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 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 u a is given by the convex cost function: The Model a b 01 cardiac care oncology

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

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: The Model (3)

The Model (4) The solution thereof is given by: and shown graphically, a b 01 cardiac care 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: –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: –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.