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

I. Introduction

In a recent paper in this Journal, Possai and Goetz [10] (P-G) offer an explanation of why a hospital might choose to provide a service (organ transplants) or continue to provide a service that, on its own merits, may appear to be unprofitable. Their explanation is based upon hypothesized (and plausible) cost and demand relationships involving economies of scope, demand complementarities, and learning-by-doing that render the net effects of the service profitable for the hospital's overall operations while appearing unprofitable on its own. Thus, the (undocumented) perception that the transplant business is unprofitable is an illusion caused by a failure to consider the full range of effects of a transplant program on costs and demands, both for transplants and other hospital outputs.

There are two fundamental and interrelated issues that P-G do not address. First, the analysis they present does not explain why hospitals that do not currently have organ transplant programs are rapidly entering this industry. Nor does it explain why hospitals that already have transplant programs are actively trying to expand the number of operations beyond that presently performed. Rather, P-G's analysis focuses on the static optimality (first-order) conditions for the four objective functions considered and describes the implications of those conditions for overall, firm-wide profitability versus service profitability. Thus, the explanation provided is one of profitability of a service that, on a more narrow accounting, appears unprofitable. Assuming the hospital is already at these optimal values (and there is no reason given why they are not), however, there is no obvious incentive for either entry or expansion, which are dynamic phenomena, to occur. The analysis we present here will more directly address these issues.

The second fundamental issue not addressed in P-G's approach is the implications for observed behavior in this industry of the persistent and severe shortage of human organs for transplantation. Both federal and state laws proscribe the purchase or sale of human organs for transplantation.(1) Such organs may be donated, but they may not be sold. As a result, the legally mandated price of this crucial input is fixed at zero, and a chronic organ shortage has plagued the industry since transplants first became feasible in the mid-1950s. That shortage has become increasingly severe in recent years.(2) It is difficult to model equilibrium conditions in this market without recognizing and incorporating the effects of this shortage on observed outcomes. Indeed, it is our thesis here that one cannot understand the underlying incentives to enter and expand in this business without first taking account of the organ shortage.

II. A Simple Model of an Input-Constrained Firm

Over the years, economists have modeled the behavior of firms subject to a variety of exogenous constraints.(3) To our knowledge, however, the particular constraint examined here - where an input price is held fixed below the equilibrium level - has not yet been explored systematically. Such a constraint is clearly relevant to an analysis of firms (hospitals) supplying human organ transplants due to the legal prohibition on purchases and sales of the organs required for such transplants. Accordingly, we begin by developing a simple model that, we believe, reflects the essential effects of this institutional feature of the transplant industry.

Assumptions

Our model makes use of the following set of notation and assumptions:

1. The price of transplantable organs, [P.sub.O], is legally fixed at zero.

2. Transplant providers receive a fixed rate, [P.sub.T], per transplant performed, paid by a third party. Recipients have a willingness to pay for transplants, but cannot be individually billed for procedures.

3. The production function for transplant operations is characterized by a fixed-proportions technology in which each operation requires one transplantable organ. Thus, we assume that [Q.sub.T] = [Q.sub.O], where [Q.sub.T] is the number of transplant operations performed and [Q.sub.O] is the number of transplantable organs acquired by the transplanting hospital.

4. The marginal cost of performing a transplant operation is constant at [MC.sub.T].

5. The supply curve of organs is given by [Q.sub.O]([P.sub.O]), with d[Q.sub.O]/d[P.sub.O] [greater than or equal to] 0, and [Mathematical Expression Omitted]. Thus, the organ supply curve is coincident with the [Q.sub.O] axis up to [Mathematical Expression Omitted], and it increases in [P.sub.O] thereafter.

6. Hospitals have significant monopsony power in the procurement of organs within their respective geographic collection regions.

A brief explanation of these assumptions may be useful. The first assumption reflects the fact that, under the National Organ Transplant Act of 1984, it is a felony to buy or sell human organs for purpose of transplantation. The second assumption captures the exogeneity of reimbursement rates for transplant procedures. These rates are set administratively either by funding agencies (e.g., the Health Care Financing Administration fully funds all kidney transplants under the End Stage Renal Disease Program) or by insurance companies and are, therefore, exogenous to the individual hospital.(4) Further, in an effort to reduce recipient bidding for transplants, guidelines prohibit additional direct charges by hospitals to patients requesting or receiving transplants, although some violations of these restrictions have apparently occurred. The third and fourth assumptions provide a reasonably accurate depiction of the transplant production process and also serve to substantially simplify the analysis. And the fifth and sixth assumptions appear to characterize the market conditions that exist in the procurement of organs for transplantation.

Moreover, it is important to recognize that assumptions five and six imply that the organ supply curve is kinked at [Mathematical Expression Omitted].(5) As a result, the marginal factor cost curve for organs faced by the monopsonist hospital will exhibit a gap at this level of organ procurement. Thus, our model is one of monopsony with kinked supply.

Initial Equilibrium with No Procurement Effort

To develop our model of the input-constrained firm, we begin with the simplest possible case. Specifically, we initially assume that the firm has no control over the supply curve of organs, [Q.sub.O]([P.sub.O]). That is, organ supply is given exogeneously and organ price is set administratively at [P.sub.O] = 0. Given these assumptions, a hospital may acquire (or accept) anywhere from zero up to [Mathematical Expression Omitted] organs for use in the corresponding number of transplant operations. If [P.sub.T] [greater than] [MC.sub.T], the profit maximizing number of transplants will equal the maximum number of organs that can legally be acquired at the zero price, i.e., [Mathematical Expression Omitted]. This result follows from the fact that the value of the marginal product of organs (the marginal net revenue of transplant operations times the marginal product of organs) is [P.sub.T] - [MC.sub.T],(6) while the marginal factor cost of organs is zero up to [Mathematical Expression Omitted]. Thus, if [P.sub.T] [greater than] [MC.sub.T], the hospital will choose to acquire [Mathematical Expression Omitted] organs for transplantation. Conversely, if [P.sub.T] [less than] [MC.sub.T], then [Mathematical Expression Omitted].(7) That is, in this latter case, the hospital will refrain from entering the transplantation industry and will accept no organ donations.

These initial equilibria are shown in Figure 1 for two alternative reimbursement rates, [P.sub.T] and [P[prime].sub.T], where [P.sub.T] [greater than] [MC.sub.T] and [P[prime].sub.T] [less than] [MC.sub.T].(8) If the hospital elects to enter the transplant industry (i.e., if [P.sub.T] [greater than] [MC.sub.T]), its profits are given by the area [Mathematical Expression Omitted]. These profits obviously increase with increases in the exogenous reimbursement rate, [P.sub.T]. Consequently, any increases in this rate over time provide a potential explanation for observed entry into the transplant industry.

Figure 1 also suggests that, where [P.sub.T] [greater than] [MC.sub.T], hospital profits will increase with exogenous increases in the value of [Mathematical Expression Omitted]. In other words, a shift in the supply of organs that causes more to become available at the regulated price of zero will raise the total profits obtained from transplants. Thus, hospitals already performing transplants would like to acquire more organs and perform more transplants (i.e., expand) if they could costlessly obtain these organs at a price of zero.

Although Figure 1 represents the marginal benefit of an organ to transplant providers as the difference [P.sub.T] - [MC.sub.T], the patients' willingness to pay for organs may be much higher. Given a targeted, use-restricted subsidy of [P.sub.T] dollars per patient, a consumer with an unsubsidized willingness to pay of $W will presumably offer up to W + [P.sub.T] for a transplant, or W + [P.sub.T] - [MC.sub.T] for an organ when procedures are sold for [MC.sub.T]. Regulations seek to limit providers' charges to [P.sub.T], yet it would be strange if the potentially substantial additional surpluses enjoyed by many recipients did not lead to some rent seeking activities. In particular, some patients hoping to become recipients, and some transplant centers, may search for creative ways to "recontract" outside the regulations. Figure 1 represents consumers' willingness to pay for organs (inclusive of the subsidy) by the marginal benefit curve [D.sub.O] (assuming that transplant procedures are obtainable at the cost [MC.sub.T]). In the absence of a restriction on organ sales, equilibrium would occur at price [P.sub.e] and quantity [Q.sub.e].

To this point, we have taken [Mathematical Expression Omitted] as exogenous to the hospital's decision-making calculus. But, in fact, hospitals have some (albeit limited) ability to shift the organ supply curve to the right by investing in activities that increase organ donations (e.g., educational activities, advertising programs, procurement teams, etc.). Such acquisition activities, of course, entail costs. By increasing organ procurement efforts, however, the hospital can shift the organ supply curve to the right. Modifying our model to endogenize organ acquisition efforts and costs provides additional insight into the hospital's optimization problem and, ultimately, the incentive to enter and expand.

Optimal Procurement Effort

Assuming that organ supply can be increased by increasing procurement efforts, we alter assumption 5 to:

5[prime]. The supply curve of organs is given by [Q.sub.O]([P.sub.O], E), with [Delta][Q.sub.O]/[Delta][P.sub.O] [greater than or equal to] 0 and [Delta][Q.sub.O]/[Delta]E [greater than] 0, where E represents the level of the hospital's expenditures on organ procurement efforts.

Given this reformulation, the hospital's optimization problem is one of selecting [E.sup.*], the profit-maximizing level of organ procurement expenditures.

With positive organ prices proscribed by law, increases in organ procurement expenditures have the effect of shifting [Mathematical Expression Omitted] to the right. Thus, with [P.sub.O] = 0, the hospital's organ supply curve, [Q.sub.O]([P.sub.O], E), effectively becomes [Mathematical Expression Omitted]. Hospital profits, then, are given by

[Mathematical Expression Omitted].

The first-order condition for maximization of equation (1) is

([P.sub.T] - [MC.sub.T])([Delta][Q.sub.O]/[Delta]E) - 1 = 0. (2)

The solution to (2) then yields the hospital's optimal organ procurement expenditures, [E.sup.*].(9) This equation simply says that the hospital will invest in organ procurement efforts up to the point at which the marginal net revenue of such efforts equals the marginal cost of acquiring the next organ at the legal price of zero. Thus, Figure 1 still characterizes the equilibrium number of organs procured and transplants performed if So is interpreted as the organ supply curve that exists at [E.sup.*]. We turn now to consider how this equilibrium condition can shed light on the incentive to enter and expand.

III. The Incentive to Enter and Expand

The basic incentive for hospitals to enter the transplant industry is closely tied to the existing shortage of transplantable organs. Specifically, the current policy mandating a zero price for organs creates rents in the transplant industry by artificially restricting the quantity of organs supplied and transplants performed.(10) Particularly in the presence of inelastic demand (which, no doubt, is the case with organ transplants), such an output restriction yields a demand price for organs of [Mathematical Expression Omitted] in Figure 1.

A hospital's ability to capture the resulting rents directly in the price charged for transplant operations is obviously constrained by the fixed reimbursement rate set by the funding agency or insurance company. Nonetheless, so long as [P.sub.T] [greater than] [MC.sub.T], some of these rents can be appropriated directly by entering the transplant industry. While it is not our purpose here to explore the potential avenues through which rents that cannot be appropriated through the reimbursement rate may be captured by transplant providers, it seems likely that such rent-seeking activities could assume a variety of forms.(11) The goodwill, prestige, and demand interdependency effects described by P-G are possible examples. In any case, increases in organ demand (which lead to increases in the organ shortage) create additional rents in the transplant industry that hospitals may attempt to capture in one form or another.

The bulk of human organs used in transplantation are obtained from cadavers. While only a small fraction of all deaths result in potentially transplantable organs, most hospitals experience a sufficient number of qualifying deaths to supply at least a small transplant center.(12) Without such a center, when a patient dies under circumstances allowing transplantable organs to be removed, the hospital has only two options - either allow the (valuable) organs to go uncollected, or collect them and ship them to another hospital that has a transplant program.(13) In either case, none of the potential rents associated with the organs are captured by the hospital making the decision to solicit the organs.

Therefore, the zero price policy creates potentially large economic rents that can be appropriated only by those hospitals that have entered the transplant industry. In terms of the model developed above, if we ignore the indirect benefits of entry, a hospital will enter the transplant industry if [P.sub.T] [greater than] [MC.sub.T] and [Mathematical Expression Omitted] at [E.sup.*]. In other words, entry will occur if profits are positive at the optimal level of procurement effort, i.e., if

[Mathematical Expression Omitted].

Any indirect benefits of having a transplant center associated with the hospital, such as those identified in P-G, will reinforce the direct profit incentive to enter provided by equation (3).

For a given distribution of the marginal costs of transplantation across hospitals, an increase in [P.sub.T] will obviously encourage additional firms to enter. With regard to the incentive to expand, we have

[Mathematical Expression Omitted].

The numerator of the expression on the RHS is negative, and the denominator is also negative (by the second-order condition for maximization of equation (1)). Therefore, [Delta][E.sup.*]/[Delta][P.sub.T] [greater than] 0. An increase in reimbursement rates will cause organ procurement expenditures to increase.

It would seem reasonable to assume that increases over time in the demand for organ transplants (which lead directly to increases in the derived demand for organs, the associated demand price, [Mathematical Expression Omitted], and the organ shortage, shown in Figure 1 as [Mathematical Expression Omitted]) will ultimately cause the reimbursement rate, [P.sub.T], to increase as well. The empirical evidence appears to support this assumption. Table I shows the marked increases in the shortage of organs for transplantation that have occurred since 1987. Although the organ shortage has existed for decades, it became substantially worse during the latter part of the 1980s and the early 1990s.(14) As a result, the (unobserved) demand price for organs has undoubtedly increased significantly as well. Moreover, this increase in the market value of transplantable organs has translated, at least in part, to an increase in transplant reimbursement rates, particularly in the charges for organ acquisition reimbursed by funding agencies. Table II provides the relevant data. Moreover, even in the absence of direct profit incentives provided by increases in [P.sub.T], less direct avenues for appropriation of increased rents provide incentives to enter and expand as organ demand grows.

Table I. Number of Patient Registrations on the National Transplant
Waiting List(*)

                              Kidney              All Organs

12/31/87                      11,822                13,115
12/31/88                      13,943                16,026
2/31/89                       16,294                19,095
12/31/90                      17,883                21,914
12/31/91                      19,352                24,719
12/31/92                      22,376                29,415
12/31/93                      24,973                33,394
7/31/94                       26,077                35,476

* The number of patients awaiting organ transplants may be fewer
than the numbers listed in this table because some patients may be
listed with more than one transplant center.

Source: UNOS Update [11].

[TABULAR DATA FOR TABLE II OMITTED]

Thus, the organ shortage, which has worsened considerably in recent years, creates economic rents that, under the existing prohibition on organ sales, can only be captured by hospitals entering the transplant industry. Consequently, a major force driving observed entry and expansion efforts in this industry is the existing policy that has created that shortage - the legal proscription of organ sales.

IV. Conclusion

In their paper, P-G attempt to explain recently observed entry and expansion efforts in the organ transplant industry that have occurred despite an alleged perception that transplantation is unprofitable. Simply put, these authors argue that this apparent anomaly is the result of inadequate accounting. According to P-G, economies of scope, demand complementarities, and learning curve effects render transplantation profitable to the hospital's overall operations, while a more narrow accounting gives the illusion that these activities are unprofitable. We have no real quarrel with that basic argument.

Rather, our work seeks to expand the P-G analysis by explicitly modeling the effects of the organ shortage on the transplant firm's (hospital's) optimization problem. This shortage is created by the existing law which sets the legal price for cadaveric organs at zero. The resulting organ shortage and the corresponding shortage of transplant operations gives rise to substantial economic rents. Because payment for organs is proscribed by law, the only avenue through which hospitals harvesting organs can capture these rents is by entering the transplant industry. It is this incentive to capture increasing rents, rather than some accounting anomaly, that appears to explain the recent entry and expansion efforts in the transplant industry. One simply cannot fully understand observed behavior in this market without first accounting for the microeconomic ramifications of this shortage.

A. H. Barnett T. Randolph Beard David L. Kaserman Auburn University Auburn, Alabama 

The authors wish to thank the anonymous referee for useful comments on a prior draft of this paper. The usual caveat applies.

1. The National Organ Transplant Act of 1984 prohibits any form of tangible compensation in interstate exchanges involving transplantable organs. More specifically, the Act states: "It shall be unlawful for any person to knowingly acquire, receive or otherwise transfer any human organ for valuable consideration for use in human transplantation if the transfer affects interstate commerce." Participation in such exchanges is designated a felony by the act. See the National Organ transplant Act, Supp. IV 1986, 274(e) [12]. Every state has passed similar legislation prohibiting intrastate commerce in organs.

2. The number of patients who died waiting for a transplant nearly doubled between the mid 1980s to early 1990s, as noted by Peters [9].

3. The seminal work in this area is that of Averch and Johnson [1]. Since that article appeared, a flood of literature has developed exploring firms' behavior under a variety of regulatory constraints. For a survey of much of this work, see Baumol and Klevorick [2].

4. The bulk of all transplants performed are covered either by Medicare or by private insurance companies. Nonetheless, some transplants are paid for directly by the patient, and, for these, the hospital may have some control over [P.sub.T]. Our analysis, however, is not sensitive to the assumption that [P.sub.T] is fixed exogenously.

5. It is perhaps worth note that the organ supply curve described by assumption 5 has nothing to do with organ procurement costs. Rather, it simply depicts the number of organs suppliers (donors) would be willing to supply (donate) at each price. Obviously, some organs (e.g., [Mathematical Expression Omitted]) are supplied (donated) at a zero price. Our positively sloped supply curve at quantities greater than [Mathematical Expression Omitted] simply reflects our assumption that positive prices paid to organ suppliers (donors) would induce some, who would not provide organs at a zero price, to allow their (family member's) organs to be harvested for transplantation.

6. With [Q.sub.T] = [Q.sub.O], the marginal product of organs equals one. The marginal net revenue of organs is [P.sub.T] - [MC.sub.T].

7. Because we have assumed that both [P.sub.T] and [MC.sub.T] are constants, either [P.sub.T] [greater than] [MC.sub.T] or [P.sub.T] [less than] [MC.sub.T] will hold throughout. As a result [Mathematical Expression Omitted] will be either [Mathematical Expression Omitted] or zero. An interior solution, [Mathematical Expression Omitted], could be obtained if [P.sub.T] were declining and/or [MC.sub.T] were increasing. Modifying our model to allow for either possibility would complicate but not materially affect our analysis.

8. The zero price constraint requires that output occur somewhere on the 0, [Mathematical Expression Omitted] closed interval. Excess demand (an organ shortage) exists anywhere along this interval, however, because the derived demand for organs, [D.sub.O], equals [Mathematical Expression Omitted] at [P.sub.O] = 0.

9. The second-order condition for maximization of (1) requires that

([P.sub.T] - [MC.sub.T])([[Delta].sup.2][Q.sub.O]/[Delta][E.sup.2]) [less than] 0.

10. A policy requiring a zero price for organs is analytically similar to the formation of a cartel agreement in the transplant industry. Either approach restricts output below the competitive level. See Barney and Reynolds [3], Kaserman and Barnett [7], Barnett and Kaserman [5], and Blair and Kaserman [6].

11. For example, in a recent article McCartney [8] reports that ". . . hospitals were offering million-dollar signing bonuses to lure coveted transplant surgeons."

12. Typically, cadaveric organs are suitable for transplantation when they are acquired from a brain-dead, infection-free, heart-beating cadaver, where the individual was relatively young and in good health at the time of the event which caused death. Such individuals are often victims of a terminal head injury.

13. In the event the organs are collected and sent elsewhere for transplantation, the hospital where the organs are harvested is compensated only for use of its operating room and other direct expenses associated with organ removal. Legally, it can receive no payment for the organs themselves.

14. see Barnett, Beard and Kaserman [4] for a discussion of opposition in the medical community to policy changes which could ameliorate this shortage.

References

1. Averch, Harvey and Leland L. Johnson, "Behavior of the Firm under Regulatory Constraint." American Economic Review, December 1963, 1052-69.

2. Baumol, William and Alvin Klevorick, "Input Choices and Rate-of-Return Regulation: An Overview of the Discussion." Bell Journal of Economics, Autumn 1970, 162-90.

3. Barney, L. Dwayne, Jr. and R. Larry Reynolds, "An Economic Analysis of Transplant Organs." Atlantic Economic Journal, September, 1989, 12-20.

4. Barnett, Andy H., T. Randolph Beard and David L. Kaserman, "The Medical Community's Opposition to Organ Markets: Ethics or Economics." The Review of Industrial Organization, December 1993, 669-78.

5. Barnett, Andy H. and David L. Kaserman, "The 'Rush to Transplant' and Organ Shortages." Economic Inquiry, July 1995.

6. Blair, Roger D. and David L. Kaserman, "The Economics and Ethics of Alternative Cadaveric organ Procurement Policies," Yale Journal of Regulation, Summer 1991, 403-52.

7. Kaserman, David L. and Andy H. Barnett, "An Economic Analysis of Transplant Organs: A Comment and Extension." Atlantic Economic Journal, June, 1991, 57-63.

8. McCartney, Scott, "Agonizing Choices: People Most Needing Transplantable Organs Now Often Miss Out." Wall Street Journal, April 1993, 1.

9. Peters, Thomas G., "Life or Death: The Issue of Payment in Cadaveric Organ Donation." Journal of the American Medical Association, March 13, 1991, 1302-305.

10. Possai, Kathleen W. and Michael Goetz, "Scope, Learning, and Cross Subsidy: Organ Transplants in a Multi-Division Hospital." Southern Economic Journal, January 1994, 715-26.

11. United Network for Organ Sharing (UNOS Update), Vol. 10, Issue 8, August 1994, p. 48, and Vol. 10, Issue 7, July 1994, p. 37.

12. U.S. Congress, National Organ Transplant Act, Pub. L. No. 98-507, 98 Stat. 2339 (codified as amended at 42 U.S.C. & 273-274 (e)) (Supp. IV 1986).