Competition and Specialization
in the Hospital Industry:
An Application of Hotelling’s Location Model
A paper by Paul S. Calem and John A. Rizzo
Southern Economic Journal (1995)
Presented by A. Barfield
December 11, 2001
Introduction
• Hospitals compete for both physicians and patients
• It is well known that hospitals compete on the
basis of quality
• Often this competition based on quality leads to a
technological “arms race” which results in
increased specialization
• Much research has been done on quality rivalry
but little on specialty mix differentiation
Introduction (2)
• The authors claim that quality and specialty mix
are the prime instruments of competition in the
hospital industry
• This paper presents a model where hospitals
compete on the basis of quality and specialty mix
• The model they use is a variation of Hotelling’s
location model where:
– Specialty mix is used instead of location
– Quality is used instead of price
– The costs of not meeting patient-specific needs is used
instead of transportation costs
Introduction (3)
• The mix of services that a hospitals chooses to
specialize in greatly affects their ability to meet
patient-specific needs
• Hospitals share costs with patients of mismatch in
specialty mix
– The costs to hospitals arise from their inability to deal
with complications
• Potential costs from litigation
• Potential costs from a damaged reputation
• Actual costs to mitigate the above
– The costs to patients are losses in the quality of care
The Model
• The Duopoly
– Two firms: A and B
– Each firm chooses:
• A specialty mix located on a line segment [0,1]
b
a
0
1
cardiac care
oncology
• A level of quality:
ua , ub  0
– The cost of achieving quality ua is given by the convex
cost function:
q
2
ca ,b  ua ,b
2
The Model (2)
• The Consumer
– Demands are uniformly distributed along
specialty mix interval
– Each consumer purchases one unit of hospital
service
– The utility of the consumer is given by
U ( x, y, s)  u  u y  s x  y
where x = specialty mix desired by patient
y = specialty mix provided by hospital y
s = cost per unit distance to patient
The Model (3)
• Market Areas
– The respective market shares of each firm is
determined by the marginal consumer
– The marginal consumer is indifferent between
choosing Firm A or Firm B.
– This condition is given by:
ua  s( xˆ  a)  ub  s(1  b  xˆ )
The Model (4)
The solution thereof is given by:
xˆ 
(1 b  a  )
2
where:
 
( u a  ub )
s
and shown graphically,
b
a
0
cardiac care
x̂
1
oncology
Competitive Effects When
Quality is Held Constant
• Duopoly Problem
– We solve the duopoly problem to find Nash equilibrium for each
hospital. Maximizing profits for firm A involves maximizing:
( p  c) xˆ   t
 (a  x)dx  t  (a  x)dx
a
xˆ
0
a
– There is similar equation for Firm B. Solving both these equations
yield the following results:
• Each hospital has incentive to move to the median specialty mix to
maximize revenues (less differentiation).
• Each hospital has incentive to move away from the center due to rising
accommodation costs (more differentiation).
• If third party payments exceed marginal costs (high), then firms seek
to maximize market share and become less differentiated
• If third party payments are below marginal costs (low), then firms seek
to differentiate themselves
Competitive Effects When
Quality is Held Constant
• Monopoly Problem
– We solve the monopoly problem to find Nash equilibrium for each
hospital. The monopolist’s objective is to minimize costs for the
joint firm:
t
 (a  x)dx   (a  x)dx  
a
xˆ
1b
0
a
xˆ
xˆ

(1  b  x)dx   [ x  (1  b)]dx
1b
– Solving this equation yield the following results:
• The optimal locations are independent of the qualities of each firm
• The specialty mixes for each firm chosen by the monopolist
minimizes accommodation costs
• Accommodation costs are likely to be higher under duopoly unless
they cooperate
• Mergers are likely to yield cost savings for hospitals and patients
Competitive Effects When Service
Mix and Quality are Variable
• Two-stage game:
– Specialty mix is chosen in first stage
– Quality is chosen in second stage
• The results:
– Each hospital has incentive to move to the median specialty mix to
enhance revenues (less differentiation)
– Each hospital has incentive to move away from the center to shift
costs onto its rival (more differentiation)
– Firms have incentive to reduce quality competition because it is
costly
– When (p-c) is high, firms earn negative profits because of intense
quality competition (ruinous competition)
– Merged hospitals are likely to provide more socially optimal
outcomes
Conclusions
• Each hospital has an incentive to move to the
median specialty mix to increase patient revenues
• Higher patient care reimbursements increase this
incentive
• Each hospital also has a counter-incentive to shift
costs onto its rival by moving away from the
median
• Intense quality competition drives hospitals to
more differentiation (away from median)
Conclusions (2)
• The Medicare reimbursement system has
reduced differentiation in markets with
intense quality competition.
• Competing hospitals differentiate too much.
A merged hospital is more efficient.
• Higher reimbursement levels lead to higher
costs through intense quality competition.
Further Study
• This model could be applied to the study of
physician services.
– The duopoly case would apply to solo
practitioners.
– The monopoly case would apply to a group
practice.