do hmos encourage prevention? an analysis of alternative health care plans

Contemporary Economic Policy(ISSN 1074-3529)Vol. 20, No. 4, October 2002, 429–439 © Western Economic Association International

DO HMOs ENCOURAGE PREVENTION?AN ANALYSIS OF ALTERNATIVE HEALTH CARE PLANS

THOMAS J. MICELI and DENNIS HEFFLEY*

We examine consumers’ choice of preventive care and providers’ choice of capac-ity (which affects the transaction costs of consuming health care) under alternativehealth care financing plans. We show that consumers choose Pareto-optimal preven-tion and providers choose optimal capacity under a pure fee-for-service (FFS) planand under a mixed plan that includes an up-front fee and a fee for service. Undera pure prepaid plan, however, consumers may over- or underconsume prevention.In the former case, capacity restrictions under such a plan (e.g., long office waits,limited options) may be interpreted as a second-best response to overconsumption.We also find that the dollar costs of health care are higher under the prepaid plan.These conclusions cast doubt on some of the presumed advantages of HMOs. (JEL(I11, I18)

I. INTRODUCTION

For roughly 20 years, federal policies haveencouraged the formation and growth ofhealth maintenance organizations (HMOs)and other prepaid forms of “managed” care.1

Recent health care reform proposals con-tinue to stress the need for managed or“consolidated” care. This favored treatmentis based on several presumed attributes ofprepaid medical plans. First, because pre-payment shifts the risk of financial lossassociated with illness from the patient to theprovider, the provider may have a strongerincentive to minimize the costs of care. Sec-ond, larger groups may enjoy economies ofscale or scope in the provision of medi-cal services. Third, because of the contrac-tual obligation to provide medical care for afixed premium, prepaid groups may have a

*We are grateful to participants in the Universityof Connecticut Applied Microeconomics Workshop andIndustrial Organization Workshop for their helpful com-ments. We also acknowledge the comments of an anony-mous reviewer.Miceli: Professor, Department of Economics, U-63, Uni-

versity of Connecticut, Storrs, CT 06269. Phone1-860-486-5810, Fax 1-860-486-4463, E-mail [email protected]

Heffley: Professor, Department of Economics, U-63, Uni-versity of Connecticut, Storrs, CT 06269. Phone1-860-486-4669, Fax 1-860-486-4463, E-mail [email protected]. For a thorough review of federal HMO policies,

see Cromley (1990).

stronger obligation to deliver preventive ser-vices that reduce the need for future treat-ment.

Economic studies of HMOs have focusedon their presumed cost advantages, asembodied in the first two attributes. New-house (1973), Gaynor (1989), and Gaynorand Pauly (1990) suggest that internal incen-tives do not necessarily work to increase pro-ductivity, reduce costs, and contain pricesin medical groups, but Lee challenges thisview on theoretical (Lee, 1990a) and empir-ical (Lee, 1990b) grounds. Recent studiesby Wholey et al. (1996) and Given (1996)find evidence of scale economies in HMOsat lower output levels but no evidence ofscope economies between commercial andMedicare enrollees.2 Reviews of the empir-ical literature cite evidence of lower per-member costs in HMOs than in comparable

2. Many of the early studies of prepaid plans simplycompare per capita costs in such plans with those in fee-for-service plans, rather than using econometric meth-ods to estimate separate production or cost functions.A notable exception is the study by Bothwell and Coo-ley (1982), which finds some evidence of overall scaleeconomies in a pooled sample of 20 HMOs.

ABBREVIATIONS

FFS: Fee For ServiceHMO: Health Maintenance Organization

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430 CONTEMPORARY ECONOMIC POLICY

fee-for-service (FFS) plans, but most of thisdifference reflects lower hospitalization ratesamong HMO members (Luft, 1981; Welch,1985; Pauly, 1986) rather than any inherenttechnological advantages of prepaid grouppractice. These lower hospitalization ratescould simply reflect a favorable (low-utilizer)selection bias in HMO enrollments, but evenwhere persons have been randomly assignedto HMO and FFS plans, significant differ-ences in hospitalization rates persist (Man-ning et al., 1984, 1987).

The third attribute, the presumed “pre-ventive orientation” of HMOs, is one thathas been widely used to promote the HMOconcept, but remarkably little theoretical orempirical research has been done to supportor refute this notion. Heffley (1982) exam-ined the optimal mix of spending on pre-vention and treatment within a constrainedhealth care budget, which could be inter-preted as a fixed HMO premium. Dowd(1982) investigated the financing of preven-tive care within health care plans, particu-larly HMOs, and concluded that enrollmentuncertainty—whether members will remainenrolled long enough for the HMO to recoupinvestments in the form of lower treatmentcosts—is an important obstacle to providingprevention in prepaid groups.

Cherkin et al. (1990) studied the empiri-cal effects of copayments on the utilizationof various types of preventive services in anHMO. They concluded that “small copay-ments for office visits have little adverseimpact on utilization of the most valuabletypes of preventive care services” (p. 37). Onthe other hand, in their comparison of indi-viduals in several FFS plans with individuals(randomly assigned and previously enrolled)in the Group Health Cooperative of PugetSound, Manning et al. (1984, p. 1507) find“the number of preventive visits was signif-icantly higher in the two GHC groups; costsharing further reduced preventive visits, toa level below the value in the free fee-for-service plan.” More recently, Goldman (1995)has found evidence of a sharp increase in theuse of outpatient services due to more gen-erous HMO coverage (lower copayments) forpreventive care and other ambulatory visits.

In this study, we develop a simple ana-lytical framework for evaluating the con-sumption of prevention by consumers underalternative health care plans. Specifically, we

examine how the method and timing of pay-ment for services affects consumers’ demand.We compare the outcomes under pure FFSplans, pure prepaid (or capitation) plans,and mixed plans that combine fixed prepay-ments (premiums or membership fees) andFFS payments. Given the hybridization ofhealth care plans noted by Feldman et al.(1989), this general approach may be usefulin addressing issues beyond those discussedhere.

The analysis is organized as follows. Thebasic model is described in section II, includ-ing the characterization of a general healthcare payment plan and the derivation ofthe first-best solution, which consists of achoice of prevention by consumers and achoice of “capacity” by providers. Inclusionof a capacity variable for providers enablesus to examine the role of waiting and othertransaction costs in determining consumers’spending on health care, a factor that webelieve is crucial in assessing the desirabilityof HMOs relative to FFS providers. SectionIII examines the choice of prevention by con-sumers as a function of the parameters ofthe payment plan and the level of providercapacity. Section IV turns to an analysis ofthe outcome under the alternative paymentplans. We show that consumers will choosethe Pareto-optimal level of prevention, andproviders will choose Pareto-optimal capac-ity under the mixed payment plan as well asunder a pure FFS plan. Under the pure pre-paid plan, however, consumers either over-or underconsume prevention compared tothe Pareto-optimum. In response, we showthat providers adjust the level of capacity toincrease or decrease the transaction costs ofconsuming care, thereby achieving a second-best level of prevention. This behavior maymanifest itself in actual HMO policy by con-straints on physician choice and longer wait-ing times for visits. We also show that thedollar costs of health care (prevention plusexpected treatment) are higher under theprepaid plan as compared to the mixed andFFS plans. Taken together, the results inthis section therefore cast some doubt onthe claimed preventive orientation and costadvantages of HMOs. Section V briefly exam-ines the impact of third-party insurance onthe conclusions, and section VI examinessome long-run implications of the model.Finally, section VII concludes.

MICELI & HEFFLEY: DO HMOS ENCOURAGE PREVENTION? 431

II. SETUP OF THE MODEL ANDFIRST-BEST SOLUTION

The model is based on Heffley and Miceli(1998) and consists of a single risk-neutralconsumer and a single provider of healthcare.3 The consumer chooses some amount ofpreventive care, x, during healthy states andreceives treatment in the event of illness. Theprobability of illness during some fixed timeperiod, p�x�, is a decreasing convex functionof preventive care;4 that is, p′ < 0 and p′′ > 0.5

Preventive care is produced at a constantaverage (and marginal) cost equal to c, andin the event of illness, the cost of treatmentis T dollars. Thus, the overall expected dollarcost of health care for the single consumerover the given time period is cx+p�x�T . Weassume that the amount of treatment is nota choice variable for the consumer but is dic-tated by the nature of the illness (e.g., by apreset protocol).

The cost borne by the consumer dependson the health care plan offered by theprovider. In the most general case, we con-sider a plan that combines an up-front pre-mium or lump sum fee, F , with an FFS thatcharges the consumer a proportion a ≥ 0 ofthe cost of preventive services, and a propor-tion b≥ 0 of the cost of treatment. (Note thatwe do not restrict a and b to be less thanor equal to one. Thus, they should not beinterpreted as coinsurance rates unless theyturn out to be less than one under an opti-mal plan.) The overall expected dollar cost of

3. We thus do not address risk aversion as a basisfor choosing among the various health plans to focusattention on incentive issues.

4. The model is static in the sense that consumersand providers take the technology of prevention and thecost of prevention and treatment as given. Although bothparties may anticipate future changes in costs and tech-nology, it is not clear whether or how these changesmight affect their current decisions. We therefore ignoresuch dynamic considerations. Although we acknowledgethat technological change affects health care costs, ourfocus here is solely on the role of the financing mecha-nism at a given point in time.

5. Prevention that directly lowers the probability ofillness (e.g., immunization) is referred to as primary pre-vention, whereas testing that screens for illness or riskfactors for illness (e.g., a cholesterol test) is referredto as secondary prevention (Leutwyler, 1995, p. 125).Although our model is explicitly one of primary pre-vention, secondary prevention can also lower expectedhealth care costs by permitting primary prevention priorto onset of an illness, or by promoting earlier andcheaper treatment. The latter case could be capturedby writing treatment costs, T , as a function of x, whereT ′�x� < 0.

this general plan to the consumer during theperiod is thus F + acx+ bp�x�T . Note thatthis plan allows, as special cases, a pure FFSplan if F = 0, and a pure prepaid plan if a=b = 0. We initially assume that the consumerdoes not purchase health insurance (exceptthat which is implicitly offered by the healthcare provider when F > 0); nor does the con-sumer’s employer offer to pay any portionof the premium or FFS as a fringe benefit.This allows us to highlight the incentive rolethat a true FFS plays when consumers actu-ally have to pay it out of pocket. In section Vwe examine how third-party insurance plansthat cover all or part of the cost of preven-tion affect the results.

A crucial element of the model is that, inaddition to the out-of-pocket costs of healthcare, the consumer incurs transaction costs.Some of these costs—for example, the oppor-tunity cost of sitting in the waiting room,scheduling costs, limited choice of physicians,and so on—are influenced by the provider’schoice of capacity; that is, the number ofphysicians employed, the length of hours, theavailability of evening and Saturday appoint-ments, facilities and equipment, and so on.Let k denote the provider’s choice of capac-ity and let C�k� be the cost of capacity, whereC ′ > 0, C ′′ ≥ 0. Given k, the transaction, orwaiting cost for the consumer is w�k� per visit(i.e., per unit of preventive care consumed),where w′ < 0, w′′ ≥ 0.6 (We assume that trans-action costs are incurred only for preven-tive care primarily for simplicity, though webelieve that these costs are relatively moreimportant for this type of care.) Thus, theconsumer’s total expected waiting costs perperiod are xw�k�.7

The consumer’s expected utility in thismodel is given by

EU =W −p�x�d�(1)

where W is spending on goods other thanhealth care and d is the disutility (in dollars)of being ill. Given the cost of health care asdescribed, including waiting costs, the con-sumer’s per period budget constraint is

W = y−F −acx−bp�x�T −xw�k��(2)

6. See Beazoglou and Heffley (1994) for a spatialanalysis of the HMO and FFS sectors that models trans-action costs as costs of travel.

7. If there are multiple patients per provider, wwould also depend on the number of patients.


where y is income per period. Substitutingthis into equation (1) yields

EU = y−F −acx−bp�x�T(3)

−xw�k�−p�x�d�

The provider’s expected profit per consumerunder the general payment plan is given by

�=F +�a−1�cx+�b−1�p�x�T −C�k��(4)

The first-best choices of prevention byconsumers, x, and capacity by providers, k,maximize joint utility and profits. (Note thatthese quantities can be summed given thatutility is measured in dollars.) That is, x andk are chosen to maximize8

EU +� = y−cx−p�x��T +d�(5)

−xw�k�−C�k��

Note that the parameters of the paymentplan, a, b, and F , do not enter this expressionbecause they are simply transfers that deter-mine the allocation of costs. The first-orderconditions for x and k, respectively, are

c+w�k�=−p′�x��T +d�(6)

−xw′�k�=C ′�k��(7)

Condition (6) says that the marginal costof an additional unit of prevention, includ-ing transaction costs, should just equal themarginal benefit in terms of the savingsin treatment costs plus the disutility ofbeing ill. Condition (7) says that capacityshould be increased to the point where themarginal savings in transaction costs equalsthe marginal cost of capacity. Denote thefirst-best levels of prevention and capacitythat result from these conditions by x∗ andk∗, respectively. These are the choices that asocial planner would impose. They will there-fore serve as a benchmark of comparison forthe outcomes under the alternative healthcare payment plans that we examine.

III. THE CONSUMER’S CHOICE OF PREVENTION

We assume that the consumer chooses pre-ventive care x to maximize expected utility

8. This problem can also be solved by maximizingEU subject to � ≥ �0, or by maximizing � subject toEU ≥ U 0, where �0 and U 0 are reservation levels ofprofit and utility, respectively.

FIGURE 1Consumer’s Optimal Choice of Prevention

in (3), taking the parameters (a�b�F �k) asgiven. The first-order condition defining theconsumer’s choice of care, denoted xc, is

ac+w�k�=−p′�x��bT +d��(8)

In this equation, ac+w�k� is the marginalcost (out-of-pocket plus waiting) of an addi-tional unit of prevention, and −p′�x��bT +d�is the marginal benefit in the form of a reduc-tion in the expected cost (out-of-pocket plusdisutility) of becoming ill. Figure 1 illustratesthe consumer’s optimal choice.

Several comparative statics follow imme-diately. First, an increase in the FFS param-eter (a) reduces the demand for preventivecare. This makes sense because an increasein a imposes a greater share of the marginaldollar cost of prevention on the consumer. Incontrast, an increase in the FFS parameteron treatment (b) increases the demand forprevention. Intuitively, as consumers expectto pay a larger share of treatment costs, allelse equal, they will invest more in preven-tion to reduce the expected cost of treatment.An increase in capacity also induces moreuse of preventive services. This is becausean increase in k lowers marginal transactioncosts. Finally, changes in the fixed fee have noimpact on prevention given that F is a sunkcost at the time that x is chosen.9

9. This follows from the fact that there are noincome effects in the model.


IV. THE PROVIDER’S BEHAVIOR UNDERALTERNATIVE PLANS

We assume that the provider chooses thecontract parameters, a, b, F , and capacity,k, to maximize the consumer’s expected util-ity in (3), subject to a minimum profit con-straint � ≥ �0, the constraint that the con-sumer’s choice of x is defined by (8) and anyconstraints on a, b, and F implied by the pay-ment plan. This formulation views providersas competing for consumers, subject to theconstraint that they must achieve a minimumlevel of profit. Although this interpretationabstracts from distortions in the pricing ofhealth care due to market power,10 it is easyto show that the conclusions are largely unaf-fected if providers maximize profits subject toa utility constraint for the consumer.11

A. The Mixed Plan

We first consider a mixed payment planthat includes both an up-front fee and feesfor prevention and treatment. Thus, a, b, andF are all choice variables along with capac-ity, k. In this case, we obtain the followingresult:12

PROPOSITION 1. The optimal mixed pay-ment plan achieves the first-best outcome. Thatis, providers choose the efficient level of capac-ity, k∗, and consumers choose efficient preven-tion, x∗.

Intuitively, the first-best outcome isachieved because the provider has three con-tractual instruments, F , a, and b, with whichto control two choice variables, k and x. Infact, there is a degree of freedom, whichallows one of the contract parameters to bechosen freely. Thus, the optimal contractin this case is not unique. One solution ofinterest is to set b = 1; that is, the consumerpays the full marginal cost of treatment. Inthis case, it also turns out that a = 1, or

10. In addition, by focusing on a representative con-sumer we ignore differences across consumers in theirwillingness to pay for health care, which would causesome to be excluded from the market.

11. In particular, only the optimal F would beaffected by this alternative specification. We show laterthat F is set to drive the provider to his or her reserva-tion profit. If instead the objective function were profitssubject to a utility constraint, F would be set to drive theconsumer to his or her reservation utility.

12. The proof of this and subsequent results are con-tained in the Appendix.

the consumer pays the full marginal cost ofprevention as well. The provider’s constraintimplies that in this case

Fm = C�k∗�+�0�(9)

or that the up-front fee under this plan (Fm)should just cover the provider’s capacity costsplus the required profit, both on a per-patientbasis.

The consumer’s optimal choice of preven-tive care, as determined by (8), is illustratedin Figure 2 for the case where a= b = 1. Theupward-sloping curve is the marginal dollarcost of providing an additional unit of pre-ventive care (the curve is positively slopedbecause p′′ > 0). It crosses the horizontal axiswhen dollar costs are minimized (i.e., whenc+p′�x�T = 0), at the point labelled x1. Thedownward-sloping curve is the negative of themarginal transaction costs plus the expectedchange in the disutility of being ill from anadditional unit of prevention. These nonmon-etary costs are minimized at x2 in Figure 2(i.e., at the point where w + p′�x�d = 0).According to (8), the consumer chooses x∗at the intersection of these marginal curves,given a = b = 1. As drawn, x1 < x∗ < x2,though this need not be the case. For exam-ple, the curves could intersect below the hor-izontal axis, in which case x2 < x∗ < x1. Weconsider both cases in our comparison of theFFS and prepaid plans.

Another case of interest is when a= 0, orpatients pay none of the costs of prevention.In this case, it turns out that

bm = 1+c/p′�x�T < 1�(10)

Intuitively, if a = 0, the patient will tendto overconsume prevention, so the providermust charge less than the full marginal costof treatment to reduce the demand for pre-vention (given that xc is increasing in b). Inaddition, the up-front fee must be increasedrelative to (13) to cover the uncompensatedprevention and treatment costs. Specifically,

Fm=cx∗+�1−b�p�x∗�T +C�k∗�+�0�(11)

By similar reasoning, when b = 0 (patientspay no treatment costs), the optimal copayfor prevention is

am = 1+p′�x�T /c < 1�(12)


FIGURE 2The Consumer’s Choice of Prevention under the Efficient Mixed Plan

In this case, full coverage of the patient’s costof treatment reduces the demand for pre-vention. Thus, the fee for prevention servicesmust be less than the marginal cost to encour-age consumption (given that xc is decreasingin a). The up-front fee in this case is

Fm=�1−a�cx∗+p�x∗�T +C�k∗�+�0�(13)

An important implication of the preced-ing results (which anticipates the subsequentanalysis) is that a Pareto-efficient plan musthave a FFS component. That is, a plan inwhich a = b = 0 will not yield the first-best solution.13 Because both monetary andtransaction costs matter to the patient, theprovider (or planner) wishes to minimizeoverall costs of care by inducing the appro-priate choice of x. By implementing an effi-cient FFS plan as described and choosing thecorrect capacity, the provider can control uti-lization through both the monetary and trans-action costs incurred by the consumer. Theefficient contract therefore requires someform of FFS. This prescription is clearly

13. Benjamini and Benjamini (1986, p. 222) suggestthat for a homogeneous group, “the HMO represents aPareto-optimal resource allocation.” Preventive services,however, are not differentiated from treatment, and theyassume that “the services given are the members’ optimalchoices ex ante, but dictated to them ex post, so there isno way the patient can consume more and create moralhazard.”

contingent to some extent on the structure ofthe model, but we believe that it is a fairlygeneral result.

B. The FFS Plan

The preceding section showed that an effi-cient plan requires a FFS component on pre-vention, treatment, or both. In this section,we consider a pure FFS plan in which theprovider charges no up-front fee (i.e., F =0).14 In this case, we obtain the following

PROPOSITION 2. The optimal FFS planachieves the efficient level of capacity and pre-vention, but in this case there are no degrees offreedom in setting the contract terms. Further,both a and b are greater than one in the opti-mal contract.

The loss of the degree of freedom is dueto the fact that we have preset F = 0, so weare left with two contract parameters (a andb) to control two choice variables (k and x).Thus, both are uniquely determined. Further,both must be greater than one to cover thefull cost of prevention and treatment, plus thefixed cost of capacity and the provider’s nor-mal return.

14. Note that the consumer’s maximization problem asdescribed is unaffected by this constraint because x doesnot depend on F . Thus, Equation (8) continues to definexc . Again, this is due to the absence of income effects.


Given the absence of a degree of freedom,it follows that if we impose an additional con-straint on a or b, for example by setting a= b,b < 1, or a < 1, then the efficient outcomewould not be attainable under a pure FFSplan because there would only be one freeparameter. The following section on the pureprepaid plan illustrates the type of second-best outcome that emerges when this is thecase.

C. The Prepaid Plan

Consider now a pure prepaid plan in whichconsumers pay no fee when receiving ser-vices (preventive or treatment). Because weimpose the constraint that a = b = 0 in thiscase, condition (8), which determines theconsumer’s choice of x, now becomes

w�k�+p′�x�d = 0�(14)

In choosing x, the consumer therefore con-siders only the transaction costs of consumingpreventive care and the expected disutility ofbeing ill. Note that this can result in eitherover- or underconsumption of prevention rel-ative to the first-best optimum because con-sumers ignore both the dollar cost and thedollar benefit of prevention. (Thus, in Figure1 both the marginal cost and the marginalbenefit curves shift down, causing an ambigu-ous effect on xc.) Because the provider canonly affect the consumer’s choice of preven-tive care by his or her choice of capacity inthis case, we have the following result.

PROPOSITION 3. Under the optimal prepaidplan, a first-best outcome is not attainable.Instead, one of two second-best outcomesoccurs: (1) providers invest less than the first-best level of capacity (k < k∗), and patientsconsume more than the first-best level of pre-vention (x > x∗); or (2) providers invest morethan the first-best level of capacity (k > k∗),and patients consume less than the first-bestlevel of prevention (x < x∗).

To understand this result, suppose thatthe provider initially sets the first-best levelof capacity, k∗. Furthermore, suppose thatat this level of capacity, the consumer over-consumes preventive care relative to thefirst-best level dictated by (6). That is, theconsumer chooses prevention of x2 > x∗ inFigure 2. The optimal (second-best) response

by the provider in this case is to increasethe transaction costs of consuming preven-tive care by reducing capacity below k∗. Thisinduces consumers to decrease their preven-tion (toward the optimal level) due to thehigher marginal transaction costs. The result-ing second-best level of prevention is givenby xp in Figure 3. In contrast, if the con-sumer is initially underconsuming prevention,then the provider’s optimal response is toincrease capacity to lower the marginal trans-action costs of consuming prevention, therebyincreasing x toward the optimal level. It isimportant to note that these second-best out-comes are driven by competitive pressure onproviders to maximize consumer utility, giventhe constraint that consumers pay no out-of-pocket costs for health care.

The results imply that purely prepaidHMOs that limit consumer choices or rationcare by restricting capacity may be imple-menting second-best plans if consumers,because of the prepaid nature of the plan, areoverconsuming preventive care. In contrast,if consumers are underconsuming preventivecare (the less plausible case), then limitingchoices works against efficiency by furtherdiscouraging consumption of x. Of course,not all HMOs are purely prepaid—manyhave copayments for services. The resultsfor the mixed plan above implies that theseHMOs may be achieving first-best solutions ifcopayments are property structured. Indeed,one would expect that if there exist providersoffering first-best plans (i.e., if there is freeentry of plans), they would attract consumersaway from second-best plans, thereby elimi-nating the latter from the market.

D. The Dollar Cost of Health Care

In this section, we compare the dollar costof health care under the three plans. That is,we consider only the expected cost of pre-vention and treatment, cx+p�x�T , given thatmost discussions of health care reform focuson controlling these costs. Recall that x1 isdefined to be the level of prevention that min-imizes expected dollar costs. We have seen,however, that efficient prevention, x∗, may belarger or smaller than x1 given that it takesaccount of the transaction and utility costs ofbeing ill in addition to the dollar costs.

In the preceding sections, we have shownthat the optimal mixed and FFS plans achieveefficient prevention, but the optimal prepaid


FIGURE 3The Consumer’S Choice of Prevention under the Second-Best Prepaid Plan

plan may result in either too little or toomuch prevention. We first consider the casewhere it leads to too much prevention, whichis the case shown in Figures 2 and 3. The rela-tionship among the different levels of preven-tion in this case is

x1 < x∗ < xp�(15)

In terms of dollar costs, the consumer there-fore “overconsumes” prevention under allthree plans, but note that the mixed andFFS plans result in lower dollar costs thandoes the prepaid plan because x∗ is closerto x1 than is xp. The reason is that thereis no charge per unit of prevention underthe prepaid plan, so the consumer does nottake into account the increase in dollar costsfrom an additional unit of prevention (givenc+p′�x�T > 0 in this case).

The other possible case occurs when theconsumer underconsumes prevention underthe prepaid plan. In that case, the relation-ship among the various levels of preventionis reversed:

xp < x∗ < x1�(16)

Although less plausible, this case neverthelessyields the same conclusion: The prepaid plan

results in higher dollar costs compared to themixed and FFS plans (though the result hereis due to too little prevention).15 To summa-rize the results in this section, we have

PROPOSITION 4. The expected dollar costsof health care ( prevention plus treatment) arehigher under the optimal (second-best) prepaidplan as compared to the optimal mixed andFFS plans.

V. THE IMPACT OF THIRD-PARTY INSURANCE

Many consumers either purchase someform of health insurance on their own orreceive it as a fringe benefit from theiremployer. Most insurance plans require pay-ment of a fixed premium up front and per-haps a copayment for the cost of servicesactually received. If the insurance plan is afringe benefit, the consumer’s employer payssome or all of these costs. To examine the

15. It is interesting to note that the results in thissection are consistent with the absence of clear evidencefor or against selection bias in different health care plans.Specifically, consumers choose greater prevention underthe prepaid plan in case 1 but greater prevention underthe mixed and FFS plans in case 2. Thus, patients willtend to be “sicker” under the FFS and mixed plans incase 1 (i.e., p�x� will be higher), but the reverse will betrue in case 2.


impact of this third-party insurance in themodel,16 let � be the portion of the fixed fee,F , that patient must pay, 0 ≤ � ≤ 1, let � bethe portion of the FFS on prevention thatthe patient must pay, 0 ≤ � ≤ 1, and let �be the portion of the FFS on treatment thatthe patient must pay, 0 ≤ � ≤ 1. The expectedutility for the insured consumer becomes

EU = y−�F −�acx−p�x��bT(17)

−xw�k�−p�x�d�

The implications of this specification are thefollowing. First, the value of � has no effecton the consumer’s choice of preventive care.This is true for the same reason that F hadno effect—any up-front payment the con-sumer must make, whether in the form ofan insurance premium or a membership feefor an HMO, is a sunk cost and thereforehas no effect on the choice of prevention.In contrast, � and � will have an impact onx. Specifically, varying � will have the sameeffect as varying a, and varying � will havethe same effect as varying b. Moreover, if� = � = 0, the consumer will behave as if heor she had a pure prepaid plan, even if it is infact an FFS or mixed plan. This will be truewhether an employer pays a and b as a ben-efit or whether an insurance company fullycovers prevention and treatment costs for afixed premium. Given the earlier results, thistransformation of a FFS plan into a prepaidplan by means of complete health insurancewill result in an inefficient outcome and willlikely increase the dollar cost of health caredue to over- or underconsumption of preven-tion by the consumer.

Note, however, that the first-best outcomeis attainable under an insurance plan that sets� = 0, provided that F and a are left uncon-strained. In particular, when b = 0 (or � = 0),a is given by (12) and F is given by (13)in a first-best solution. This is an interest-ing special case because � = 0 fully insuresa risk-averse consumer against the risk asso-ciated with becoming ill, given that the onlyuncertainty in this model arises from treat-ment costs. Although providing “insurance”for prevention costs (i.e., � < 1) does notmake sense from a risk-sharing perspective

16. We focus here on the impact of insurance onincentives rather than on risk sharing, given that the con-sumer is risk neutral.

(these costs are not random), it neverthelessturns out to be efficient to set a < 1 in thiscase (by [12]) to provide patients the correctincentives regarding the amount of preven-tion to consume. Thus, actual insurance plansthat charge an up-front premium, a copay forprevention, and no charge for treatment arepotentially consistent with the first-best solu-tion. In this case, risk sharing and incentivesmay be fully consistent with each other.17

VI. A NOTE ON THE LONG RUN

The model in this article is static in thesense that prevention and treatment occurwithin the same time period. In reality, thebenefits of prevention in terms of reducedtreatment costs generally occur in the future.It has been argued that this works against thepreventive orientation of HMOs because ifpatients are free to switch plans, the savingsfrom increased prevention may be enjoyed byother providers.

A simple extension of the model allows usto shed some light on this issue. Suppose thatconsumers enter a given health care plan witha predetermined probability of illness in thecurrent period, p0, based on past prevention,and a probability of future illness, p�x�, thatdepends on current prevention in the man-ner described. Further, suppose there is someprobability that the consumer will leave thecurrent plan after consuming current treat-ment and prevention but before future treat-ment is needed. What will be the outcomeunder the various plans examined?

It turns out that the conclusions continueto hold under the mixed and FFS plans.18

Specifically, both plans continue to achievethe efficient levels of prevention and capac-ity. (This is true even if the consumer leavesthe plan with certainty after consuming pre-vention.) Although providers do not accountfor the full benefits of prevention, consumersdo because they must ultimately pay for thefull treatment costs somewhere. Thus, thereis no externality.

The conclusion is different, however,under the pure prepaid plan. In this case,providers will tend to invest in less capac-ity compared to the second-best level. Intu-itively, providers reduce their capacity to

17. See Holmstrom (1979) for an analysis of thepotential conflict between risk-sharing and incentives ina principal-agent framework.

18. Proofs are available from the authors on request.


discourage preventive care given that theyexternalize some of its benefits. This conclu-sion does seem to reflect the above concernsregarding prepaid HMO plans.

VII. FINAL REMARKS

Prepaid health care plans have beentouted as procompetitive, cost-reducing alter-natives to traditional FFS arrangements. Inthe absence of convincing empirical evidenceof procompetitive effects or economies ofscale and scope, proponents have often citedthe preventive orientation of such plans as apotential benefit to consumers and a sourceof long-run savings. Prepaid plans further thisimpression by advertising the availability ofpreventive services, yet empirical evidence onthe actual delivery of such services suggeststhat the tendency of prepaid plans to encour-age prevention is at best uncertain. Results ofthe present analysis may help explain, froma theoretical perspective, why prepaid plansmay not always result in higher levels of pre-ventive care than pure prepaid plans, and whythey might not lead to lower costs even whenthey do increase prevention.

We began the analysis by deriving thePareto-optimal choices of prevention by con-sumers and capacity by health care providersin the context of a simple model. Giventhis benchmark, we then examined the out-comes under different health care paymentplans. The results of the analysis showed that,although a pure FFS or a hybrid paymentplan can achieve the Pareto-optimal solution,a pure prepaid plan cannot. Although risksharing may be an argument in favor of pre-paid plans, our results show that the first-bestchoice of prevention can be achieved, alongwith full insurance of consumers against therisk associated with the cost of treatment, aslong as a prepayment and FFS on prevention(which is not subject to risk) can be charged.

APPENDIX

Proof of Proposition 1

The Lagrangian that determines the optimal mixedplan is given by

L = y−F −acx�a�b�k�−bp�x�a�b�k��T(A1)

−x�a�b�k�w�k�−p�x�a�b�k��d

+��F + �a−1�cx�a�b�k�

+ �b−1�p�x�a�b�k��T −C�k�−�0��

The first-order conditions with respect to a, b, F , and k,respectively, are19

cx��−1�+�� x/ a��a−1�c(A2)

+ �b−1�p′�x�T �= 0

p�x�T ��−1�+�� x/ b��a−1�c(A3)

+ �b−1�p′�x�T �= 0

−1+�= 0(A4)

−xw′�k�−�C ′�k�+�� x/ k��a−1�c(A5)

+ �b−1�p′�x�T �= 0�

Equation (A4) implies that � = 1. Substituting this into(A2) and (A3) yields the single condition

�a−1�c+ �b−1�p′�x�T = 0�(A6)

Substituting this equation along with � = 1 into (A5)yields

−xw′�k�−C ′�k�= 0�(A7)

Comparing (A7) to (7) shows that the provider choosesthe first-best level of capacity, k∗, given x.

Consider next the choice of prevention. Recall that thefirst-best level of prevention, x∗, is determined by Equa-tion (6), and the consumer’s actual choice of preventionis determined by (8), given a, b, and k. It is easy to showthat these conditions are consistent with each other—that is, that the consumer is induced to choose thefirst-best level of prevention—if condition (A6) holds.Because a and b can both be chosen to satisfy this singleequation, one of the parameters can be freely chosen aslong as the other is chosen to satisfy (A6). Q.E.D.


The first-order conditions for the provider’s optimalchoices of a, b, and k in this case are again given by(A2), (A3), and (A5), respectively. The provider’s profitconstraint in this case implies that

�a−1�cx+ �b−1�p�x�T = C�k�+�0�(A8)

Thus, either a or b (or both) must be greater than one tocover the provider’s capacity costs plus a normal profit,given the absence of an up-front fee. Combining (A2)and (A3) implies that

��−1�cx/� x/ a�= ��−1�p�x�T /� x/ b��(A9)

Because x/ a < 0 and x/ b > 0, (A9) implies that� = 1. Thus, equations (A2) and (A3) again collapse to(A6). This further implies that capacity is chosen effi-ciently as determined by equation (A7), given x. As for aand b, they are determined simultaneously by (A6) and

19. Note that the terms � EU/ x�� x/ t�, t = a�b�k,drop out of these conditions due to the EnvelopeTheorem.


the provider’s constraint in (A8). Solving these equationsyields

af =1−#p′�x��C�k∗�+�0�/c�p�x�−xp′�x��$>1(A10)

bf =1+#�C�k∗�+�0�/T �p�x�−xp′�x��$>1�(A11)

Thus, in the efficient FFS plan, both a and b are greaterthan one. Finally, if we substitute the optimal values ofa and b into (8), it reduces to (6). Thus, the consumerchooses the first-best level of prevention. Q.E.D.


The optimal plan in this case satisfies conditions (A4),(A5), and the provider’s profit constraint, given a= b =0. The latter condition implies that the provider’s up-front fee, denoted Fp, is given by

Fp = cx+p�x�T +C�k�+�0�(A12)

That is, the up-front fee must cover the expected cost ofprevention and treatment as well as capacity costs andrequired profits. The provider’s optimal choice of capac-ity is determined by (A5). Given � = 1 from (A4) anda= b = 0, this becomes

−xw′�k�− �c+p′�x�T �� x/ k�= C ′�k��(A13)

In interpreting this condition, note first that the expres-sion c+p′�x�T may be positive or negative depending onthe value of x. If c+p′�x�T > 0, the consumer’s choiceof prevention is too high, or x >x∗. In that case, the term−�c+p′�x�T �� x/ k� is negative given x/ k > 0, imply-ing that k < k∗, or the provider underinvests in capacityrelative to the first-best level. The reverse holds whenc+p′�x�T < 0. In that case, x < x∗, so the consumerunderconsumes preventive care. The provider’s second-best response in this case is to increase capacity relativeto the first-best level (i.e., k > k∗). Q.E.D.

REFERENCES

Beazoglou, T., and D. Heffley. “Reevaluating the ‘Pro-Competitive’ Effects of HMOs: A Spatial Equilib-rium Approach.” Journal of Regional Science, 34,1994, 39–55.

Benjamini, Y., and Y. Benjamini. “The Choice amongMedical Insurance Plans.” American EconomicReview, 76, 1986, 221–27.

Bothwell, J., and T. Cooley. “Efficiency in the Provisionof Health Care: An Analysis of Health Mainte-nance Organizations.” Southern Economic Journal,48, 1982, 970–84.

Cherkin, D., L. Grothaus, and E. Wagner. “The Effectsof Office Visit Copayments on Preventive Servicesin HMOs.” Inquiry, 27, 1990, 24–38.

Cromley, E. “The Impact of Federal Policy onthe Geographical Distribution of Health Main-tenance Organizations and Competitive MedicalPlans,” in Geographic Dimensions of United States

Social Policy, edited by J. Kodras and J. Jones III.London: Edward Arnold, 1990, pp. 154–77.

Dowd, B. “Financing Preventive Care in HMOs: A The-oretical Analysis.” Inquiry, 19, 1982, 67–78.

Feldman, R., J. Kralewski, and B. Dowd. “HealthMaintenance Organizations: The Beginning or theEnd?” Health Services Research, 24, 1989, 191–211.

Gaynor, M. “Competition within the Firm: Theory PlusSome Evidence from Medical Group Practice.”Rand Journal of Economics, 20, 1989, 59–76.

Gaynor, M., and M. Pauly. “Compensation and Pro-ductive Efficiency in Partnerships: Evidence fromMedical Group Practice.” Journal of Political Econ-omy, 98, 1990, 544–73.

Given, R. “Economies of Scale and Scope as anExplanation of Merger and Output DiversificationActivities in the Health Maintenance OrganizationIndustry.” Journal of Health Economics, 15, 1996,685–713.

Goldman, D. “Managed Care as a Public Cost-Containment Mechanism.” Rand Journal of Eco-nomics, 5, 1995, 277–95.

Heffley, D. “Allocating Health Expenditures to Treat-ment and Prevention.” Journal of Health Eco-nomics, 1, 1982, 265–90.

Heffley, D., and T. Miceli. “The Economics of Incentive-Based Health Care Plans.” Journal of Risk andInsurance, 65, 1998, 445–65.

Holmstrom, B. “Moral Hazard and Observability” BellJournal of Economics, 10, 1979, 74–91.

Lee, R. “The Economics of Group Practice: A Reassess-ment,” in Advances in Health Economics and HealthServices Research, vol. 11, edited by R. Schefflerand L. Rossiter. Greenwich, CT: JAI Press, 1990a,pp. 111–28.

. “Monitoring Physicians: A Bargaining Model ofMedical Group Practice.” Journal of Health Eco-nomics, 9, 1990b, 463–81.

Leutwyler, K. “The Price of Prevention.” Scientific Amer-ican, 272, 1995, 124–29.

Luft, H. Health Maintenance Organizations: Dimensionsof Performance. New York: Wiley, 1981.

Manning, W., A. Liebowitz, G. Goldberg, W. Rogers, andJ. Newhouse. “A Controlled Trial of the Effect ofa Prepaid Group Practice on Use of Services.” NewEngland Journal of Medicine, 310, June 7, 1984,1505–10.

Manning, W., J. Newhouse, N. Duan, E. Keeler, A.Liebowitz, and S. Marquis. “Health Insurance andthe Demand for Medical Care: Evidence for a Ran-domized Experiment.” American Economic Review,77, 1987, 251–77.

Newhouse, J. “The Economics of Group Practice.” Jour-nal of Human Resources, 8, 1973, 37–56.

Pauly, M. “Taxation, Health Insurance, and Market Fail-ure in the Medical Economy.” Journal of EconomicLiterature, 24, 1986, 629–75.

Welch, W. “Health Care Utilization in HMOs: Resultsfrom Two National Samples.” Journal of HealthEconomics, 4, 1985, 293–308.

Wholely, D., R. Feldman, J. Christianson, and J. Eng-berg. “Scale and Scope Economies among HealthMaintenance Organizations.” Journal of HealthEconomics, 15, 1996, 657–84.

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