1.2, so
urban supply elasticity is about +1.2.
• Supply of housing services?
• Early estimates were  +14.
• What do we know about flat curves?
– Little or no increasing returns to scale
– Constant costs, indicative of competition.
Long run housing
I use an analysis from Vernon Henderson.
Q = housing;
K = capital
L = land;
R = Rent
r = payment to capital.
Start with:
Q(u) = Q (K(u), L(u))
Profit () is:
 = p(u)Q(K(u), L(u)) – rK(u) – RL(u)
We get standard maximization, where MR = MC.
Zero profits imply that unit costs must always vary through
land costs to equal output prices.
Q = housing; K = capital
L = land;
R = Rent
r = payment to capital.
What happens as land rents (hence housing prices) change?
KEY – Profit doesn’t change as they move.
Therefore:
Q(u) [p(u)/u] = L(u) [R(u)/u]
(1.13)
Rearranging (1.13), leads to, for land rent:
[R(u)/u] = [Q(u)/ L(u)] [p(u)/u]
(1.14)
Divide both sides by R(u), and multiply RHS by p(u)/p(u), leads to:
[R(u)/u]/R(u) = [p(u)Q(u)/ R(u)L(u)] {[p(u)/u]/p(u)} (1.16)
LHS: Pct. Change
in Rents
RHS: Pct. Change in Prices,
multiplied by 1/rental share – Call
rental share L.
Q = housing; K = capital
L = land;
R = Rent
r = payment to capital.
[R(u)/u]/R(u) = (1/ L) {[p(u)/u]/p(u)}
(1.16)
Define elasticity of substitution as:
 = ln (K/L)/ln (R/r).
So:
ln (K/L)/u =  dln (R/r)/u = ( / L) ln p(u)/u.
Since r doesn’t change, dln (R/r) = dln R.
So, a 1% in housing prices  a ( / L) increase in capital land ratio
Most of the time, we don’t see density changing as fast as factor costs, so  < 1.
If  = 0.7 and L = 0.1, we see that a 1% in housing prices  a (0.7 / 0.1), or
7% increase in capital land ratio. Also, land rents change much more
quickly than housing prices:
Q = housing; K = capital
L = land;
R = Rent
r = payment to capital.
This is simple to see:
p(u) = sK r + sL R(u)
p(u)/u = sL R(u)/u
R(u)/u = (1/sL) p(u)/u
This also means that factor shares aren’t constant as implied in Cobb-Douglas
production functions that are otherwise very serviceable.
This is a LR analysis. It assumes that people live in house trailers. Yet, for
many aggregate analyses, a lot of the predictions are really pretty good.
It is also important to note (over and over) that when we talk about housing
price, we are talking about unit price. This is why it is sometimes very
important to deal w/ expenditures, rather than price.
NEXT: Demand