Increased Capacity May Exacerbate Rationing Problems: \\ With Applications to Medical Care\footnote {We are grateful to the referees and the editor for their suggestions. }

Increased Capacity May Exacerbate Rationing Problems:
With Applications to Medical Care1

Amihai Glazer
Department of Economics, University of California, Irvine
, Lawrence S. Rothenberg
Department of Political Science, University of Rochester

Mar 22, 2001


Denial of service is more costly or difficult when the capacity to serve an individual exists (or when serving him does not reduce the service provided others) than when limited capacity makes it effectively impossible to serve some persons. In the presence of such differential costs of limiting service, a reduction in capacity (even when free) may increase social welfare. A review of data on medical care suggests that reductions in capacity may be necessary to limit the provision of care.

Corresponding author:
Amihai Glazer
Department of Economics
University of California, Irvine
Irvine, CA 92612
Telephone: 949-824-5974
Fax: 949-824-2182

The provision of medical care differs from the provision of other goods in several ways, many of them stemming from the terribly high importance consumers place on it. One feature, well studied in the literature, is the demand for medical insurance and the moral hazard problems that arise from it. Another characteristic, however, has been little studied-the difficulty of denying care to a person who wants it.

We focus on two observations. First, limiting service can be costly. When denying care is so costly as to be impractical, we can view it as not credible, or can say that government is unable to commit to denying service to some people.

The essential idea that some policies may not be credible appears in works on trade protection (Staiger and Tabellini (1987), Matsuyama (1990), and Tornell (1991)), disaster relief (Rodrik and Zeckhauser (1988)), monetary policy (Barro and Gordon (1983), Kydland and Prescott (1977), Persson (1988)), medical insurance, (Pauly (1989, 1990), Glazer and Niskanen (1992)), and medical care. Fuchs (1968) and Mechanic (1994) discuss the ``technological imperative," an inclination to use medical interventions, however costly, that promise any possible benefit, however small. These papers simply assume the inability to commit, and view it as a constant.

We instead examine the conditions under which denial of a service is more or less difficult, and examine how policy can affect the severity of the commitment problem. We do so by relying on our second observation, the difference between specific and abstract restrictions on service. Specific restriction denies service to a particular person, who knows he is denied service, and who knows that if a person in authority (e.g. physician, government bureaucrat, or HMO officer) changed a decision the consumer would be served. Specific restriction, we claim, imposes costs, costs which are smaller when capacity is low. Such capacity reduction, in turn, forces authorities to make explicit trade-offs. In contrast, we call supply limitations via capacity constraints abstract restriction, since at the time the capacity is set the identities of the persons who will be denied care are unknown.2

The distinction was well stated by Schelling (1968, p.129). ``Let a six-year old girl with brown hair need thousands of dollars for an operation that will prolong her life until Christmas, and the post office will be swamped with nickels and dimes to save her. But let it be reported that without sales tax the hospital facilities of Massachusetts will deteriorate and cause a barely perceptible increase in preventible deaths-not many will drop a tear or reach for their checkbooks.''

The claim has been subject to little empirical study. But data do support it. Schwing (1979) compares different programs by their costs of extending longevity. Of the programs he studies, 12 involve health care (as opposed, for example, to pollution control). Of these 12 programs, 3 involve treatment of identified lives (these programs are for kidney transplant, home kidney dialysis, and hospital kidney dialysis). These 3 were the most expensive of the 12 programs. For example, the cost of increasing longevity by kidney dialysis was about 20 times the cost of increasing longevity by screening for cancer.

We interpret rationing broadly. In particular, restrictions on service by pricing involve specific restriction-someone must tell a specific individual who wants care that he will be denied service because the patient is unwilling or incapable of paying for it. The person who does not get the service knows who he is, and may exert effort to obtain it either at a lower price, or even for free.3 And since the moral or political revulsion at denying medical care is far greater than the pain of denying a movie ticket or a new car, abstract rationing may be especially common in health care. It is also worth noting that the United States increasingly uses direct, specific, restrictions, which do not rely on pricing-health maintenance organizations charge members a fixed fee per year, and a low marginal fee for care.

1  Assumptions

We build on a simple model of moral hazard, extending it in two directions. First, we consider how a change in capacity changes the quantity supplied and changes social welfare. Second, we allow denial of care, which entails a social cost.

Let capacity, a choice variable of government or other organization, be K. To highlight the effects, let its cost be zero. The variable cost of providing medical care in the quantity q is cq.

The quantity demanded decreases with the price, p. The price need not be the market price, but can instead be the highest price which does not result in moral revulsion, or the highest price considered morally acceptable. In some cases the price relevant for our purposes is zero, even though the market price is higher. The reduced demand resulting from a non-zero price would then represent specific rationing. We take the price a consumer faces as fixed. Of course, non-price rationing may lead to misallocation of services-the people who mostly highly value the good need not be the ones who receive it (for evidence of this effect in housing markets, see Glaeser and Luttmer (1997)). The existence of such inefficiencies would call for a greater quantity of service than implied by our analysis below. For simplicity, however, we shall ignore this affect, assuming that any quantity of service provided is given to those who most highly value it.

Nevertheless, restricting care is costly, because of rent-seeking activities by persons denied care, because of the emotional pain suffered by a person when he denies care to a particular individual, or because of citizen's moral revulsion when they hear of persons denied care. This cost increases with the difference between the quantity consumers would demand at the morally acceptable price and the quantity supplied, and increases with capacity.

2  The effects of increased capacity

In Figure 1, let the demand curve be DD, which also represents the marginal benefit of service to consumers. We suppose for simplicity that demand does not vary with capacity.4 The marginal social cost of service is c, and the morally acceptable price is p. In the absence of rationing, the quantity supplied would be QD, where the marginal private benefit equals the price. The socially optimal solution, ignoring all rationing costs, is at Q0, where marginal social cost (c) equals marginal benefit.

The amount of care provided can be less than that demanded at the morally acceptable price. Curve QD R1 shows the marginal cost of rationing care with a given capacity, say K1. The number of persons denied care is measured not from the origin, but by the distance to the left of QD. The marginal rationing cost is positive, and increases as more persons are denied care. One reason for the increasing marginal rationing cost is that as fewer persons are served, the benefit they would receive from care increases, and so the moral revulsion of denying care, or the rent-seeking efforts by potential benefits, increases. Thus, we would expect rationing costs to be higher the higher the marginal benefit of service, as given by curve DD. The total cost of specific rationing is the area under curve QDR1 between the quantity of service provided and QD. Given this rationing cost, the socially optimal solution is not at Q0, but at a greater quantity, Q1. At this point the marginal benefit of increasing service equals the marginal cost. The marginal benefit of increasing service consists of the marginal benefit of consumers (given by the height of the demand curve at Q1, minus the cost c), plus the reduction in rationing costs (equal to the height of curve QDR1, or the distance Q1G). The net marginal benefit is zero at Q1, since distance EF equals distance Q1G. Note that costliness of specific rationing makes the optimal solution provide more service than Q0.

Consider an increase in capacity. By assumption this does not increase demand, and does not increase the marginal cost of service. But critical to the analysis is the assumption that for any given level of service, rationing costs increase with capacity. Partly this may occur because efforts by persons to obtain care will be low if they know that few additional persons can be served. And partly it may reflect the moral and emotional anguish persons suffer when denying care to save money, rather than because there is no choice.

The increased capacity thus shifts the curve showing marginal rationing costs from QDR1 up to QDR2. The new optimal solution is at quantity Q2, where the distance JK equals the distance Q2H. Note that an increase in capacity here increases the service provided. Note further that it can reduce net social benefits. First, the increase in service increases social loss (the difference between the cost and benefit of service) by the area of trapezoid EJFK. Second, since the marginal rationing cost increased for each level of service, but the quantity supplied also increased, rationing costs have changed by the area of triangle HMQD minus the area of trapezoid GQ1Q2M.5 The total effect can be that even if capacity is costless, increased capacity lowers social welfare.6 Thus, rational voters may favor a reduction in capacity, even when realizing that they may thereby be denied care. One reason is that the lower service thereby induced reduces costs and so reduces taxes or premiums for medical insurance. The other reason is that for any level of service rationing costs decline.

3  Medical care

We do not know how to test our model directly. But the evidence is consistent with the assumptions and results of our model. Most notably, as expected by our analysis, government rarely denies important treatment when capacity exists. Additionally, abstract restrictions have worked. Nations which restrict capacity have more effectively limited treatment than has the United States, which does not constrain capacity.7

Following are some examples:

(1) Ontario, Canada controls both the number of hospitals allowed to perform coronary artery bypass surgery (CABS) and the number of procedures, New York State limits only the number of hospitals offering the procedures, and California curbs no services. These differences affected the amount of treatment given. Older residents of Ontario, Canada were less likely than New Yorkers and Californians to receive CABS. While younger residents (20-44) and middle-age residents (45-54) of Ontario were more likely and as likely respectively to receive CABS as their counterparts in California, the rate for older (65-74) and elderly (75+) Californians was 2.1 and 6.6 times higher (Anderson et al., 1993).

(2) Consider bone marrow transplants for treatment of chronic myeloid leukemia, which are most effective for patients in leukemia's early, chronic, stage. Such transplants are less productive, if effective at all, in later stages. Also, older patients are far more likely to die from the treatment than are younger patients. A comparison of treatment patterns in ten wealthy countries shows that, as expected given the high capacity in the U.S., during the period 1989-1991 the U.S. had one of the highest rates of treatment for patients not in the chronic phase (30 percent, compared, for example, to 21 percent in Canada) and the highest rate of transplants for patients aged 55 or older (General Accounting Office (1994)).

A similar pattern is found in transplants provided in these ten nations for patients with acute myeloid leukemia. While transplants are likely to be effective in the early stages of the disease, for advanced leukemias the transplants are often futile. Once again, the United States, with its extensive capacity, was unable to prevent the quick provision of care, even where the advanced state of the acute leukemia makes treatment largely pointless. Thus, with the possible exception of France, the U.S. had the highest rate of treating patients who had advanced disease, but the shortest time from diagnosis to treatment. Countries with limited capacity showed the opposite treatment pattern. For instance, patients in the United Kingdom and New Zealand had long waits from diagnosis to treatment, but care went overwhelmingly to those patients who would most benefit from it.

(3) A comparison of the United States with Great Britain (which uses abstract restrictions far more than does the U.S.) highlights how abstract restrictions can reduce delivery of services.8 Consistent with our model, Britain has most restricted care which requires large capital expenditures or costly investments in training highly specialized staff.

Illustratively, dialysis in Britain is far more limited than in the U.S. because the requisite equipment, expenditures, and investments in training qualified nurses and technicians are constrained; admission to intensive care units for all but the most severe cases is difficult because of the limited facilities; and CAT scans are used at 20 percent of the U.S. rate. When capacity is not a constraint, as in radiation therapy, British rates of treatment approximate U.S. rates.9 Generally, it is far more difficult in Britain to get treatment which requires considerable time from specialized personnel or which requires much use of physical plant (e.g., operating rooms).

(4) By contrast, since abstract restrictions are ineffective when fixed costs are small, care that can be given by regular medical personnel or with drugs and supplies is comparatively easy to receive in Great Britain. For example, Britain spends as much on Total Parenteral Nutrition (the provision of nutrition which bypasses the digestive system), which requires little capital and can be allocated by physicians on a case-by-case basis, as on CAT scans. In contrast, it is difficult to restrict the supply of pharmaceuticals,10 partly because they can be imported, and Britain has not much limited the use of pharmaceuticals as compared to the United States (Hutton 1994).

(5) Also reflecting the logic of abstract restrictions are the common delays in Britain (and other national health care systems) in hospital admissions and for capital-intensive care. In Britain, one-third of all patients admitted had waited for three months or more; six percent waited for over a year. By contrast, such delays are rare in the United States, largely because capacity has been expanded rather than constrained. Diverse policy choices-ranging from generous Medicare reimbursement rates to the authorization of tax-exempt bonds-subsidized capital projects that expanded hospital capacity (Stevens 1989). Reflecting this large capital stock, American physicians complained far less than physicians in other countries about a lack of well-equipped medical facilities (Blendon et al., 1993).

4  Conclusion

In short, evidence from the medical sector suggests that restricting service requires restricting capacity; in line with our assumption that specific rationing is costly, the existence of large capacity induces treatment of many patients. Though we described an increase in capacity as an increase in capital, we can also view it as a technological change, or as improved incentives. Patient stays, for example, may become shorter. The usual view supposes that such a decrease in the time required to serve a customer increases welfare. But in the world we are discussing, it can cause more persons to be treated, increasing total costs and reducing social welfare.

Such findings suggest that delays in providing medical service may be a hallmark of successful rationing (since the capacity constraints needed to limit service can impose waits for all but emergency treatment) rather than a reflection of inefficiency, poor management, or misguided cost savings. Stated differently, patients in countries with lower health expenditures may have longer waits than American patients not because excess demand is greater outside the U.S. (although it may be) but because political pressures make specific rationing costly; exceptionally high U.S. health care costs result partly from failure to restrict capacity and assure queuing.

Our perspective and findings have a broad implication for public policy: policies which seem inefficient may reduce the inefficiencies associated with the political pressures generated by specific rationing. Though we do not claim that apparent inefficiencies always reflect strategic behavior by savvy politicians, one of the few means to control pressures for service is by increasing costs, creating delays, reducing capacity, and establishing queues. Minimally, some bad effects of government actions may be inadvertently mitigated by such behavior.

As seen in our examination of health care, government may have an incentive to provide services directly (e.g., through a national health service) to restrict physical capacity and services-even when the private sector can produce them more cheaply. Government may prefer public housing to private subsidies because it can more effectively restrict the number of persons assisted; government may run job training programs rather than contract out because it wants to limit the number of spots available. Similarly, when capacity constraints restrict personnel, seemingly arcane work rules (e.g., those preventing nurses from delivering drugs) which limit supply may enhance efficiency.

We do not claim that the only reason government produces services that could be more efficiently provided by the private sector is to counter political pressures by restricting capacity. Nor do we claim that the only motive for personnel restrictions is to restrict service. Similarly, we do not assert that the underlying motive for all byzantine bureaucratic procedures is the desire to restrict service. Nonetheless, one byproduct of such activities may be a form of abstract rationing that constrains the provision of governmental services.

5  References

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Anderson, G., M. Anderson, et al., 1993, Use of coronary artery bypass surgery in the United States and Canada, Journal of the American Medical Association 269, 1661-1666.
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Blendon, R.J., et al., 1993, Physician's perspectives on caring for patients in the United States, Canada, and West Germany, New England Journal of Medicine 328, 1011-1016.
Chassin, M. R., K. L. Kahn, and D. H. Solomon, 1987, Does inappropriate use explain geographic variations in the use of heath care services?, Journal of the American Medical Association 258, 2533-2547.
Fuchs, V. R., 1968, The growing demand for medical care, New England Journal of Medicine 279, 190-195.
General Accounting Office, 1994, Bone marrow transplantation: International comparisons of availability and appropriateness of use, Report No. PEMD-94-10.
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1We are grateful to the referees and the editor for their suggestions.

2 Mechanic (1997) makes a similar distinction between explicit and implicit rationing, where his explicit rationing resembles our abstract restriction. His insightful criticisms of explicit rationing concentrate largely on equity and imperfect information. Unlike us, however, he does not consider the cost to a decision maker of denying care to a specified person.

3 See Thaler (1985), Russell and Thaler (1985), and Kahneman, Knetsch, and Thaler (1986a, 1986b). The courts also find in other areas that denial of service by pricing is wrong. In Bodie vs. Connecticut 401 US 371 (1971), the Supreme Court ruled that a state may not require filing fees for divorce. In Harper vs. Board of Elections, 338 US 663 (1966) the Supreme Court ruled that a poll tax establishes an unreasonable classification based on wealth.

4 Consistent with our assumption, Martin and Smith (1999) find that in Britain changes in waiting times did not affect demand. Similar results apply if the demand curve does shift, but that an increase in capacity benefits marginal consumers more than inframarginal ones.

5 Of course, depending on the shape of the two curves depicting marginal rationing costs, the difference could be positive or negative. Analytical proof is available from the authors that under reasonable specifications the effect of increased capacity can be to reduce social welfare.

6 In this model, at the optimal solution all capacity is used. If, however, the model is extended to consider stochastic demand and waiting times which decline with capacity, then optimality would require excess capacity on average.

7 Limited capacity may not be the only, or main, cause for differences in treatment in different areas. Chassin, Kahn, and Solomon (1987) examine differences in the appropriateness of three procedures (coronary angiography, carotid endarterectomy and upper gastroinstestinal endoscopy) in geographic areas with different rates of use. The data were in the direction of the hypothesis that less appropriate or more inappropriate procedures were found in areas of high use. But in no case can differences in appropriateness explain the large differences in overall rates. They speculate that regional social and cultural differences may produce the differences in use.

8 The data on Britain are taken from Aaron and Schwartz (1984). Also Martin and Smith (1999) find evidence that an increase in the number of beds increases, though not by much, the quantity of service provided. The focus here, however, is on more specific capital constraints

9Aaron and Schwartz (1984, p. 44) report that though Britain has only 44 percent as many megavolt machines available per capita as the U.S., it has more radiotherapy technicians per patient, and with higher utilization has enough equipment to treat all patients who would benefit. Moreover the costs of radiotherapy are low-$500 million in the US, and less than $125 million in Britain. Thus the British could not save much by reducing the quality and quantity of radiotherapy treatment.

10 In contradiction, however, Britain uses far less chemotherapy for cancer treatment than does the US, perhaps because British physicians believe the toxic side effects outweigh the therapeutic benefits (Aaron and Schwartz (1984)).