Scope, learning, and cross subsidy: organ transplants in a multi-division hospital.

• Author: Possai, Kathleen W.

1. Introduction

   According to their own statements, hospitals view organ transplants as unprofitable or "money losing" procedures. Industry representatives believe that only a few large transplant centers make money on transplants.(1) At the same time, hospitals continue to petition the Department of Health and Human Services and the United Network for Organ Sharing or UNOS, the regulatory body, for permission to open new transplant centers and expand existing centers. This paper examines this anomalous behavior: entry into and expansion of a money losing segment of an industry.

   We propose to explain this behavior by the interaction of inter and intra-divisional economies of scope, and learning effects in a two division, three output model of a transplant hospital which we build in section II. The concept of economies of scope is central to our paper. Scope exists when the cost of producing two or more outputs jointly is less than the sum of the costs of producing each output independently. Scope stems from two sources, shared overhead and resources.

   The divisional structure of the hospital separates "other services" which are produced in division 1 from the two services produced in division 2, the transplant division. Within division 2, intra-divisional economies of scope are due to the resources shared by transplants and related services, say kidney dialysis and cardiac catheterization. Overhead shared between the two divisions create inter-divisional scope economies. Overhead, joint or common costs are those costs not unambiguously assigned to a particular output. On the demand side of our model, transplants are assumed to exhibit learning effects and demand complementarity with related services.

   Section III postulates several goals for the hospital and section IV analyzes the consequences of these goals on hospital behavior. We conclude that rational hospitals can attempt to expand their transplant facilities and simultaneously argue that such procedures are "money losers" due to the likely existence of cross subsidization. The paper concludes with some tentative policy recommendations and the outline of an empirical test for our model.

2. The Model

   The hospital is partitioned into two divisions which operate independently, but are under the blanket administration of the hospital. The partitioned hospital is represented in Figure 1.

   Division two contains the production of transplants and those services related to transplants through demand and cost interactions. The simultaneous operation of divisions one and two require the use of common resources termed shared overhead expenses which generate hospital level or inter-divisional economies of scope. Examples of shared overhead expenses are general nursing staff, laundry and dietary services, and admissions. Overhead represents the general administration of the hospital and is common to the production of all outputs. Inter-divisional economies of scope is generated by the cost savings associated with spreading this overhead over more than one output. Hicks explains economies of scope generated by shared overhead in the following way;

   |A~lmost every firm does produce a considerable range of different products. It does so largely because there are economies to be got from producing them together, and these economies consist largely in the fact that the different products require much the same overhead |8, 372~.

   Intra-divisional economies of scope are generated within division two, through the use of shared or public inputs. For heart transplants and general cardiac services, examples of shared inputs include cardiac physicians, specialized heart monitoring equipment and cardiac nurses. The production of cardiac services requires both human and physical capital inputs that are also used in the transplantation process. Any firm wishing to enter the transplant market producing transplants in isolation of other cardiac services must invest in resources that are duplicates of those used in general cardiac production, raising costs.

   The source of the demand complementarity is a "halo" or prestige effect which is generated by patients and/or referring physician's belief that transplant hospitals are some how better at performing related procedures due to knowledge gained from the transplantation process. In light of this external or learning effect, transplant hospitals are perceived to be state of the art facilities rendering superior care. This halo or prestige effect covers non-transplant services that are related to transplants. Related services would include cardiac services, in the case of heart transplants, or nephrology (kidney) services, in the case of kidney transplants |1~.

   The demand functions for transplants and related services are given in (1) and (2), respectively, where the S terms are shift parameters.

   |P.sub.tr~ = f(|Q.sub.tr~, |S.sub.tr~) (1)

   |P.sub.r~ = f(|Q.sub.r~, |Q.sub.tr~, |S.sub.r~) (2)

   where |Mathematical Expression Omitted~.

   Hospital consumers are assumed to view the number of transplants performed as a measure of experience and quality, perceiving busier centers to be more prestigious. The demand for related services, therefore, shifts outward as the quantity of transplants rises and consumers are willing to pay higher related services prices at busier transplant hospitals.

   Division one contains the production of what are termed "other" services. These services are assumed to be unrelated to transplants and/or related services; the existence of a transplant department has no effect on the ability of the hospital staff to produce "other" services.(2) Examples of "other" services include appendectomies, tonsilectomies and obstetric services. The following represents the demand for "other" services, where S is a shift parameter.

   |P.sub.o~ = f(|Q.sub.o~, |S.sub.o~) (3)

   where |Delta~|P.sub.o~/|Delta~|Q.sub.o~ |is less than~ 0.

   The cost function for the hospital is built up from divisional cost functions. Equation (4) represents the cost function for the entire hospital and is a function of all three outputs. Equations (5) and (6) represent the cost functions for divisions one and two. The exact relationship between (4)-(6) is developed below.

   |C.sub.3,t~ = |C.sub.3~(|Q.sub.tr,t~|Q.sub.r,t~|Q.sub.o,t~|Gamma~) (4)

   |C.sub.1,t~ = |C.sub.1~(|Q.sub.o~) (5)

   |C.sub.2,t~ = |C.sub.2~(|Q.sub.tr~, |Q.sub.r~, |Gamma~) (6)

   Learning by doing is arguably important for organ transplants. Specifically,

   |A~ firm that has produced a large volume of output has in many cases encountered and solved a number of practical problems that were not foreseen when production began. This experience, along with the increased proficiency gained by repetition, should translate into lower costs |13, 107~.

   As cumulative output rises and a firm moves down its "learning curve," the average cost of production declines due to a downward shift in the average cost curve. Due to learning, incumbent firms have a cost advantage over subsequent or potential entrants.

   In the early years of transplantation, most transplant centers were large, university based, metropolitan hospitals which had monopoly positions within their relevant market |20; 21~. UNOS membership rules restrict the number of hospitals that can transplant organs. One possible explanation for these restrictive entry criteria is quality maintenance. Given the shortage of available organs, UNOS must constrain the number of firms that can produce if...