Competition and Specialization in the Hospital Industry: An Application of Hotelling

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Competition and Specialization in the Hospital
IndustryAn Application of Hotellings Location
Model

• A paper by Paul S. Calem and John A. Rizzo
• Southern Economic Journal (1995)
• Presented by A. Barfield
• December 11, 2001

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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

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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 Hotellings
  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

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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

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The Model

• The Duopoly
• Two firms A and B
• Each firm chooses
• A specialty mix located on a line segment 0,1
• A level of quality
• The cost of achieving quality ua is given by the
  convex cost function

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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

where x specialty mix desired by patient y
specialty mix provided by hospital y s cost
per unit distance to patient
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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

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The Model (4)

• The solution thereof is given by
• and shown graphically,

b
a
0
1
cardiac care
oncology
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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
• 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

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Competitive Effects When Quality is Held Constant

• Monopoly Problem
• We solve the monopoly problem to find Nash
  equilibrium for each hospital. The monopolists
  objective is to minimize costs for the joint
  firm
• 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

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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

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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)

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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.

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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.