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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner Chapter 4: Health Insurance System Literature: Peter Zweifel, Breyer, Friedrich and Mathias Kifmann ,2009, Health Economics, 2 nd edition, Springer, Berlin, Chapter 5, 6, 8,10.4 & 12. Breyer, Friedrich and Wolfgang Buchholz ,2009, Ökonomie des Sozialstaats, 2 nd edition, Springer, Berlin, Chapter 6. 4. Health Insurance System Page 1

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Chapter 4: Health Insurance System Literature: Peter Zweifel, Breyer, Friedrich and Mathias Kifmann ,2009, Health Economics, 2nd

edition, Springer, Berlin, Chapter 5, 6, 8,10.4 & 12. Breyer, Friedrich and Wolfgang Buchholz ,2009, Ökonomie des Sozialstaats, 2nd edition,

Springer, Berlin, Chapter 6.

4. Health Insurance System Page 1

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.1 Reasons for Government Intervention Medical services are private goods: Individuals can be excluded from medical services and there is clearly rivalry for medical

treatments. Thus, health services do not posses the properties of public goods.

Question: Do other properties of health services justify government intervention?

4. Health Insurance System Page 2

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Altruism for the sick and the injured,

− because it could easily happen to everybody (veil of ignorance), and

− because the provision of health care is sometimes a matter of life and death.

− Thus, people are willing to accept government interventions to ensure that insurance

is provided.

External effects of communicable diseases:

− Individual utility does not take into account the social benefits of vaccination.

− This would lead to underprovision without government enforced compulsory

vaccination programs.

4. Health Insurance System Page 3

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Option good property of health insurance:

− Individuals obtain utility from knowing that they will get medical treatment in

case they need it and wherever they need it.

− In order to provide full insurance at every location, private health service providers

would have to invest in every location (overinvestment).

− This form of increasing returns to scale (provision at every location) leads to a

natural monopoly that justifies government coordinated provision of health

services.

4. Health Insurance System Page 4

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Illnesses lead to loss in output:

− Since labor is complementary to capital, not only workers lose in case they are

unable to worker, but also capital owners lose, if no output is produced.

− If health insurance were provided on the private market, individuals would underinvest in their health, since they do not take into account the effect of an

illness on complementary factors of production.

− Thus, mandatory health insurance can be Pareto improving.

4. Health Insurance System Page 5

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Health services are expert goods:

− Patients don’t know which treatment is necessary or appropriate.

− Patients cannot judge the quality of a treatment.

− This asymmetric information problem between doctors and patients cannot be

resolved, because patients don’t consume the good several times (no time to build up

reputation).

− This is likely to induce moral hazard and cause market failure.

Expert goods require external quality standards:

− A private health service market would not provide the quality standards that are

socially optimal.

− Thus, the government regulates the licensing of doctors to practice medicine and the

quality standards for drugs.

4. Health Insurance System Page 6

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Asymmetric information in the insurance market (see Chapter 2.3):

− If the individual knows more about his/her health risk than the insurance company,

then full insurance for all health-risk types is not possible.

− Compulsory full insurance can be Pareto optimal, if no separating market equilibrium

exists.

− Compulsory partial insurance can be Pareto optimal, even if a separating market

equilibrium exists.

− Genetic diagnostics could reduce the information asymmetry. This, however, is not

accepted by the public, since it would imply different premiums already at birth.

4. Health Insurance System Page 7

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Conclusion:

− These properties of health services and health insurance markets require

government intervention, e.g., regulation and compulsory (partial) insurance.

− Government intervention does not necessarily imply that public production of health

services is socially optimal.

4. Health Insurance System Page 8

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.2 Risk of Rising Insurance Premiums In Chapter 2.3 we already analyzed optimal insurance contracts and the role for government intervention in a one period insurance game. Premium risk in a multi-period setting: − The risk of becoming ill might increase over time due to e.g. chronic illnesses. − The diagnosis of a chronic illness implies increased expenditures in future periods. − Patient, who are not chronically ill, have an incentive to change to a new insurer that

charges a premium that does not include chronically ill people. − Since it is profitable for insurers to offer such contracts to not chronically ill people,

patients with a chronic illness have to pay a higher premium for all future periods.

It is difficult for the private market to insure individuals against the risk of increasing premiums.

4. Health Insurance System Page 9

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.2.1 If future treatment costs are certain in case of a chronic illness

Assume that a risk averse individual lives for n periods.

Simple framework: L treatment cost in case of a chronic illness π risk to become chronically ill in each period r = 0 for simplicity no discounting

Question: What is the optimal insurance contract and the respective risk premium in each period j = 1,2,…n?

4. Health Insurance System Page 10

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Contract A: A fair premium for each health risk type in every period Fair premium πL as long as the individual is not chronically ill and a premium equal to the treatment L cost for all future periods, if the individual becomes chronically ill. Problems: − Insurance is only provided for the first period of the illness. − No insurance against the increasing risk premium. − Contract A cannot be optimal!

4. Health Insurance System Page 11

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Contract B: Long-term insurance contract that covers the remaining treatment costs − If an individual becomes ill in period 1, the treatment cost for the remaining n periods

is equal to nL. − If an individual becomes ill in period j, the treatment cost for the remaining n – j + 1

periods is equal to (n – j + 1)L. Thus, the fair premium declining over time, i.e. Period 1: πnL Period 2: π(n – 2)L Period n: πL Note: The optimal insurance contract covers the remaining treatment cost.

4. Health Insurance System Page 12

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.2.2 If future treatment costs are uncertain Assume that a risk averse individual lives for 2 periods. Simple framework:

L treatment cost in case of an illness, πL risk in the first period to become ill, πK probability of having a higher risk in period 2, πH probability for high risk type to become ill in the second period, r = 0 for simplicity no discounting

Question: What is the optimal insurance contract and the respective risk premium in the first and second period?

4. Health Insurance System Page 13

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Contract I: Long-term contract with a constant fair premium that provides full insurance.

Total expected treatment costs in period 1:

− In period 1, the treatment cost for for each individual is equal to πLL.

− In period 2, the fraction πK of individuals have the high expected treatment cost

πKπHL and the fraction 1 – πK have the expected treatment cost (1 – πK)πLL.

− Total expected treatment costs are therefore given by

G = [πL + πKπH + (1 – πK)πL]L

If the premium should be constant over time, the fair premium is given by G/2.

4. Health Insurance System Page 14

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Problem:

− In the second period the low risk individuals have an incentive to sign a new

insurance contract with a premium πLL < G/2.

− Since low risk individuals no longer subsidize high risk individuals in the second

period, high risk individuals have to pay the high premium πHL.

− Thus, contract I cannot provide insurance against increasing premiums.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Contract II: Long-term contract with an up-front payment that provides full insurance. The up-front payment plus the premium in period 1 is equal to

G – πLL = [πKπH + (1 – πK)πL]L

And the premium in period 2 is given by πLL. Thus, low risk individuals in the second period have no incentive to sign another contract since they will always pay the premium πLL in the second period. In practice: The up-front payment πK (πH – πL)L is used as provision in case an individual becomes a high risk type in period 2. This provision is transferable to other insurers, if the individual changes insurer in the second period. Problem: Calculating the appropriate provision.

4. Health Insurance System Page 16

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Contract III: Two insurance contracts, one to insure health, one to insure the premium risk. The health insurance premium in period 1 and 2 is given by πLL. The premium risk insurance in period 1 will cost,

πK (πH – πL)L

Note: Contracts II and III are cost equivalent. Conclusion: The private insurance market is not likely to provide an effective insurance against the premium risk. Thus, government interventions can stabilize premiums over time.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.3 Health insurance contracts in case of moral hazard

Moral Hazard Problem: If the cost for medical treatments is full paid for by the insurer, individuals have no incentive to reduce the costs of the health system. 4.3.1 Ex-ante moral hazard If individuals are fully insured, they do not take appropriate precautions to reduce the risk of becoming ill or of having an accident. Thus, individuals smoke and drink too much, eat unhealthy food and engage in dangerous activities.

4. Health Insurance System Page 18

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Optimal private contracts: − Private insurer charge an additional premium, if an individual’s behavior increases

the health risk. − In Germany there are discussions about introducing additional premiums for

unhealthy behavior in the public health system. Problems: − Additional premiums reduce the full insurance objective of a health insurance

system. − Such premiums could sometimes imply a punishment for an addiction, which

actually needs medical treatment (e.g. smoking). Alternative policies: Taxing the consumption of unhealthy goods and activities in order to reduce the consumption of such goods.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.3.2 Ex-post moral Hazard If individuals are fully insured, they have no incentive to reduce the cost of a treatment in case they need medical help. Thus, individuals consume more health goods than socially optimal, since they do not have to pay the cost, i.e. marginal utility is not equal marginal cost. Consequences: − Cost of the health system increase. − If the capacities of the health system are limited by the resources provided by the

government, the patients have to wait for the treatment, i.e. the marginal cost are not monetary costs but the cost of waiting (and the deterioration of the health status due to the waiting period).

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.3.3 Cost sharing insurance contracts under ex-post moral hazard In order to reduce the incentive for individuals to increase the demand for medical treatment beyond the socially optimal level let us consider the following cost sharing contracts:

(1) Full insurance (benchmark)

(2) Indemnity insurance

(3) Proportional cost sharing

(4) Absolute per period deductable

4. Health Insurance System Page 21

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(1) Full insurance Price of

health good

Demand of health good

Price of the health good p. Demand curve h(p) for the health good is downward sloping, i.e. h’(p) < 0. Full insurance implies p = 0. Demand is therefore given by h(0) = H.

4. Health Insurance System Page 22

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(2) Indemnity insurance Price of

health good A fixed subsidy by the insurer is given by d. Demand is shifts upward, i.e. is given by h(p – d). Patients have the incentive to look for providers that charge p ≤ d. Patients still trade off marginal utility with marginal cost (price), if p > d. Demand of

health good

4. Health Insurance System Page 23

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(3) Proportional cost sharing Price of

health good Proportional cost sharing equal to the fraction α of the price. Demand curve turns upward, i.e. is given by h(α p). Patients still trade off marginal utility with marginal cost. However, the marginal cost is distorted downward, i.e. α p. Demand of

health good

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(4) Absolute per period deductable

The insurer pays the price p for all treatments in one period minus the deductable F, i.e. ph(p) – F, if ph(p) > F, and zero if ph(p) ≤ F.

Patients pay the total costs as long as ph(p) ≤ F, i.e. they still trade off marginal utility with marginal cost, if ph(p) ≤ F. They consume h(p) and receive the consumer rent EDB.

Patients pay the total deductable, if ph(p) > F, consume h(0) and receive the consumer rent 0AB.

Whether patients consume h(0) or h(p) depends on the difference in the consumer rents, which again depends on the price p. Patients consume h(0) if 0ADE > F.

If 0AB > F there exists a p* such that 0ADE = F.

Thus, demand for health good is given by h(p) if p ≤ p* h(0) if p > p*

4. Health Insurance System Page 25

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4. Health Insurance System Page 26

Consumer rents for a given price Demand with fixed sum excess

Price of health good

Price of health good

Demand of health good

Demand of health good

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Examples in the German health insurance system: (1) Full insurance Majority of medical services provided (2) Indemnity insurance Some dental treatments (3) Proportional cost sharing 10% Drugs or pharmaceuticals, minimum 5 Euro, maximum 10 Euro. (4) Absolute per period deductable 10 Euros for visiting a physician in a quarter. 10 Euro per day in hospital, no more than 280 Euro per year.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.4 Physicians as suppliers of medical services Physicians − are the first to be contacted by patients, if they need medical help. − treat the patients themselves or they refer the patient to other providers (specialists,

hospitals, etc.) − act as providers of medical services and as advisors concerning the service to be

demanded by the patient Supplier induced demand hypotheses: Use physicians their informational advantage to secure high volume of business even in circumstances where one would expect to see idle capacity. Question: How can one measure supplier induced demand?

4. Health Insurance System Page 28

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.4.1 Supplier induced demand hypotheses

Benchmark: Perfectly competitive market

for medical services

Result: An increase in the supply of

physicians leads to an

increase in medical services consumed and to a decline in prices for medical services.

4. Health Insurance System Page 29

Demand of health good

Price of health good

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Supplier induced demand: Incomplete information about

the true needs of a patient implies

that the volume of medical services

consumed mirrors the decision of

the supplier, i.e. the recommendations

Price of health good

made by physicians to their patients.

Favorable conditions for SID:

− Full insurance (no cost sharing)

− Riskless medical technology

− Complicated medical technology

Demand of health good

4. Health Insurance System Page 30

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Simple theoretical model: Assume that physicians don’t act as perfect agents for their patients. Instead they maximize their own utility. Simple framework:

p regulated price for a medical service, t working time of a physician with a capacity 0 ≤ t ≤ 1, M medical demand (in units of time t) without demand inducement, δ ratio of physicians to inhabitants in a given area, s ≥ 0 time units of supplier induced demand.

The utility of a physician is given by: u = ln(pt) – t – γs The utility increases with income pt decreases with working time t and decreases with the units of supplier induced demand s, because of ethical reasons.

4. Health Insurance System Page 31

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

The demand is given by − the medical demand without demand inducement is given by M/δ, where nM is the

total demand and a = nδ is the total number of physicians in a given area, − the supplier induced demand s.

The demand is measured in time units. The time constraint of a physician is given by: t = min[M/δ + s, 1] Constraint utility maximization:

max[(ln(p(M/δ + s)) – (M/δ + s) – γs) + λ(1 – M/δ – s)] Kuhn-Tucker conditions: ∂u/∂s = 1/(M/δ + s) – 1 – γ – λ ≤ 0, s ≥ 0 and s ∂u/∂s = 0 ∂u/∂λ = 1 – M/δ – s ≥ 0, λ ≤ 0 and λ ∂u/∂λ = 0

4. Health Insurance System Page 32

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Given the time constraint, there are three possible outcomes: (1) Limited supply of physicians (no demand inducement needed), where s = 0 and t = 1 This occurs if, M/δ ≥ 1 (2) High ethics prevent SID, where s = 0 and t < 1 This occurs if, 1 > M/δ ≥ 1/(1 + γ) (3) Supplier induced demand, where s > 0 and t < 1 This occurs if, M/δ < 1/(1 + γ) SID: s = 1/(1 + γ) – M/δ

4. Health Insurance System Page 33

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Question: How does the quantity of medical service consumed per patient change with the ratio of physicians to inhabitants? Quantity consumed per patient: q

δ

q = δ, if δ ≤ M

∂q/∂δ = 1,

q = M, if M < δ ≤ M(1 + γ)

∂q/∂δ = 0,

q = M + δs(δ), if δ > M(1 + γ)

∂q/∂δ = 1/(1 + γ) > 0.

4. Health Insurance System Page 34

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Alternative Explanations for the positive correlation between the ratio of physicians to inhabitants δ and the quantity consumed per patient q.

Permanent excess demand by patients If there is permanent excess demand by patients or equivalently limited supply of physicians, then an increase in the ratio of physicians to patients relaxes the rationing of medical services (situation equal to q = δ, if δ ≤ M).

Decreasing indirect cost, improved quality of treatment The positive correlation can also be the result of the demand decision by well informed patients, if e.g. the waiting time (indirect cost) in a practice decreases or the time a physician takes to treat a patient (quality of the treatment) increases with an increasing ratio of physicians to patients.

Reverse causality The positive correlation could also be explained by the location choice of physicians, i.e. if physicians locate in areas with high demand.

4. Health Insurance System Page 35

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.4.2 Empirical evidence for the supplier induced demand hypotheses Any empirical evidence has to rule out the three alternative explanations for the positive correlation between physician density δ and consumed quantity q. Early evidence by Fuchs (1978) and Cromwell and Mitchell (1986) suffer from poor identification as Drvanove and Wehner (1994) show. They show that using these misleading specifications one can find supplier induced demand for childbirth. More convincing evidence is provided by Gruber and Owings (1996), who show that a drastic decline in fertility in the US was accompanied by a large increase in the most highly reimbursed type of delivery, the caesarean section.

4. Health Insurance System Page 36

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Based on Norwegian data Carlsen and Grytten (1995) found a strong effect of physician density on office visits in regions where physicians are relatively scarce. This supports the limited supply hypotheses. Rice (1983) analyzed a natural experiment in Colorado 1977, where Medicare reimbursement rates were sharply increased in non-urban areas only. They found that service intensity deceased sharply in non-urban areas. Yip (1998) looked at the 1988 Medicare fee reform in which reimbursement rates for some services were reduced dramatically and found significant increases in the volume of surgery performed that compensated up to 70% of the income loss associated with the lower reimbursement rates.

4. Health Insurance System Page 37

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.4.3 Payment schemes for physician (A) Factors of production employed Physicians are reimbursed according to the cost incurred (working time, equipment, etc.) Problem: − Total input reimbursement provides no incentive to produce cost efficiently. Even the

services provided need not be administered cost effectively. − Reimbursement according to cost incurred provides an incentive to induce additional

demand.

4. Health Insurance System Page 38

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(B) Types and quantities of services provided This “fee-for-service” payment scheme is based on fee schedules that values each service with an absolute or a relative price. Advantage: − “Fee-for-service” payment schemes provide an incentive to produce cost efficiently.

Problem: − These payment schemes still provide an incentive to induce additional demand.

In Germany: − Before 2007 physicians were paid according to a point schedule that values each

service with relative prices, i.e. the reimbursement depended on the total amount of points earned by physicians.

− Since 2007 physicians are paid according to absolute prices. In order to prevent SID, physicians are paid only 10% after they administered a fixed volume of treatments.

4. Health Insurance System Page 39

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Supplier induced demand with relative prices: Assume that a physicians supply their services in an area with n inhabitant, i.e. δ = a/n.

Total expenditures are capped by E, i.e. E = p Σj=1 tj a

Utility of physician j:

ln(E(M/δ + sj)/(aM/δ + Σj=1 sj)) – (M/δ + sj) – γsj a

Optimal SID, if the time constraint is not binding:

∂u/∂sj = 1/(M/δ + sj) – 1/(aM/δ + Σj=1 sj)) – 1 – γ = 0 a

since sj = si : sj = – M/δ < 1/(1 + γ) – M/δ 1 a – 1

1 + γ a Thus, physicians have a lower incentive to induce additional demand as with absolute prices. The advantage declines with the number of physicians a.

4. Health Insurance System Page 40

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(C) Flat rate per treatment This payment scheme pays a flat rate per treatment irrespective of the cost incurred. Advantage: − The flat rate payment scheme provides an incentive to produce cost efficiently.

Problem: − The flat rate payment provides an incentive to induce additional demand by making

the wrong diagnosis, i.e. forecast higher treatment cost. Used in the US and Germany in hospitals: The flat rate per treatment payment scheme is widely used in hospitals, since medical services provided by hospitals are less likely to be subject to SID (risky treatments). Patients are first diagnosed. Then, depending on the diagnosis, the hospital receives a flat rate that depends on the diagnosis (Diagnosis Related Groups, DRG).

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(D) Number of potential patients At the beginning of the accounting period, every insured has to register with a particular physician who is in turn paid according to the number of registrations. Advantage: − The payment scheme provides no incentives for SID or wrong diagnosis. − The payment scheme encourages preventive actions.

Problem: − Although the scheme is well suited for physicians, it is less well suited for specialists

and hospitals due to the high uncertainty of treatment costs in this area. − The system provides incentives to select healthy people (by treating less healthy

people unfavorable). − If patients are not perfectly mobile (costs associated with changing a physician), then

the system provides incentives for lowering the quality of medical care.

4. Health Insurance System Page 42

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Supplier induced demand with “potential patients” payment scheme: Assume that each physician is paid the fixed amount pM per patient. If a physician provides the same quality (time spend with a patient) as all other physicians in equilibrium, then a physician has n/a = 1/δ patients in the next period. If a physician provides less quality as all other physicians in equilibrium, then a physician has no patients in the following periods. Utility maximization in a single period: max[ln(pM/δ) – t – γs] Supplier induced demand: ∂u/∂s = – γ < 0 s = 0. The fixed payment per potential patient provides no incentive for SID.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Quality of service under the “potential patients” payment scheme:

If there is only one period, physicians have no incentive to spend time with their patients,

∂u/∂t = – 1 < 0 t = 0.

However, if the relationship lasts infinitely long, there is an incentive for physicians to spend time with their patients.

Payoff, if the physician provides the same quality t* as all other physicians (discount rate r), i.e.

U = [ln(pM/δ) – t*] / r. Payoff is zero, i.e. U = 0, if the physician provides less quality t < t* than others.

The quality t* provided by all physicians has to satisfy: ln(pM/δ) ≥ t*

There exist many equilibria. The optimal quality M/δ is only ensured, if price is chosen such that ln(p*) = (M/δ)/ln(M/δ).

4. Health Insurance System Page 44

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.5 Pharmaceuticals 4.5.1 The market for pharmaceuticals The success probability of an investigated substance is 1:10,000. Out of 10,000 substances only 20 make it to preclinical tests and only 1 survives the rigorous testing in clinical trails. It takes on average 12 years for a drug to be approved. The cost of developing a new drug (out of 10,000 substances) is currently estimated at around US$ 800 million. Approved pharmaceuticals that enter the market earn a relatively high return (10-15%) due to the temporary monopoly granted by patent protection.

4. Health Insurance System Page 45

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Question: What determines the demand and the return for pharmaceuticals? Demand for pharmaceuticals:

h(p) = √ (M/δ) lni – α p where

M/δ demand, i degree of innovation, p price paid to the pharmaceutical industry, α cost sharing factor of the patient, with 0 ≤ α ≤ 1.

4. Health Insurance System Page 46

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Return for pharmaceuticals: − The net present value of a pharmaceutical depends on the initial cost of

developing the drug, i.e. ci (which depends on the degree of innovation), − and the stream of profits earned once the product is approved and protected by

patent rights for some time t ≤ T, where T is the economic life-time of the drug. Per period profit during patent protection:

π = ph(p)

where we assume that the cost of producing a drug is zero, once it is invented.

4. Health Insurance System Page 47

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

π = (1/α) (√ (M/δ) lni – h) h

FOC (Optimal quantity):

∂π /∂h = (1/α) (√ (M/δ) lni – 2h) = 0 Price, quantity and profits during the monopoly:

Price: pm = ½ (1/α) √ (M/δ) lni

Quantity: hm = ½ √ (M/δ) lni Per period profits: πm = ¼ (1/α) (M/δ) lni

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Price, quantity and profits during the monopoly

Quantity

Price

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.5.2 The innovation decision and patent protection

Given the (expected) per period return π for a drug, the time period t during which the firm can charge the monopoly price due to patent protection and the cost associated with an additional degree of innovation c, the firm decides on the optimal level of innovation i.

Maximization problem: П = maxi[t π – ci] = maxi[t ¼ (1/α) (M/δ) lni – ci]

FOC: i = [t ¼ (1/α) (M/δ)] / c

The pharmaceutical firm invests more in innovation i, if patent protection t lasts longer, if patients pay a lower share α of the cost, if the demand M/δ is higher.

4. Health Insurance System Page 50

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Question: What is the optimal length for patent protection? Assume a government that maximizes the aggregate utility of all individuals (consumer rents) and the profit of the pharmaceutical firm in the economy. During the periods T – t without patent protection, competitors copy the drug and produce it at zero marginal cost. Thus, firms make zero profit and charge the price pc = 0,

sell the quantity h(0) = √ (M/δ) lni , with innovation equal to i = [¼ t (1/α) (M/δ)] / c. Thus, the consumer rents (= welfare) during the period without patent protection are given by:

Wc = [½ h(0) p(h = 0) ](T – t) = [½ (1/α) (M/δ) lni](T – t)

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Consumer rents (welfare) without patent protection

Quantity

Price

4. Health Insurance System Page 52

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

During the t periods with patent protection, the pharmaceutical firm is a monopolist with profits equal to

π = pm hm = ¼ (1/α) (M/δ) lni

The consumer rent during the t periods with patent protection is given by

C = ½ hm [p(h = 0) – pm] = (1/8) (1/α) (M/δ) lni

Thus, welfare during the period with patent protection is given by:

Wm = [π + C] t – ci

= [(3/8) (1/α) (M/δ) lni] t – ci where the cost of the innovation ci has to be deducted from aggregate welfare.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Consumer rents and profits with patent protection

Quantity

Price

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Aggregate Welfare: The government maximizes aggregate welfare by choosing the optimal length of patent protection t. W = maxt[Wc + Wm] = maxt[(1/α) (M/δ) lni [(1/2)T – (1/8)t] – ci]

subject to: i = [(1/4) t (1/α) (M/δ)] / c FOC:

4(T/t*) – 3 = ln[(1/4) (1/α) (1/c) (M/δ)] t*

The lhs is a strictly decreasing function in t* with support (0, T] and domain [∞, 1]. The rhs is a strictly increasing function in t* with support (0, T] and domain [-∞, ln[(1/4) (1/α) (1/c) (M/δ)] T].

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Optimal length of patent protection

rhs lhs,

t

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Comparative statics: − An increase in the cost sharing factor α decreases the optimal length of patent

protection. − An decrease in the cost of innovation c decreases the optimal length of patent

protection. − An increase in the demand M/δ decreases the optimal length of patent protection.

Problem: Since the optimal length of patent protection is different for different drugs, the government needs an additional instrument (price regulation) to ensure a welfare optimum for every drug!

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Comparative statics

t

rhs lhs,

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.5.3 Price regulation of pharmaceuticals (1) Direct price regulation: Prices of new drugs and changes in prices of existing drugs that are reimbursed by social health insurance require approval by a public authority (e.g. France, Italy, Spain, …). Usually prices are negotiated with international comparisons serving as a benchmark. Idea: For a given length of patent protection t* and a drug specific demand Mj/δ, the price pj

r is chosen such that profits during the period of patent protection ensures that the optimal level of innovation i chosen by firms maximizes aggregate welfare.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Problems:

− Since investment costs are sunk once prices are negotiated, the social health insurance authority has an incentive to demand low prices.

− International trade of pharmaceuticals encourages national authorities to shift the burden of funding the development cost to foreign countries by charging a low price. This implies that international comparisons are not “objective” benchmarks.

− The implied uncertainty about the future regulated price of a new drug discourages investment into new drugs.

− The price regulation mechanism induces a strong incentive to build up a large lobby group to ensure high prices.

− Since the price is above marginal cost of production to ensure enough profits to pay the investment cost, firms have an incentive to induce additional demand (gifts to physicians).

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(2) Reference prices (indemnity insurance) Pharmaceuticals are grouped according to their therapeutic properties and a reference price is fixed for each group. Firms can charge a higher price. The difference (or a fraction α of the difference) is paid by the patient. Germany, the Netherlands and Denmark use such a system. Idea: For a given length of patent protection t and a drug specific demand Mj/δ the subsidy dj to the patient (equal to the reference price dj = pj

r) adjusts the effective demand such that the optimality condition for welfare maximizing innovation is satisfied for each group j of drugs, i.e.

4(T/t*) – 3 = ln[(1/4) (1/α) (1/c) (Mj/δ + dj)] t*

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Advantage:

− Reference prices induce competition among products with similar therapeutic properties, if prices lie above the reference price.

Problems:

− No competition below the reference price, i.e. patients have no incentive to switch to the cheaper (more cost effective) drug.

− The price regulation mechanism induces a strong incentive to build up a large lobby group to ensure a high reference and to induce additional demand via physicians.

− Thus, reference prices are usually so high, that firms do not need to compete.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

(3) Rate-of-return regulation The national health authority determines a certain rate of return during the period of patent protection. Pharmaceutical firms can charge any price as long as the implied rate of return does not exceed the agreed level. The UK uses this form of regulation. Idea: For a given length of patent protection t and a drug specific demand Mj/δ the pharmaceutical firm can charge a price p that ensures the rate of return necessary to obtain the welfare maximized level of innovation. Advantage:

− No incentive to induce additional demand. Problems:

− The system creates an incentive to enlarge the capital stock, since the rate of return is measured as operating profits per capital employed.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.6 Financing the health system 4.6.1 Contribution rates proportional to labor income Most countries finance their health system by compulsory contributions proportional to (labor) income. The proportional contribution rate acts like a tax and distorts labor supply. Internal margin of labor supply

Since most workers, especially men, work full-time irrespective of the tax burden, the distortion on the internal margin of labor supply (number of hours worked) is less important.

Only the decision of whether to work part- or full-time is influenced by the tax burden.

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

External margin of labor supply More important is influence of the tax burden on the external margin of labor supply, i.e. on the workers’ decision to work or not to work. Only, if the gain from working part- or full-time compared to not working is high enough than unemployed workers have a sufficient financial incentive to take up work. Especially, unskilled workers whose wage incomes are not a lot higher than unemployment benefits have due to the low wage incomes no financial incentive to take up work. Question: Is a lump-sum health insurance contribution, which is paid independently of whether an individual is working or not, better suited to provide the right financial incentives to take up work?

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Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

Work incentives with proportional contributions

net income

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gross labor income

Economics of the Welfare State Winter Semester 2010/2011 Prof. Dr. Christian Holzner

4.6.2 Lump-sum contributions Every individual has to pay the same lump-sum contribution irrespective of his/her labor income. However, in order to make health insurance feasible for everybody, the government has to subsidies (or pay) the lump-sum contribution of individuals with low income. The subsidy to the lump-sum contribution must decrease with an individual’s labor income.

This decreases the incentives to take up work.

Thus, a lump-sum contribution with a subsidy to low income individuals does not necessarily distort labor supply less than proportional contribution rates on labor income.

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gross labor income

Work incentives with lump-sum contributions

net income