Chimnesia has two equally sized groups of people: smokers and nonsmokers. Both types of people have utility U = ln(C), where C is the amount of consumption that people have in any period. So long as they are healthy, individuals will consume their entire income of $15,000. If they need medical attention (and have no insurance), they will have to spend $10,000 to get healthy again, leaving them with only $5,000 to consume. Smokers have a 12% chance of requiring major medical attention, while nonsmokers have a 2% chance. Insurance companies in Chimnesia can sell two types of policy. The low deductible (L) policy covers all medical costs above $3,000, while the high deductible (H) policy only covers medical costs above $8,000.
(a) What is the actuarially fair premium for each type of policy and for each group?
(b) If insurance companies can tell who is a smoker and who is a nonsmoker and charges the actuarially fair premiums for each policy and group, which policy will two groups purchase? Compute the expected utility of each group with each policy. Now suppose that smoking status represents asymmetric information: each individual knows whether or not they are a smoker, but the insurance company doesn't.
(c) Explain why it is impossible, at any prices, for both groups to purchase L-policies in this setting.
(d) Mathematically show that it is possible for both groups to purchase insurance, with one group buying L-policies and one group buying H-policies. (show the feasibility from the perspective of smoker, nonsmoker, and insurance company, respectively)
Chimnesia has two equally sized groups of people: smokers and nonsmokers. Both types of people have utility U = ln(C), where C is the amount of consumption that people have in any period. So long as they are healthy, individuals will consume their entire income of $15,000. If they need medical attention (and have no insurance), they will have to spend $10,000 to get healthy again, leaving them with only $5,000 to consume. Smokers have a 12% chance of requiring major medical attention, while nonsmokers have a 2% chance. Insurance companies in Chimnesia can sell two types of policy. The low deductible (L) policy covers all medical costs above $3,000, while the high deductible (H) policy only covers medical costs above $8,000.
(a) What is the actuarially fair premium for each type of policy and for each group?
(b) If insurance companies can tell who is a smoker and who is a nonsmoker and charges the actuarially fair premiums for each policy and group, which policy will two groups purchase? Compute the expected utility of each group with each policy. Now suppose that smoking status represents asymmetric information: each individual knows whether or not they are a smoker, but the insurance company doesn't.
(c) Explain why it is impossible, at any prices, for both groups to purchase L-policies in this setting.
(d) Mathematically show that it is possible for both groups to purchase insurance, with one group buying L-policies and one group buying H-policies. (show the feasibility from the perspective of smoker, nonsmoker, and insurance company, respectively)
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Related questions
A health insurance company knows that there are two types of customers (smokers and non-smokers), each facing different health risks. The probabilities of getting sick and the healthcare costs in the case of illness for the two customer types is given in the table below.
Group | Healthcare costs | Probability of getting sick |
Smokers | $1200 | 50% |
Non-smokers | $1200 | 20% |
Assume that each customer has a monthly income of $1600 and has a utility function given by U(x)=sqrt(x), where x is the remaining income after medical/health insurance expenses have been paid.
a. Explain the problem of âadverse selectionâ and the problem of âmoral hazard.â Give one example of a market in which adverse selection occurs and one example of a market in which moral hazard can be observed. What is the difference between the two information problems? Explain the consequences of adverse selection and moral hazard for the principal â agent relationship.
b. Discuss in detail the two ways (screening and signaling) in which the principal or the agent can try to resolve the problem of adverse selection. Give an example of screening and signaling and explain how the parties involved benefit from these strategies.
c. For the numerical example above construct the lotteries associated with the income that remains after healthcare expenses have been paid for smokers and for non-smokers (assuming agents do not have health insurance). Calculate the expected utility associated with the lotteries for smokers and non-smokers. Calculate the certainty equivalent of the two lotteries. What is maximum amount that smokers and non-smokers are willing to pay for full insurance? Calculate the actuarially fair health insurance premium for the two groups of customers (i.e. the expected healthcare costs).
dAssume the company cannot distinguish between smokers and non-smokers and offers a full insurance contract to all customers. How much should the company charge for the full insurance contract? Which customer group will purchase full insurance?
The CEO of St. Sebastian Health System, a moderate-sized hospital system in a mid-sized, Midwest city has hired you to help turn things around. The CFO is projecting a $3.7 million operating loss this year, which will be more than offset by non-operating income. However, the board has made it clear that the situation must improve. If the system cannot produce a positive operating margin in 2017, someone else is going to be the CEO. The CEO and CFO have asked you to recommend strategic approaches to sell their services in the community that will help turn the financial ship around.
Your Health System
St. Sebastian is a community-based health system. The senior management team has an average tenure of 17 years. The exception is the Chief Medical Officer (CMO). She has been in her position for two years and is the fourth CMO in that role in the past ten years. The CEO and COO have each been in their current roles for ten years. The system is comprised of the following:
Two large, acute care hospitals
Two long term care facilities
Two skilled nursing facilities
One long-term acute-care hospital (LTAC)
Four geographically distributed outpatient centers
Four Urgent Care Centers
Two free-standing ambulatory surgery centers (ASCs)
A 400 member employed physician group that includes 180 Primary Care Providers (PCPs). All 28
PCP practices are certified Level III Patient-Centered Medical Homes by NCQA.
The remainder of the 1,000 members medical staff is generally comprised of large, independent groups who have varying degrees of loyalty to the system. The Radiology and Emergency groups, for example, do 100% of their work at St. Sebastian and have no ownership of any outside facilities. The Gastroenterology Group, on the other hand, does work at the hospital but also owns its own, freestanding endoscopy center. The orthopedic group does 75% of their work at St. Sebastian but maintains privileges at other facilities. They do not own their own ASC.
In the current year, St. Sebastian is projecting 220,000 patient visits (combined IP and OP) with an average cost per visit of $1,727. They have an average charge per visit of $4,545.
Over the past ten years, St. Sebastian has been active in pursuing many different strategic projects including:
They have established clinical institutes in cardiovascular, orthopedic, oncology, maternity, and neurologic care. Each of these has been built through a co-management agreement between the system and the internal or external physician group who would be most logical. Each institute is led by a dyad of an administrator and medical director.
Five years ago, they consolidated maternity programs to one facility, a move that justified investing in a Level III Neonatal Intensive Care Unit (NICU)
They have established a research division in the hopes of working with national pharmaceutical companies and/or tertiary care hospitals in the Midwest.
They have established a Physician Hospital Organization (PHO) and intend to become an Accountable Care Organization (ACO) that can participate in the Medicare Shared Savings
Program (MSSP) and/or enter into global risk contracts with third-party payers. The PHO is currently evaluating whether or not they should purchase an insurance license so that they could offer commercial, Medicare Advantage, and Managed Medicaid insurance products.
5. They have established a Business Health division to service the corporate health needs of the employers in the region. This would include things like EAP programs, on-site wellness, drug screening, on-site clinics, etc. This division also recently built two large, full-service fitness centers.
The competition The community is currently served by three other major health providers:
Mercy is the competitor acute care system in town and has two hospitals and various outpatient centers. They have not been active in physician employment they employ a group of 60 PCPs, but no specialists. Similarly, they have not been engaged in branching out with different strategic initiatives, preferring instead to focus on cost-efficient care. They do not have clinical institutes, research divisions, a PHO, or a Business Health division. They have 230,000 visits per year, with an average cost of $1,435 per visit and an average charge of $4,348.
General Pediatric is a pediatric teaching hospital. Five years ago, they signed an affiliation agreement with Johns Hopkins to gain access to clinical and research capabilities that would have been beyond their reach, given their size. The employee essentially all of the pediatric subspecialists and have a PHO, which includes 75% of the region's primary care pediatricians. They will have 200,000 visits this year, with an average cost of $2,100 per visit and an average charge of $5,000 per visit.
General University is an adult teaching hospital affiliated with the local university's medical school. They staff the region's free-care clinics and historically, have been the region's hospital for indigent/uninsured patients. They are the region's Level I trauma center and are well regarded for intensive services like trauma, stroke, and cancer care. However, their location and reputation for taking indigent patients mean that they are not preferred for normal medical care by commercially insured or Medicare patients. Besides the community health centers, they own an inpatient rehab hospital, but no other facilities. They have explored affiliations with national leaders in academic medicine, but so far have not signed any such agreements. They see 180,000 visits per year with an average cost of $1,833 and an average charge of $5,556 per visit.
There are no other hospitals currently operating, though there are 23 skilled nursing facilities (SNFs) and 3 inpatient rehab facilities throughout the region. They are independent actors and for the most part, are struggling to stay profitable. Several single-specialty physician groups operate ambulatory surgery centers and one chain of independent diagnostic treatment facilities (IDTFs). Three years ago, there was a significant change in the state government, and that resulted in the long-time Certificate of Need (CON) program is all but scrapped (Skilled Nursing Facilities are still heavily regulated). Several for-profit hospital companies have recently done some analysis around entering your market, but have not done so yet.
The community is a Midwest city and surrounding suburbs in the midst of a transition from a manufacturing employment base, which unfortunately accelerated with the 2008 economic downturn. The hospitals have seen this over the past several years in a tightening of benefits offered by local employers. Benefits continue to be offered, but increasingly are likely to have a significant deductible associated with them. Unemployment has been above the national average and is projected
to remain that way. This means that the average wage in the region is actually below where it was in 2008 when the last recession hit. The number of Medicare-age residents is projected to rise over the next 10-20 years while working-age patients are projected to stay flat or fall slightly. Similarly, birth rates are expected to fall slightly over the coming decade.
The community is 60 miles south, 45 miles east, and 50 miles north of other, similarly-sized cities. Until 20 years ago, that made this city effectively an island unto itself. Increasingly, however, the suburbs of each of these communities have become very close to each other. As that has happened, providers in each community have followed and established practice sites and free-standing outpatient centers.
The community has a normal looking mix of Commercial, Medicare, and Medicaid patients. Because the state's governor was fiercely against the Affordable Care Act, the Medicaid expansion that happened in other states hasn't happened here. Thus, the community also has a sizable population without insurance today. As you'd expect, different hospitals see a different mix of these patients. The local health council was able to provide you with the most recent years payer mix by hospital below:
Patient visits |
Commercial |
Medicare |
Medicaid |
Uninsured/Self-pay |
Mercy |
80,500 |
105,800 |
23,000 |
20,700 |
St. Sebastian |
99,000 |
101,200 |
11,000 |
8,800 |
Gen. Pediatric |
70,000 |
4,000 |
110,000 |
16,000 |
Gen. University |
63,000 |
45,000 |
45,000 |
27,000 |
Community Total |
312,500 |
256,000 |
189,000 |
72,500 |
Reimbursement the CFO was able to supply you with their best estimate for what various payers are reimbursing for services. In general, the commercial plans are paying 50% of charges, regardless of location, except at General Pediatric. There, the monopoly on pediatric services has allowed them to negotiate rates of 80% of charge, but only for the commercial plans. Medicare currently pays 30% of charges at all hospitals, and Medicaid pays 25% of charges everywhere. Uninsured patients are generally paying 2% of charges.
refer back to St. Sebastian and the facts laid out in the background reading and Case #1and consider:
What products are in this industry vs. part of another distinct group?
What is the geographic scope of competition?
Identify the participants and segment them. Who are,
The buyers and buyer groups?
Suppliers and supplier groups?
The competitors?
The substitutes?
The potential entrants?
Which of these forces is strong/weak and why?
If possible, analyze the industry structure.
Why is the level of profitability what it is?
Which are the controlling forces for profitability?
What are the recent and likely future changes in each force, both positive and negative?