DRE Research Seminar
15 February 2006
Why is real estate market an
oligopoly?
James D. Shilling
University of Wisconsin- Madison
School of Business
Tien Foo Sing
National University of Singapore
Department of Real Estate
Why is real estate market an oligopoly?
Presentation Outline
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Introduction – Bertrand’s Paradox
Basic model and assumptions
A mono-centric city model with capacity
constraints
A Multi-nodal urban land market model
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Differentiated markets in Hotelling’s linear space
Mergers and predatory pricing strategies
Variable price structure
Conclusions & future extensions
Why is real estate market an oligopoly?
Industrial organization and real estate
market
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Industrial organization (IO) literature is expanding rapidly
 Issues relating to functioning of market, like market structure,
incomplete information, and predatory strategies, exit and entry
deterrence etc.
Limited IO studies in real estate market
Real estate market has unique features for IO study because of
the inherent spatial characteristics
Differ by location (distance from city centre), by property type
(sub-markets), by countries/cities (institutional features)
Real estate market provide a good platform for IO studies
 Products are typically heterogeneous – differentiated by location
and by type
 Information is inefficient/imperfect
 Supply side constraint – fixity in land / density control through
zoning
Why is real estate market an oligopoly?
Basic model and assumptions
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A static game theoretic model with two players
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They develop homogenous products at a fixed location, xi
Two firms compete on prices to optimize profits
Information complete and decisions are simultaneous
Demand function is given as
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Di(pi, pj) = a – bpi + dpj
b = demand elasticity; d = cross-elasticity of substitution
Such that 0 < d < b
The market is pareto-efficient
In Nash equilibrium, duopoly firms earn zero profits
Prices will be driven down to equal to costs
The result is welfare sub-optimal
Bertrand’s Paradox
Why is real estate market an oligopoly?
Bertrand’s Nash Equilibrium
Rj
pi
Ri
Nash equilibrium
pi*=pj* =c
 D( Pi ) if pi  p j



Di ( pi , p j )   D( Pi ) / 2 if pi  p j



 0
if pi  p j
pi *
pj*
pj
Why is real estate market an oligopoly?
Bertrand’s paradox and real estate market
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Real estate markets are not monopoly, and they are dominated
by several players, and the number of players in each market
varies
The responsiveness of the market may vary across cities and
sub-markets
Is real estate market a special test case that rejects Bertrand’s
paradox?
If not, why are the following questions not answered?
Why are mergers and predatory strategy not operative in real
estate market?
Is the real estate market welfare sub-optimal?
Could developers earn more than zero profits?
What factors that drive an oligopoly real estate market?
Why is real estate market an oligopoly?
Why is real estate market an oligopoly?
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In manufacturing technology, the adoption of flexible technology
promote concentration of market (Eaton and Schmitt, 1994)
Firms avoid diversification and expansion of basic products, and
thus reduce fixed costs
Ownership structure is irrelevant, and mergers and cartels are
welfare optimal strategies that lead to concentration of market
Flexible technology is not applicable to real estate markets
 Land is fixed and immobile, and ownership of lands is a
prerequisite of any development activities
Is oligopoly structure of real estate market welfare optimal? why?
Other forces limiting concentration of real estate market:
 Capacity constraint (The Edgeworth’s solution, 1987)
 Differentiated products/ spatial characteristics of real estate
market
 Imperfect information
 Dynamic market / repeated strategies
Why is real estate market an oligopoly?
Flexible Production Structure by Eaton
and Schmitt (1994)
Xi
Xj
Xh
Why is real estate market an oligopoly?
Limiting forces: (1) Capacity constraint
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In a mono-centric city where both developers co-exist at xi
Supply is inelastic and density on each land parcels is
controlled by zoning
Maximum density is binding in each market at xi,
 such that
qi  q j  q
Capacity constraint is imposed by , where [0    1]
Demand functions:
D1 ( p1 , p 2 )  q1    q
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In Nash Equilibrium
 (b  (b  d ) ) p1  (2  1)d .c 
q a

1


*
1
D 2( p1 , p2 )  q2  (1   )  q
 ( (b  d )  d ) p 2  (2  1)c 
q 2*  a  




Why is real estate market an oligopoly?
Capacity constraint and demand structure
0.95
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Fraction of maximum market demand, ()
1.00
Why is real estate market an oligopoly?
Proposition 1:
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Capacity constraint,, in a duopoly market is a function
of the demand elasticity, b, and cross elasticity of
substitution, d. In a market with highly substitutable
products, and where buyers are less insensitive to price
changes, i.e. inelastic demand, a developer requires a
higher capacity constraint of m in order to preempt
entrants and earn monopoly return ■
In a market with highly substitutable product, developers are
required to increase their capacity substantially to preempt entry and
obtain monopoly profit
This is commonly observed in highly homogenous market, and
lower end housing markets
Why is real estate market an oligopoly?
Limiting forces: (2)
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A multi-nodal urban land model
Spatial features are incorporated using Hotelling’s linear city
kernel (1929)
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(x, q) = [(x1, q1), (x2, q2), …. ,(xN, qN)]
where X m, [m = (1, 2)] indicates a bi-nodal urban market
[x1 < x2 < x3 <….. xN]
distance vector is a continuous function that increases in an
equally space distance, n  ( X 2  X 1 ) N
Two developers, each of them establishes competitive edge at
the two city centroids

C ( x )  (c  r )( X

 x )D ( p , p )  n( X
C1 ( xi )  (c  r )( xi  X 1 ) D1 ( p1 , p2 )  n( xi  X 1 ) K
2
i
2
i
2
1
2
2
 xi ) K
Why is real estate market an oligopoly?
Cost structure in Hotelling’s linear city
C2 ( xi )  c  r ( X 2  xi )
X 1  x1
C1 ( xi )  c  r ( xi  X 1 )
X 2  xN
Why is real estate market an oligopoly?
Solving for optimal market boundary
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Assume that price is inelastic
Aggregate profit functions over a distance, (|Xi, xi|):


 m  pm  [c  r (| xi  X m |)] qi  n(| xi  X m |) K
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In Nash equilibrium, [p*1 = p*2 = MC*i(x1)]
Equilibrium price is equal to the marginal cost of the second
most efficient developer:
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MC*i(x1) = max [MC1(xi), MC2(xi)]
Market boundary where both developer earn optimal profits is
derived as:



1
x *  ( X 2  X 1 )

2rq 2  nK
1 
2rq1  nK






Why is real estate market an oligopoly?
Aggregate Profits in duopoly market


i
(c)
(a)
(e)
(b)
X1
(d)
Xe
X*
X
f
X
2
i
Why is real estate market an oligopoly?
Optimal market boundary of duopoly
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Optimal market boundary, (x*)
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Why is real estate market an oligopoly?
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1.0
0.02
Aggregate Profit for developer 1, ( 1)
Aggregate profit of developer 1
Why is real estate market an oligopoly?
Proposition 2:
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Given the optimal market boundary that gives welfareoptimal return to each of the developers,   1    2 ,
aggregate profits of the developers increase with an
increase in the linear size of a bi-modal city. However,
the aggregate profits of developers will be lower, if they
face an increasing capacity constraint.
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Both developers are better off when the city size is expanded
Aggregate profits decreases when capacity is raised by either one of
the developer
The above two conditions are sufficient to reject a monopoly market
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Why is real estate market an oligopoly?
Entry and mergers in real estate market
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Proposition 3:
There are positive profits for new entrants to establish strong
foothold in space along the linear city, (| X  X |) , and the profits of
incumbents will be eroded with the new entrants. The loss in profits
for incumbents as indicated by shaded area (a) and dotted area (c)
is dependent on the location at which the new entrants possess
competitive edge in their production technology. The loss for
incumbent developer m increase, when (| X e  X m |) is smaller.
2
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1
Proposition 4:
Merger of two developers with established home market reputation
in adjacent markets are welfare optimal. However, there are no
externality effects on the developer outside the merger. The profit
level of the developer not involved in the merger remains
unchanged.
Why is real estate market an oligopoly?
Effects of entry and mergers


i
(c)
(a)
(e)
(b)
X1
(d)
Xe
X*
X
f
X
2
i
Why is real estate market an oligopoly?
In a multi-nodal city with elastic demand
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Demand function: qi = Di(pi, pj)
 X i2 x *2
*


(
p
,
p
)

rq


x
X j  Xi X
j
 i i j
 2
2


 x *2 X i2

*



 x Xi 
j  rq i

 2

2



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Proposition 5:
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In an elastic market where demand is responsive to price changes,
the profits of developers will be an increasing function in the crosselasticity of substitution, d, and an decreasing function in the
demand elasticity, b.
Why is real estate market an oligopoly?
Variable price structure
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Utility function of buyers:
U m ( pm , xi )  S  pm  t (| xi  X m |)
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Profit function
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
 m  pm  t (| xi  X m |)  [c  r (| xi  X m |)] qi
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Proposition 6:
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When the marginal rate of increase in unit cost is lower than the
marginal disutility rate, developers will be able to maximize the profit by
stretching their market boundary outward from their home-base. When
[t < r], there is no incentive for developers to expand their market
boundary, and it would be better off for the developer to focus only on
its home-market where he has competitive advantages.
Why is real estate market an oligopoly?
Limitations & possible extensions
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Reputation of developers
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D1(p1, p2) = a – (b-)p1 + dp2
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Incomplete information on cost structure
c1e   c1L  (1   ) c1H
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Location dependent capacity constraints
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Different sub-market and switching costs
q m    ( xi ) q i

xs
m
 p m,a  [c m,a  r  ( xi  X 1 )dxi ]  nK ( x s  X 1 )
X1
xi
 p m,b  [c m,b  r  ( xi  X 1 )dxi ]  n( K  S )( xi  x s )
xs
Why is real estate market an oligopoly?
Urban land pricing structure for two
different uses
p1,a
p1,b
X1
Xs
Why is real estate market an oligopoly?
Conclusion
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For manufacturing firms with homogenous products, flexible
production technology promotes market concentration (Eaton and
Schmitt, 1994)
Costly to expand basic products
In real estate market, flexible production technology is not applicable
Ownership in real estate market is critical
Fixity in supply and capacity is constrained
Using Hotelling’s linear city kernel, models with two city centroids
were developed
Given capacity constraints, and also that cost structure of
developers is tied to location advantage
Forces that promote concentration of market are ineffective
Real estate market is an oligopoly, yet there is no reason to reject
that the market is welfare sub-optimal
Empirical hypotheses can be developed to further verify
propositions that reject concentration of ownership in real estate
market
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Thank you!