Managed Care

Throughout its history, Medicaid provided health insurance for the nation’s poor. It did this by reimbursing providers on a fee-for-service basis. In the 1990s, however, California and other states decided to let private insurance companies bid for the right to provide services for Medicaid patients. These HMOs would receive a fixed per patient per month payment and the private insurer would be responsible for providing health care to Medicaid enrollees.

HMOs may be more efficient than the government since 1) they have an incentive to keep enrollees healthy to save cost, 2) they can negotiate lower input prices, and 3) competition may lead to higher quality, lower priced medical care. On the other hand, keeping the government run fee-for-service program may have been more efficient if 1) the government’s size and negotiating power could decrease input costs, 2) there may be increasing returns to scale, 3) the HMOs may include significant markups in their bids, and 4) HMOs may offer medical services which do not appeal to unhealthy enrollees (i.e., adverse selection).

A paper by Mark Duggan in the Journal of Public Economics in 2004 aims to see if contracting out Medicaid health care provision to private HMOs decreased costs. Duggan uses the fact that California enacted a mandate that all AFDC Medicaid enrollees must switch to a private HMO. For other individuals, such as those on SSI and those who were disabled, deaf or blind, the switch to the HMO was voluntary. This mandate was enacted between January 1993 and December 1999 depending on the county. The author uses variation in the county enactment date to find the effect of Medicaid HMOs on cost.

Background

The manner in which California instituted the transitioned individuals into private managed care plans can be categorized into 3 groupings:

1. Geographic Managed Care. “the state government contracts with several commercial HMOs to coordinate care for Medicaid recipients. Plans initially applied by submitting a menu of prices at which they would be willing to insure each type of Medicaid recipient. The government then awarded contracts to the plans most likely to deliver high quality medical care at a low price, though the weight placed on quality and spending was not specified.”
2. County Organized Health System (COHS). “Under this model, the not-for-profit, community-based HMO was reimbursed a fixed amount per recipient-month that varied by eligibility category.” Individuals did not have any plan choice and the state did not allow bids from for-profit firms.
3. “Two plan” counties. In these counties, the Medicaid enrollees would be able to choose between one private, commercial plan and one not-for profit plan. “…the state solicited bids from private companies and awarded a contract to just one of the plans.”

The following chart gives the type and date of managed care mandate by county.

Methods

Duggan uses the following equations to estimate spending.

• ManCare_jkt = α₁ + γ₁Mandate_kt + μ₁X_jkt + θ_1j + λ_1t + t*ρ_1k + ε_1jkt
• Spending_jkt = α₂ + γ₂Mandate_kt + μ₂X_jkt + θ_2j + λ_2t + t*ρ_2k + ε_2jkt

Subscripts j, k, and t index individuals, counties, and years respectively. The variable Mandate is equal to the fraction of individual j’s Medicaid eligible months in which a mandate was in effect. ManCare is equal to the fraction of the j’s eligible months in which he is actually enrolled in an HMO. Spending is equal to the Medicaid spending for person j at time t.

Results

Duggan finds that the managed care mandate increased Medicaid spending. Medicaid spending increased by between 17% and 23% for counties in which the mandate came into effect. These results, however, were less pronounced where there was competitive bidding between insurance companies (i.e., the Geographic Managed Care and “Two plan” counties).

Also, despite the increased spending, the author finds no evidence of increased quality in terms of better infant birth outcomes.

• Duggan, Mark (2004) “Does contracting out increase the efficiency of government programs? Evidence from Medicaid HMOs” Journal of Public Economics, v 88(12): 2549-2572/

David Whelan chronicles the rise (and possibly future fall) of Medicare Advantage programs in his article “Unfilled Prescription” in Forbes.

Earlier laws privatizing Medicare, starting with a pilot program in 1985, were written to give insurance companies only 95% of the money otherwise spent per Medicare member. The insurers were supposed to figure out how to make up the difference. It was a blunt way to save the Treasury money, but few companies stepped up…

The 2003 law hiked the payments to lure more insurers into the market. In some counties minimum payments to these plans reached as much as 128% of the amount Medicare traditionally spends per patient. Insurers rushed in, and costs soared. In the most remunerative counties, two times as many old people are enrolled in Medicare Advantage as the national average. As a result, taxpayers now pay an average of 12% more per private-plan beneficiary, not 5% less.

Whenever we talk about cost we also need to talk about quality.  Are people who opt for Medicare Advantage plans getting higher quality care than in traditional Medicare?  Are they able to see doctors in a more timely manner?  Is care more coordinated?  If this is the case, then the extra costs may be worth the money.

Nevertheless, an economist would guess that Medicare Advantage plans should be cheaper.  Even though the private plans have higher administration and advertising costs, they likely are more efficient than the government plans.  Further, one would anticipate that healthier seniors would choose the Medicare Advantage plans and sicker senior would be more likely to choose traditional Medicare.  This selection problem should make Medicare Advantage cheaper.

I agree that the federal government should not pay more money for private plans than it does for traditional Medicare.  It should reimburse the plans the same (or less if there is adverse selection) as it costs for the government to administer traditional Medicare and if firms want to increase the price, than seniors can pay the difference.  If seniors do not want to pay the difference, they can always opt for traditional Medicare.

Doctors often complain that health insurers are squeezing their profit margins. These insurers offer the physicians access to patients as part of their network in exchange for discounted fees. Physicians can decide not to join the network and charge higher prices, but may be left with fewer patients. The bargaining power of the health insurer depends on how many patients they are able to channel towards these physicians.

In the U.S., most health insurers restrict provider choice ex ante by using either prohibiting patients from visiting providers outside the network or charging the patients significantly higher co-payment rates if go to a provider outside the network. In the Netherlands, almost all care is free to patients so insurer need to use ex post incentives (e.g.: bonuses, gift certificates, and extra services) in order to entice the patients to use the services of the preferred provider.

A paper by Boonen, Schut and Koolman in the most recent edition of Health Economics examines how well the ex post incentives function in the Netherlands’ pharmacy market. Since pharmacies are regulated and prescription drugs are a homogeneous commodity, quality differences between pharmacies are negligible. The authors use data from two health insurers who attempt to direct their enrollees to specific pharmacies.

Using a multinomial logit framework, the authors find that convenience (i.e.: distance to the pharmacy) has a large impact. The financial incentives offered by health insurer A and B cause many enrollees to use the preferred provider. Health insurer A, however, gave a 10 € for the patient’s first visit to the pharmacy and 5 € for their second visit to the pharmacy. Under this incentive structure, individuals were more likely to switch to the preferred provider and then return to their original pharmacy after the incentives had disappeared. Only 25% of those who switch to the preferred provider continue to use them after the financial incentives disappear.

Health insurer B offered a discounts on products offered at the preferred pharmacy and these incentives were made permanent. Unsurprisingly, enrollees also were more likely to go to the preferred provider after the financial incentive regime was enacted.

One interesting item of note is that Health insurer B’s preferred pharmacy was in the same building as a general practitioner (GP). Since GPs function as gatekeepers in the Dutch system (i.e.: one cannot a prescription without the GPs approval), having the GP in the same building as the pharmacy was a huge convenience. Further, the GP could influence the patient to use the preferred pharmacy.

In summary, it was shown in the Dutch setting that even small incentives can have a large effect on provider choice.

• Boonen LH, Schut FT, Koolman X. “Consumer channeling by health insurers: natural experiments with preferred providers in the Dutch pharmacy market.” 17(3):299-316.

According to the San Diego Union Tribune, yesterday PacifiCare was fined $3.5 million and the California Department of Managed Health Care is seeking up to $1.3 billion in additional penalties for “130,000 alleged claims-processing violations…in California between July 1, 2005, and May 31, 2007.” PacifiCare is the second largest HMO in San Diego and the fourth largest health insurer in California.

These violations have prompted California Insurance Commissioner Steve Poizner begin an audit of the eight largest California health insurers to determine whether or not these companies have engaged in similar billing practice.

Joe Paduda of Managed Care Matters argues that the ruling is another piece of evidence which favors a  single-payer system.  Mr. Paduda states:

For those (including me) forever excoriating health systems and hospitals for their outrageous error rates, the debacle at Pacificare, the recently-acquired division of United Healthcare (one of my past employers) make the delivery sector look like a paragon of performance. I’m not overly surprised, as mergers involve systems conversions, the amalgamation of provider networks and contracts, and the shifting of work around to different call centers and processing locations. Duplicate staff positions are identified and people laid off, and when they walk out the door so does the expertise and understanding that enabled the operation to run smoothly.

The question remains, would a single-payer system perform better?  The government is not known as the paragon of efficiency.  With a single payer system, likely one of two things will happen:

• Government administrators will make claims processing errors just as health insurance administrators do now, or
• government administrators will deny less claims erroneously, but this will likely coincide with the acceptance of more unnecessary or false claims, thus increasing overall health care costs.

A single payer system may lead to improved claims processing.  However, for anyone to be convinced that a single payer system is the way to go, one must not only show that the present system is flawed, but that a single payer system is a significant improvement.

Laurence Baker is a health economist at Stanford’s Center for Health Policy. Much of Mr. Baker’s work has dealt with how HMOs have affected care levels. Today I will briefly review three of Baker’s articles:

HMO Penetration and the Cost of Health Care (AER 1996)

In this paper, Baker and Corts look how HMO market penetration affected health care premiums. I think the article is most pertinent to the health care atmosphere in the late 80s and early 90s when the distinction between HMOs and other insurance plans was starker than it is now.

The authors argue that there are four reasons why increased HMO penetration may affect the cost of traditional insurance.

1. Patient Self-Selection: Healthier patients may sort into HMO leaving traditional insurers with more unhealthy patients.
2. Physician Selection: HMOs may attract physicians who prefer a more conservative style of medicine.
3. Promulgation of Conservative Practice Styles: A higher level of HMO penetration may influence the ’standard of care’ prevalent in a given metropolitan area.
4. Cost shifting. If HMOs are good negotiators, providers may simply accept low margins for HMO patients and charge even higher rates to traditional insurance plans. This argument, however, is illogical if providers are assumed to be profit maximizers.
5. Plan characteristics. Traditional insurers may make their plans less generous in order to compete with HMOs.

Using data from 1991, the authors do find that increased HMO market share decreases premiums when the HMOs first enter the market (i.e.: HMO market share is between 0-10%). Additional HMO market penetration (i.e.: HMO market share above 10%), however, is actually found to increase health insurance premium in a local area.

Effect of HMO Market Share on Cancer Screening

The authors posit that HMOs may be more likely to screen patients for cancer since these health plans are more cost-conscious and take a longer-term view of health care. Spillovers effects non-HMO providers may occur where 1) physician practice patterns change due to an increased HMO presence, 2) patients may be more exposed to information regarding cancer screening in areas with high HMO concentration, and 3) areas with a high HMO market share may attract providers who are more likely to screen patients.

The authors use the 1996 Medical Expenditure Panel Survey-Household Component (MEPS-HC) to test their hypothesis. HMO market concentration is measure by segmenting markets into highest, middle two and lowest quartiles, as well as by using a Hirschman-Herfindahl index (HHI). The authors find that an increase in HMO market share increases the probability of breast and cervical cancer screening, but does not affect the propensity for men to get a prostate exam.

Calculating HMO Market Shares

How do Baker and colleagues calculate HMO market share? A paper studying the factors association with mammography screening has an appendix which details how the HMO market shares were calculated. In the paper, the authors find that those who were more likely to be screened were younger, had smaller families, higher education and income, had a recent Pap smear; reported breast problems; lived in an area that had more mammography facilities with reminder systems, areas with higher HMO market shares and higher screen charges.

• Baker; Corts (1996) “HMO Penetration and the Cost of Health Care: Market Discipline or Market Segmentation?” The American Economic Review, Vol. 86, No. 2, (May, 1996), pp. 389-394.
• Baker; Phillips; Haas; Liang; Sonneborn (2004) “The Effect of Area HMO Market Share on Cancer Screening” Health Services Research 39 (6p1), 1751–1772.
• Phillips; Kerlikowske; Baker; Chang, Brown (1998) “Factors associated with women’s adherence to mammography screening guidelines.” HSR, 33:1, pp. 29-53.

The RAND health insurance experiment (HIE) demonstrated that increasing coinsurance rates decreases medical care utilization. The HIE also found that health outcomes did not vary between individuals with high, low and zero coinsurance rates.

A working paper by Chandra, Gruber and McKnight (”Patient Cost Sharing…“) re-examines whether or not this is the case using a more current dataset specifically focused on the elderly. The medical utilization data the authors use is for of all CalPERS retirees between January 2000 and September 2003. Almost all of the retirees are covered by Medicare, but since Medicare typically has a 20% coinsurance rate, CalPERS provides supplemental insurance to their retirees. The authors conduct a difference in difference estimation comparing copayment changes from the CalPERS decision to raise PPO copayment rates in February 2001 and then to raise HMO copayment rates beginning in January 2002.
The authors find that physician office visits and prescription drug utilization are very price sensitive. For office visits, the estimated price elasticity is between -1.38 and -1.90 and for pharmaceuticals the price elasticity is between -0.20 and -1.4. These findings are surprising since it is typically assumed that the demand for medical care is inelastic.

The authors also found that increased cost sharing led to a slight increase in hospitalizations. However, when the subpopulation of individuals with chronic health conditions is examined, large increases in hospitalization rates are found. This means that individuals with chronic health conditions forego office visits and drug purchases due to the increase in price, but this decision will worsen their health and thus increase the chance they are hospitalized.

Why would an insurance company want to increase the number of expensive hospitalizations? It turns out that the CalPERS insurance plans pay for the ‘first-dollar’ of office visit and pharmaceutical costs. Thus, by increasing copayments, office visits and drug use decrease. Since Medicare pays for the ‘last dollar’ of medical costs (i.e.: Medicare pays for expensive hospitalizations and surgical procedures), the CalPERS plans do not incur the cost of the increased hospitalizations. To summarize, CalPERS receives the majority of the cost savings from increased copayments whereas Medicare bears the cost of the increased hospitalizations when office visit and pharmaceutical demand decreases.

This papers shows that it is always important to take a more global, more systematic view whenever a researcher is investigating the medical field.

• Candra, Amitabh; Gruber, Jonathan; McKnight, Robin (2007) “Patient Cost-Sharing, Hospitalization Offsets, and the Design of Optimal Health Insurance for the Elderly,” NBER Working Paper #12972.

There is an interesting post at GoozNews (”Getting Doctors to Compete“) in which Merrill Goozner comments on Harvard Business School professor Michael Porter’s belief that competition and integrated care are the solutions to the nation’s health care woes.

“Where we need to go is an integrated practice model,” he said. His model entails patient-focused practice groups that knit together every specialty needed to treat an individual’s medical condition. It’s not that physicians will no longer specialize; it’s that they’re no longer going to practice in specialty silos divorced or only marginally connected to all the other people providing that particular patient’s care.

Competition enters this new system by giving individuals information about the relative performance of these integrated practices.

It has been shown in various studies and opinion polls that consumers generally believe that HMOs provide an inferior level of care than non-HMO plans. This is true even when more objective measures of medical service quality are taken into account. Why is HMO satisfaction so low?

A study by Reschovsky, et al. (2002) claims that people who are dissatisfied with their medical care are more likely to report that they have an HMO. The authors use the Community Tracking Study. The CTS asks survey respondents what type of insurance they have. Later, they contact the individual’s insurance company in order to glean the details (copayment and coinsurance rates, deductibles, referral requirements, insurance type, etc.) of the person’s true insurance coverage.

As an outcome variable, the authors looked at various patient satisfaction measures (e.g.: the level of trust they have with their current physician, their satisfaction with their last doctor’s visit). When they compare people who have an HMO and correctly report this, with those who have an HMO but report they have non-HMO coverage, the authors find that those with the correct reporting have lower satisfaction scores. On the other hand, comparing people with a non-HMO insurance who correctly report this with those who have a non-HMO but report having an HMO, they find the people incorrectly reporting that they have an HMO had lower satisfaction scores. Below is the results for the dependent variable of “percent dissatisfied with their health care in general.”

Thus, they conclude that reporting of HMO coverage may be negatively correlated with actual satisfaction and may not accurately reflect the survey respondant’s true coverage. As the title indicates: “It’s not whether you are in an HMO but whether you think you are”

Reschovsky; Hargraves; Smith (2002) “Consumer Beliefs and Health Plan Performance: It’s Not Whether You Are in an HMO But Whether You Think You Are” Journal of Health Politics, Policy and Law, Vol 27, No. 3 pp.353-377.

As insurance markets began to develop in the U.S., we observed two types of insurance emerging: indemnity plans and health maintenance organizations (HMOs).  Indemnity plans compensated providers on a fee-for-service basis and HMOs used a capitation scheme.  Typically, HMOs used gatekeepers to restrict services while indemnity plan restrictions were few and far between.  Typical analysis of managed care’s affect on patient utilization involved simply comparing the average medical service usage in the two groups–after controlling for patient covariates and adverse selection.

Nowadays, all insurance plans are in some way ‘managed.’  If this is the case, how can a health economist measure the affect of managed care on service utilization?  Grembowski, et al. (2003) use a three tiered system to create an index of ‘managedness.’ Their system is described below:

1. Plan level: The authors use an index to rank plans according to the following characteristics: gatekeeping and lock-in provisions, the plan’s referral preauthorization requirements, and whether the plan versus the provider was at financial risk (FFS vs. capitation).  They also included an two benefits indexes measuring the benefits covered by the plan as well as cost-sharing (copayments, coinsurance, deductibles) for providers both inside and outside of the plan’s network.  The first benefits index looks at only in-network information and the second benefits index examines out-of-network data.
2. Office managed care: This was measured by examining office use of: utilization management, financial incentives (the percentage of the office’s revenue from capitation), and whether or not the office uses referral guidelines. 
3. Physician managed care: This measure was developed by examining whether the physician was compensated via a capitation or FFS scheme, whether financial withholds for referrals were put into place, and the number of Agency for Health Care Policy and Research (AHCPR) guidelines read or employed by the physician.

With these continuous indexes in place, healthcare economist can now perform a more subtle analysis of how managed care affects utilization.

Grembowski; Martin, Dieher; Patrick; Williams; Novak; Deyo; Katon; Dickstein; Engelberg; Goldberg (2003) “Managed Care, Access to Specialists, and Outcomes among Primary Care Patients with Pain” Health Services Research, v38(1 Pt 1) pp. 1-19.

Health economists frequently examine the effect of physician payment method on the provision of medical services.  It is often found that patients whose doctors are compensated via capitation or salaried schemes receive fewer services than patients whose doctors are compensated through a fee for service mechanism.  This finding is robust to a variety of medical settings and holds even after controlling for the possibility of patient adverse selection in insurance plans. 

Fred Hellinger (1996) shows that there are other potential biases to worry about.  The first is physician selection.  It is possible that physician who practice a more conservative (i.e.: less input intensive) brand of medicine will decide to work under capitations or salaried schemes, whereas doctors who prefer a more liberal style (i.e.: a higher quantity of service provision) may choose a fee for service.  It is possible that physician preference and not financial incentives are the cause of the above findings.  One small trial (Hickson, et al 1987) randomly assigned eighteen physicians (residents) to either a capitation payment scheme ($20 per month per patient) or a fee for service scheme ($2 per patient visit).  The study found that residents reimbursed on a per-visit basis scheduled and attended 22% more visits per capital than residents on a per month capitation scheme. 

A second source of bias analyzed by Hellinger is that of unmeasured plan characteristics.  When conducting a regression analysis, using dummy variables such as ‘HMO’ or ‘fee-for-service’ is likely too crude a categorization.  Ideally, one would like to have information on 1) benefit structure (copayments, deductibles), 2) use of guidelines, 3) method of physician reimbursement, and 4) utilization review.  Without this information, a researcher’s evalution may not be fine enough to produce any revealing conclusions regarding the state of healthcare in this country. 

Hellinger, Fred (1996) “The Impact of financial incentives on physician behavior in managed care plans: A review of the Evidence,”  Medical Care Research and Review, vol 53(3), pp. 294-314. 

Hickson, G.B.; Altemeier, W.A.; Perrin, J.M. (1987) “Physician reimbursement by salary or fee-for-service: effect on physician practice behavior in a randomized prospective study,” Pediatrics, vol 80(3), pp. 344-350.

Years ago, when someone needed care from a doctor they visited the physician directly whether they were a general practitioner or a specialist.  Nowadays, it is rarer for patients to visit a specialist without a referral.  The typical referral comes from a primary care physician, but it is also common for a specialist to refer the patient to another specialist (cross-referral).  Even when a patient sees a specialist without consulting another physician, this is now called a self-referral. 

Forrest and Reid (1997) use 1989 to 1995 data from the National Ambulatory Medical Care Survey to give more detail on the nature of referrals.  The authors compare the amount of referrals which occur inside and outside of managed care.  One might think that referrals are less common in managed care since these organizations are known to restrict the supply of specialist services; on the other hand, managed care organizations often require more referrals (fewer self-referrals are allowed) so it is possible that the number of referrals is higher in managed care as well. 

The authors found that primary care patient visits in the HMO setting were 66% more likely to lead to referrals than such visits under an indemnity plans.  Patients in HMOs were less likely to be able obtain self-referrals, however.  Thirty one percent of specialists’ managed care patients were self referred compared to 49.5% of their patients in indemnity plans.  Cross referrals between specialists occurred at similar rates in the managed care and fee for service settings. 

Economists have focused on primary care physicians’ financial incentives to refer patients to specialists.  Stephen Shortell (1973) claims that a social exchange model may more accurately reflect how referrals are performed today.  Mr. Shortell’s article in the Journal of Health and Social Behavior claims that non-financial incentives largely influence to which specialist a patient is referred.  Shortell hypothesizes that 1) a specialist’s status in the field, 2) their friendship level with the primary care physician, 3) their office’s distance from the primary care physician’s office, and 4) whether or not they are on the same network as the primary care physician likely influence the primary care physician’s decision-making process. 

 Forrest, Christopher; and Reid, Robert; (1997) “Passing the baton: HMOs’ Influence on Referrals to Specialty Care,” Health Affairs, vol 16(6), pp. 157-162.

Shortell, Stephen M.; (1973) “Patterns of Referral Among Internists in Private Practice: A Social Exchange Model,” Journal of Health and Social Behavior, vol 14(4), pp. 335-348.

Introduction 

Much of health care today is paid for by managed care plans.  If the managed care plans are profit maximizers–which I assume them to be–then they face a tradeoff.  By offering a lower quality of care, they will make more money; but lowering the quality of care reduces the demand for their insurance product.  In their 2000 Journal of Health Economics article, Frank, Glazer and McGuire create a model which employs “shadow prices” to measure the managed care firm’s incentives to provide care.  The shadow price “character[izes] the incentives a plan has to distort services away from the efficient level.  The shadow price captures how tightly or loosely a profit maximizing plan should ration services in a particular category in its own self interest.”

Model

Let us assume there is a vector of medical services (‘m_i‘) for each individual ‘i‘, and each medical service is indexed by ‘s‘.  Utility for each person is equal to:

• u_i(m_i)=v_i(m_i) + μ_i
• u_i(m_i)=[SUM_s  {v_{is}(m_{is})}] + μ_i

The individual will choose a plan if ‘u_i>u_i‘ where u_i is the valuation the individual places on the next preferred plan.  Thus we have:

• μ_i> u_i-v_i(m_i)

The managed care plan does not know μ_i but does know the distribution of μ_i.  Given ‘u_i, m_i’, the probability individual i chooses the plan is:

• n_i(m_i)=1- Φ_i[u_i - v_i(m_i)]

The individual maximizes their utility so that:

• v’_{is}()=q_s

On the firm side, the managed care organization sets a shadow price (’q_s‘) for each service in order to maximize the following profit function:   

• π(q)=SUM_i{n_i(q) * [r_i - SUM_s{m_is(q_s)}]}

The first order condition becomes:

•  SUM_i{(dn_i/ dq_s) * π_i - n_i*m’_is}
• π_i = r_i - SUM_s{m_is(q_s)}

The authors eventually solve this system of equations for ‘q_s‘ and find:

• q_s = (Sum_i{n_i * m_is})/(SUM_i {Φ’_i * m_is * π_i})

What does all this math mean?  Frank et al. explain it well as follows:

“The use of a shadow price as a description of rationing in managed care permits a natural interpretation of the division of responsibility between the ‘management’ of a plan, presumably most interested in profits, and the ‘clinicians’ in a plan who face the patients. Cost-conscious management allocates a budget or a physical capacity for a service. Clinicians working in the service area do the best they can for patients given the budget by rationing care so that care goes to the patients that benefit most. In this environment, management is in effect setting a shadow price for a service through its budget allocation. It is evident in data that individuals with the same disease get different quantities of service. The constant shadow price assumption is consistent with managed care rationing but with more care being received by patients who ‘need’ it more.”

Now we can return to the dilemma faced by profit maximizing managed care firms. These firms choose the optimal q but face a tradeoff.  By increasing the shadow price of a certain medical service (’q_s‘) the firm can make more money (- n_i*m’_is) since their costs have decreased as less services will be provided.  On the other hand, firms face the problem that for given per-person profit level (’π_i‘), increasing the shadow price will decrease the probability that any individual would like to purchase the managed care plan in the first place (dn_i/ dq_s <0).  This model can explain the appearance of the following phenomenon:

“Under simple capitation payments that now exist, providers and plans face strong disincentives to excel in care for the sickest and most expensive patients.  Plans that develop a strong reputation for excellence in quality of care for the sickest will attract high-cost enrollees.” Miller and Luft (1997 p. 20).

It not uncommon to observe an HMO offering free gym memberships (which are a perfectly predictable cost) in order to attract new healthy members, but to provide poor services to very sick patients.

Frank, Richard; Glazer, Jacob; McGuire, Thomas; (2000)  “Measuring adverse selection in managed health care” Journal of Health Economics, Vol 19, pp. 829-854.