Competition and Specialization in the Hospital Industry: An Application of Hotelling’s Location Model

1. 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

2. 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

3. 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

4. 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

5. b a 0 1 cardiac care oncology 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:

6. 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

7. 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:

8. The Model (4) The solution thereof is given by: and shown graphically, b a 0 1 cardiac care oncology

9. 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

10. 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

11. 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

12. 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)

13. 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.

14. 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.