werkgroep opgaven Flashcards

0
Q

John’s nut van een extra euro neemt meer toe als hij 10.000 euro heeft vergeleken met een situatie waarin hij 1.000 euro heeft. We kunnen op basis hiervan concluderen dat John:
risico zoekend is
risico mijdend is
een negatief marginaal nut van vermogen heeft
risico neutraal is

A

risico zoeken

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1
Q

Stel dat individuen van een bepaalde groep een kans gelijk hebben aan 0.5% om arbeidsongeschikt te worden dit jaar en dat de overheid geen arbeidsongeschiktheidsregeling heeft ingesteld.

Eddy behoort tot deze groep. Zijn jaarinkomen is 25.000 euro. Hij overweegt een arbeidsongeschiktheidsverzekering af te sluiten die 75% van zijn inkomen vergoed in geval van arbeidsongeschiktheid. De premie van deze verzekering is gelijk aan 110 euro.

Welk gedeelte van de premie vraagt de verzekerings-maatschappij voor het vergoeden van haar administratie kosten, het behalen van haar winst en eventueel het voorkomen van moral hazard?

A

AFP = 0,0050,7525000= 93,75 => 110 – 93,75 = 16,25 => B

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2
Q

Stel: Marcel heeft een kans op een ziekte gelijk aan 5% en de zorgkosten die hij zou moeten betalen zijn gelijk aan 5.000 euro.

Wat is de actuarieel faire premie die Marcel aan een verzekering zou moeten betalen
Wat is de maximale premie die Marcel (in het geval van vraag 1) zou willen betalen?

A

AFP: 250 = 5000*5/100

Omdat hij risico neutraal is, wil hij maximaal de AFP betalen = 250 euro

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3
Q

Beschrijf de verschillende onderdelen van de maximale premie die Marcel (in het geval van vraag 2) zou willen/moeten betalen.

A

Verschillende onderdelen: AFP + certainty equivalent (met daarin gedeelte administratiekosten + stukje winst voor verzekeraars + stukje voor moreel gevaar)

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4
Q

Stel het totale inkomen van Marcel is gelijk aan 5000. Laat op de grafiek zien wat de certainty equivalent is en bereken de certainty equivalent.

A

nut met verzekering is gelijk aan nut zonder verzekering
200(5000-AFP-CE)0.5 = 0,05200(0) 0.5 + 0,95200 (5000) 0.5
= 0,95
200*70,71

(5000 – AFP – CE) 0.5 = 0,95*70,71 = 67,15
(5000- AFP – CE) = 4512
5000 – 250 -4512 = CE = 237

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5
Q

Geef een definitie van aanbod geïnduceerde moreel gevaar en consument geïnduceerde moreel gevaar. Geef een voorbeeld van beiden (anders dan die van de hoorcollege).

A

Consument geïnduceerde Moreel gevaar treedt op als het patiënt meer of duurdere zorg verschaft dan strikt noodzakelijk is gegeven zijn gezondheidstoestand, omdat de kosten (gedeeltelijk) vergoed zijn.

Voorbeeld: Naar de huisarts gaan omdat jij je grieperig voelt (wel verzekerd, maar niet strikt noodzakelijk)
Aanbod geïnduceerde moreel gevaar treedt op als een zorgaanbieder bij zijn beslissing over het geven van zorg aan een patiënt rekening houdt met de verzekeringsstatus van dit patiënt.

Voorbeeld: Een patiënt met nekklachten sturen naar een fysiotherapeut die hogere tarieven hanteert dan anderen (met vergelijkbare professionele kwaliteiten) omdat deze fysiotherapeut een goede bekende is.

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6
Q

Jan en Peter zijn net afgestudeerd en willen, voordat ze gaan solliciteren, een expeditie in een gebied waar veel infectieziekten voorkomen ondernemen. Beiden overwegen hiervoor een reisverzekering af te sluiten. Het initiële vermogen van Jan bedraagt 3.600 euro en die van Peter 10.000 euro. Beiden hebben een nutsfunctie van vermogen W gelijk aan: u = w 0,5

Tijdens de expeditie lopen zowel Jan als Peter een risico van 20% op het maken van onvoorziene ziektekosten van 3.600 euro. De premie die de verzekeraar vraagt bedraagt 1.100 euro.
Wat is de actuarieel faire premie voor Jan en Peter?

A

afp van beiden is 0,2 x 3600 = 720

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7
Q

Laat met behulp van een berekening zien of Peter zich al dan niet laat verzekeren.

A

Nut zonder verzekering = Nut met verzekering

0,8 *10.0000,5 + 0,2 * 6.4000,5  = (10.000 – premie) 0,5
80 + 16  = (10.000 – premie) 0,5
9216 = 10.000 – premie  premie = 784  
Peter gaat zich dan niet verzekeren
0
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8
Q

Is de maximale premie die Jan zou willen betalen hoger of lager dan de maximale premie die Peter wil betalen? Beargumenteer kort je antwoord (zonder de maximale premie van Jan te berekenen).

A

De maximale premie die Jan wil betalen ligt hoger dan die van Peter omdat hij verliest als zijn vermogen als hij ziek wordt.

(0,8 *3.6000,5 + 0,2 * 00,5 = (3600 – premie) 0,5
48 = (3600 – premie) 0,5
2304 = 3600 – premie
premie =1296
0
Titel in voettekst, aanpassen via Voettekst aanpassen, tab VU

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9
Q

Jan en Peter krijgen nu ook een doorlopende verzekering aangeboden. Deze verzekering geeft niet alleen dekking voor hun expeditie, maar ook voor al hun andere reizen. Het verbaast hen dat de premie die daarvoor gevraagd wordt niet veel boven de 1.100 euro ligt. Geef hier twee redenen voor.

A

Er zijn veel mensen die een doorlopende verzekering hebben. Daarom geldt de wet van de grote getallen wel en het toeval middelt zich.
Daarnaast zijn de administratiekosten van een doorlopende verzekering minder hoog.

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10
Q

1) Give two reasons why the market for dental care could not be considered as perfectly competitive. Use concepts from the economic theory that have been discussed during the course.

A

In some areas, too few dentists to allow competition
Dental products can not always been seen as homogeneous: the competitors are differentiated by reputation, patient loyalty etc.
Need to have a certificate to enter the market (no free entrance to the market)
Information is likely to be incomplete (especially on quality?)

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11
Q

Say two cities A and B can choose between buying small care equipment and buying food for poor populations in a developing country. At the beginning of the spell, city A has 100 boxes of care equipment and 200 boxes of food. The total number of boxes of small care equipment available is equal to 300 and the total number of boxes of food available is equal to 400.

1- Is the market of small care equipment perfectly competitive? Explain.

A
Many buyers, many suppliers => yes
Homogeneous product => yes
Perfect information on prices and quality => yes
No barriers to enter => yes
Externalities => no
Firms maximize profit? Yes

The market of small care equipment can be considered as perfectly competitive. This is a necessary condition to apply the theory that we learnt about Pareto efficiency!!

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12
Q

6- If the outcome of trade is Pareto Optimal (such as at C) government intervention is unnecessary and undesirable. Discuss.

A

A Pareto optimal equilibrium is not always equitable. Therefore, the government may intervene to redistribute the goods between the two cities. After redistribution, a Pareto optimal equilibrium can be reached that is considered as equitable by the society.

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13
Q

Suppose that only two goods can be produced in a country: units of Aspirin and units of Food. The price of Aspirin is €1 per unit and the price of Food is €1 per unit.

a. Discuss first whether the market for Aspirin can be considered as perfectly competitive.

A

The market for aspirin may be considered as perfectly competitive because:

  • there are many buyers and sellers (and there is no patent anymore on aspirin if I am correct).
  • The products are homogeneous
  • Almost everybody can sell aspirin.
  • Price and quality are relatively easy to assess (also because there are regulations on medicine, and that there are enough controls to see if what it is sold is really aspirin)…
  • No externalities.
  • Firms maximizing profit.
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14
Q

e. Give a definition of Pareto efficiency in output mix.

A

The producers produce the combination of products that the society wants to consume.

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15
Q

The graph above shows Luigi’s utility function of wealth (Wealth is on the X-axis, and the utility of wealth in on the Y-axis). His initial wealth equals € 100. He faces a probability equal to 50% of becoming ill. If he becomes ill, he will have to pay € 100 health care costs.

1) Give first a definition of an actuarial fair premium. What is Luigi’s actuarial fair premium?

A

The actuarial fair premium is the premium which is equal to the expected payments of the insurance company.

AFP = 100*0.5 = 50

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16
Q

2) Is he risk-neutral? Explain your answer.

A

Luigi is risk adverse. His utility function is concave => the utility that Luigi will get from a certain amount of money is higher than the utility he will get from the same expected amount of money.

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17
Q

3) Show on the graph above what Luigi’s certainty equivalent is. How much is it? Explain your answer.

A

Compute first Luigi’s expected wealth and the expected utility of his expected wealth:

Expected wealth = 0,5 *100 + 0,5 (100-100) = 50 => U(50) = 5

The certainty equivalent is equal to 25. This is the extra premium that Luigi is prepared to pay because he is risk-adverse. The utility that Luigi will get when he is insured (namely after he pays the actuarial fair premium and the certainty equivalent) is equal to the utility he will get would he be not insured. (equal to 5).

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18
Q

4) Assume that Luigi’s utility function is given by U = (w)0.5 = √W. Compute his certainty equivalent.

A

The maximum premium is when the Luigi’s utility without insurance is equal to Luigi’s utility with insurance.

Luigi’s utility with insurance equals:

U= (wealth –AFP- certainty equivalent)0.5 = (100 –50 – certainty equivalent)0.5

Luigi’s utility without insurance equals:

= 0.5* (wealth without being ill)0.5 + 0.5 (wealth if he gets ill)0.5
= 0.5* (100)0.5 + 0.5 (0)0.5
= 5

Solve the equation: U(insured) = U(uninsured)
=> 5 = (50 –certainty equivalent)0.5
=> 25= 50 – certainty equivalent
=> certainty equivalent = 25

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19
Q

Maarten’s wealth “w” is €400. He faces a probability of becoming ill equal to 20%. If he becomes ill, he will have to pay health care costs amounting to €300. His utility function is given by: U = (w)0.5 = √W. Assume that Maarten is willing to maximize his utility.

1) What is Maarten’s expected loss?
2) What is Maarten’s expected wealth?

A

(0.2)(300) + (0.8)(0) = 60.

  1. His expected wealth is
    (0. 2)($100) + (0.8)($400) = $340.
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20
Q

3) What is Maarten’s expected utility?

A

(0.2)u($100) + (0.8) * u($400) = 0.210 + 0.8*20= 2 +16 = 18.

21
Q

4) Maarten is willing to purchase a private health insurance to cover his full health care expenses. What is the maximum premium that Maarten wants to pay?

A

18 = U($ 400 - $max.premium) = (400- max. premium) 0.5
182= 400 – max. premium = 324
Max premium = 400-324 =76

22
Q

5) Say that the health insurer offers the insurance for the premium computed in question 4 and that the health insurer has to deal with adverse selection. Explain first using your own words what “adverse selection” is. Does your answer to question 4 vary because of adverse selection? Why or why not?

A

It describes a situation wherein an individual’s demand for insurance (the propensity to buy insurance and/or the quantity purchased) is positively correlated with the individual’s risk of loss (higher risks buy more insurance), and the insurer is unable to allow for this correlation in the price of insurance.

The premium calculated in question 4 is from the perspective of the individual: the answer to question 4 remains unchanged, as it is based on his own idea of getting ill.

23
Q

6) Assume that answer to question 4 is €75. For which probability “p” of having health care costs the insurer will have losses? Assume that there are no procession costs.

A

75/300 = 0.25

In case of a average probability equal or higher than 0.25, the insurer is going to have losses.

24
Q

1) Explain why individuals who are risk-lovers do not want to purchase insurance.

A

The utility of a risk-lover individual will always be lower with insurance than without insurance. The utility of a certain amount of money will always be lower than the utility of the same expected amount of money.

25
Q

2) Which maximum premium does an individual who is risk-neutral want to pay?

A

AFP, he does not want to pay an extra premium to avoid bearing the risk. He does not care whether or not he bears the risk.

26
Q

The Egalitaria’s population is insured for a broad range of health care costs using a social insurance. As in other countries, the health care costs are growing.
According to health economists, the social insurance is one of the causes of the growing health care costs because this results in an inefficient use of health care resources.

1) Explain why a social insurance may contribute to an inefficient use of health care resources.

A

A social insurance is such that all inhabitants are not confronted anymore with the actual price of care, and that there may have high levels of moral hazard. Moreover care providers may also be less likely to use cost-effective technology because of the fact that they may also not be aware of the actual prices.

27
Q

The government wants to slow down the increase in health care costs by introducing own payments. The question is: which kind of “own payments” works the most efficiently?

2) What kinds of “own payments” exist? Explain in which ways these “own payments” have different effects on the demand for health care.

A

Types of own payments:
​-​(een eigen risico aan voet): deductible
​-​(een vaste eigen bijdrage): copayment
​-​(een procentuele eigen bijdrage of procentuele bijbetaling): coinsurance

Deductible has no effect anymore on the demand for care as soon as the patient has more health care expenses than the deductible. (unfair for chronic patients)

Co payment: does not work well with expensive care, and may still limit the access to care for individuals with low SES.

Coinsurance: may limit the access to care for individuals with lower SES.

28
Q

3)​Egalitaria has a gatekeeper system, meaning that a patient needs a referral from the G.P. to access secondary care. Would you advise to introduce a system of “own payments” at the level of the G.P. or at the level of secondary care, in order to decrease health care costs? Explain why in short.

A

A system of “own payments” at the level of the G.P. because the patient is very likely to follow the advice of the G.P.
On the contrary, visiting the G.P. is on the initiative of the patient, and health care costs may be reduced by a system of “own payments” at the level of the G.P.

29
Q

The government decides to introduce a copayment equal to € 8 per day for the duration of the hospital stay. A day at the hospital costs €800. The demand function for hospital stay is given by:

P = - 0,1 Q + 5000

where P refers to the “out of pocket payment” that patients have to pay per day at the hospital and Q refers to the number of days spent in hospital. The processing costs for the introduction of “own payments” for hospital care are estimated to be equal to € 500.000.

4)​Calculate whether the introduction of own payments for hospital care will result in a reduction of the hospital costs. Assume for simplicity that the policy measure has no effects on the health of Egalitaria’s population.

A

Costs without own payments:

  • Inhabitants pay 0 euro à Demand = 50.000
  • Price per day at the hospital equals: € 800
  • Total costs: 50.000 * 800 = € 40,000,000

Costs with own payments:
- Demand equals 49.920 for price = € 8
- Price for the government per day at the hospital: € 800 - € 8 = € 792
- Total costs 49.920 * 792 = € 39,536,640
Difference situations 1 – 2: € 40000000 - € 39,536,640 = 463,360

Niet invoeren, want de besparing kleiner is dan € 500,000

30
Q

Assume that there are two types of nursing assistants: “good” nursing assistants and “bad” nursing assistants. The demand for nursing assistants (in hours) is perfectly elastic and unlimited. Insurers are willing to pay 5 Euro a hour for a bad assistant and 10 Euro a hour for a good assistant. The supply of nursing assistants is also perfectly elastic. Bad nursing assistants are prepared to work for a minimum of 4 Euro a hour and good nursing assistants are prepared to work for a minimum of 8.5 Euro a hour (reservation wage). 60% of the nursing assistants can be considered as “bad”. Each assistant knows whether he or she is good or bad. In total, there are 1000 nursing assistants and each of them can work a maximum of 10 hours a day. The market for nursing assistants is perfectly competitive and everybody is risk neutral.

1) Assume first that the insurer knows before offering a contract whether an assistant is good or bad (symmetric and complete information): How many hours a day are worked by bad nursing assistants? Which salary do they receive? Answer the same questions for the good nursing assistants.

A

The insurers will pay the bad nursing assistants 5 Euro a hour and the good nursing assistants 10 Euro a hour.

The bad nursing assistants will work: (60 % *1000) *10 = 6000 hours a day.
The good nursing assistants will work: (40 % *1000) *10 = 4000 hours a day.

31
Q

Assume then that there is asymmetric information and that the insurers cannot assess the quality of the nursing assistants: How many hours a day are worked by bad nursing assistants? Which salary do they receive? Answer the same questions for the good nursing assistants.

A

The insurer only know the average quality of the nursing assistant and will therefore offer them an average salary: 7 Euro per uur (they are risk-neutral):
w = 60%*5 + 40% * 10 = 7

The reservation wage of the good nursing assistants is 8.50. Therefore all good nursing assistants will decide not to work. Consequently only the bad nursing assistants will work a total of (60 % *1000) *10 = 6000 hours a day. The insurers will first pay them 7 Euro, but will soon realize that they should pay then only 5 Euro.

32
Q

3) How can that be explained by adverse selection? Give two ways to limit the extent of adverse selection.

A

Two methods to limit adverse selection:
1- Screening: bv. Testing the quality of the work of the assistants before offering them a contract.
2- Signaling: the good assistants could get a diplom in order to show that they are better qualified than the other assistants.

33
Q

Qv0 and Qv1 are the formula’s for the demand for medical care with and without supply induced demand.

Qv0 = -50p + 5000
Qv1 = -50p + 5100

Assume that all care required in “Egalitaria” can be provided. Assume further that the doctors receive 100 euro per unit of provided care and that this amount does not vary with the quantity of provided care. Assume finally that all inhabitants in Egalitaria are fully insured for the care they need.

1) Compute the extra amount of care that is demanded because of supply induced demand.

A
Qv0 = -50*0+ 5000
Qv1 = -50*0 + 5100
Difference = 100

100 * 100 = 10.000 euro

34
Q

2) Explain using your own words what the difference is between supply-induced demand and supply-induced moral hazard.

See lecture .

A

Supplier induced demand may occur when asymmetry of information exists between supplier and consumer. The supplier can use superior information to encourage an individual to demand a greater or lower quantity of the good or service they supply than the pareto efficient level, should asymmetric information not exist. The result of this is a welfare loss.

Ex post moral hazard: the additional quantity of health care demanded, due to the decrease in the net price of care attributable to insurance (ex post MH), by principal (patient) or agent (HC provider)

35
Q

3) Discuss two ways of preventing supply induced demand.

A

By using, e.g., selective contracting and utilization review.

36
Q

Assume that insurers bear risks for 25% of all medical costs (meaning that they are responsible for a maximum of 25% of the costs and the rest is met by the government). The government wants to reduce supply-induced demand and ex post moral hazard by increasing this percentage from 25% to 50%.

4) Would this policy intervention reduce supply-induced demand and/or ex-post moral hazard? Explain your answer.

A

It will reduce supply induced demand but will have no effect on ex post moral hazard.

37
Q

The Atkins diet advocates a diet very low in carbohydrates, such as bread, pasta, potatoes and rice and very high in proteins and fats such as beef, chicken, fish, butter, mayonnaise and bacons. Most doctors and dieticians still consider the Atkins diet a prescription for heart disease and an early death. Instead of this diet, mainstream medicine advocates a diet low on fat and protein and high in carbohydrate. Several articles in serious journals appeared questioning the conventional wisdom among doctors and showing better diet and health outcomes among low-carbohydrate dieters than among low-fat dieters. Fred and Caroline have both a restaurant.

1) Consider first the market for food. Is this market competitive? Motivate shortly your answer. (1 point)

A

Yes, it is. It satisfies to a large extent the assumptions of perfect competition: large number of buyers and sellers, perfect information, price-takers, no barriers to entrance.

38
Q

Oefententamen :Consider the following initial endowments for Fred and Caroline. Fred has 50 kilo of beef and 20 kilo of pasta and Caroline has 100 kilo of beef and 30 kilo of pasta. (This is point A.)

2) Draw an Edgeworth box depicting the situation described (For consistency, put pasta on the x-axis and beef on the Y axis, and place Fred in the lower-left corner) (1 point)

A

Zie oefententamen

39
Q

3) At the initial endowment point A, Fred is willing to give up one kilo of beef for one kilo of pasta, and Caroline is willing to give up five kilo of beef for one kilo of pasta. Draw the two marginal rates of substitution in graph of question 2). Is point A Pareto-efficient? Explain. (1 point)

A

Zie oefententamen

No, point A is not efficient, because the two marginal rates of substitution are not equal.

40
Q

5) Although there are many possibilities, draw a Pareto-efficient point given the initial endowment. Label the point B. Draw an indifference curve for both Fred and Ethel at that point. What is true about the MRS for Fred and Caroline at the Pareto-efficient point? (1 point)

.

A

MRS are equal

41
Q

6) Although there are many possibilities, draw a contract curve. We assume that the economy is in equilibrium. What are the technical conditions in terms of MRS and MRT required for Pareto efficiency? (1 point)

A

Zie oefententamen

MRS(Caroline) = MRS(Fred) = - ppasta/pbeef

42
Q

7) We now want to analyze how the economy adapts to the change in tastes due to the widespread adoption of the low-carbohydrate diet by millions of Americans. Can you indicate how the size of the Edgeworth box is going to be affected? (1 point)

A

More beef produced and less pasta produced.

43
Q

“A Pareto optimal allocation is better than any allocation that is not Pareto optimal; consequently, a policy that moves us from a non-Pareto optimal allocation to a Pareto optimal allocation is necessarily making an improvement.”

Is the above statement True or False? Explain your answer.

A

Yes, but the new situation does not have to be equitable.

44
Q

Eric and Saskia go on holidays. They both are willing to purchase a travel Insurance in order to cover the health care costs that they may have to make during their holidays. Initially, Eric has 3.600 euro and Saskia has 10.000 euro. Their utility function is given by:

U = W 0.5

where U denotes utility and W denotes wealth. They both face a probability equal to 20% of having health care costs The total health care costs that they then have to pay equal 3.600 euro. The premium that the insurer asks for the travel insurance equals 1.100 euro.

1) Compute the Actuarial Fair Premium for Eric and Saskia. (1 point)

A

De AFP is gelijk aan de verwachte kosten die gemaakt worden, ofwel een kans van 20% op 3600 euro, voor zowel Eric and Saskia: 0,2*3600 = 720 euro.

45
Q

2) Saskia does not want to buy the Insurance and prefers to bear the risk. Show using some calculation whether Eric wants to purchase the insurance or not. (2 points)

A

Eric vergelijkt het nut van verzekeren met dat van niet verzekeren.

In geval van verzekeren staat zijn vermogen vast: 3600-1100 aan premie = 2500. Dit levert een nut op van (2500)^0.5 = 50.

Bij niet verzekeren heeft hij 80% kans op 3600 euro, en 20% kans op 0 euro, dus een verwacht nut van 0,8U(3600)+0,2U(0)=0,860+0,20=48. Dit nutsniveau is lager dan 50 euro, dus zal Eric zich verzekeren.

46
Q

3) Compute the maximum premium that Eric wants to pay for the travel Insurance. Explain why this premium is higher or lower than the maximum premium that Saskia wants to pay for the travel insurance. (2 points)

A

Eric zal zich willen verzekeren tegen een maximale premie die hetzelfde nut oplevert als bij onzekerheid (=48). Gelijkstellen levert dan op:

U(3600-premie) = 48 => 3600-premie=48^2=2304. Dus de maximale premie = 3600-2304=1296. Aangezien de premie hieronder ligt zal eric zich verzekeren.

Voor Saskia is het nutsverlies door inkomensterugval veel geringer dan voor Wouter. Voor hem is verzekeren dus minder waard, en hij zal een lagere premie maximaal willen betalen.

47
Q

Health care costs are rising in all countries. That has been the case since World War II. Ever since WWII, but especially since the eighties, politicians have worried about this increase. Do you think it is a problem? Please argue why (not) in 100 words max.

A

Answer
Extra health care expenditures have been shown to be cost effective from a societal point of view. It also seems to be more beneficial than investing in other sectors, but the net benefit in other sectors is often hard to estimate. Extra investments may harm unemployment if (and only if) the country is not competitive. Health care expenditure growth reduces purchasing power for other products, and may lead to an increase in income transfers because people paying of often not (or less so) the people using. This increased level of solidarity may not be sustainable.

48
Q

a) What are the health system goals according to Murray and Frenk of the WHO? Please explain the goals briefly.

A

Health (HALY) (level and distribution)
• Responsiveness (patient experiences, autonomy, dignity, provider choice etc) (level and distribution)
• Equity in financial contribution

49
Q

b) Why does the WHO differentiate between level and distribution of these goals?

A

Level captures the average attainment level

• Distribution captures the equity component.

50
Q

c) Which of the goals (level or distribution) is most important behind a ‘veil of ignorance’?

A

Distribution of health followed by the level.