Demand for Health Insurance

1. Demand for Health Insurance

2. Expected Value 0.4 $5000 $2600 Choice 1 $1000 0.6 0.6 $5000 $2600 Choice 2 -$1000 0.4 Which Investment will you pick

3. Attitude towards risk • In the absence of any objective criteria, how an individual or organization deals with uncertainty depends ultimately on their attitude towards risk and whether they are risk averse, risk neutral or a risk taker.

4. Attitude towards risk • Someone who would prefer, for example, the certainty of $1,000 rather than a 50% probability of $3,000. • Someone who is indifferent, for example, between the certainty of $1,000 rather than a 50% probability of $2,000. • Someone who would prefer, for example, the 50% probability of $5,000 rather than the certainty of $3,000. Risk averse Risk neutral Risk taker

5. Different Approaches to Risk: • Expected Value • Maximin • Maximax • Hurwicz alpha index rule

6. Payoff Matrix 2 Choices for investment:

7. Expected Value: sum of probabilities  Payoffs EV1= 0.2 (-1000) + 0.7 (1000) + 0.1 (10,000) = 1500 EV2= 0.1 (0) + 0.6 (1000) + 0.3 (3000) = 1500

8. Maximin: Pessimistic/conservative risk attitude • Minimum gain of each choice

9. Maximin: Pessimistic/conservative risk attitude • Minimum gain of each choice

10. Maximin: Pessimistic/Conservative risk attitude • Minimum gain of each choice • Which is Maximum

11. Maximax: Optimistic Criterion • Maximum gain of each choice

12. Maximax: Optimistic Criterion • Maximum gain of each choice

13. Maximax: Optimistic Criterion • Maximum gain of each choice • Which is Maximum

14. Hurwicz alpha index rule: • The Hurwicz alpha variable is a measure of attitude to risk. It can range from  = 1 (optimist) to  = 0 (pessimist). A value of  = 0.5 would correspond to risk neutrality. • The Hurwicz criterion = maximum value x   + minimum value x (1 – )

15. Hurwicz alpha index rule: • Weighted average of min and max for each choice. For  = 0.5 : The Hurwicz criterion for First Choice: 0.5 (10,000)+0.5 (-1000)=4500 The Hurwicz criterion for Second Choice: 0.5 (3,000)+0.5 (0)=1500

16. Hurwicz alpha index rule: • Weighted average of min and max for each choice. • Select the action with the maximum value For  = 0.5 : The Hurwicz criterion for First Choice: 0.5 (10,000)+0.5 (-1000)=4500 The Hurwicz criterion for Second Choice: 0.5 (3,000)+0.5 (0)=1500

17. Hurwicz alpha index rule: • Weighted average of min and max for each choice. • Select the action with the maximum value For  = 0.1 : The Hurwicz criterion for First Choice: 0.1 (10,000)+0.9 (-1000)=100 The Hurwicz criterion for Second Choice: 0.1 (3,000)+0.9(0)=300

18. Hurwicz alpha index rule: • The maximin strategy equates to the Hurwicz approach with a value of  = 0. • The maximax strategy corresponds to  = 1.

19. Insurance Logic • The consumer pays insurer a premium to cover medical expenses in coming year. • For any one consumer, the premium will be higher or lower than medical expenses. • But the insurer can pool or spread risk among many insurees. • The sum of premiums will exceed the sum of medical expenses.

20. Characterizing Risk Aversion • Recall the consumer maximizes utility, with prices and income given. • Utility = U (health, other goods) • health = h (medical care) • Insurance doesn’t guarantee health, but provides $ to purchase health care. • We assumed diminishing marginal utility of “health” and “other goods.”

21. Diminishing marginal utility of income Utility Income

22. Utility of Different Income Levels • Assume that we can assign a numerical “utility value” to each income level. • Also, assume that a healthy individual earns $40,000 per year, but only $20,000 when ill. Income Utility Sick $20,000 70 Healthy $40,000 90

23. Utility of Different Income Levels Utility when healthy Utility 90 A B 70 Utility when sick $20,000 $40,000 Income

24. Probability of Being Healthy or Sick • Individual doesn’t know whether she will be sick or healthy. • But she has a subjective probability of each event. • She has an expected value of her utility in the coming year. • Define: P0 = prob. of being healthy P1 = prob. of being sick P0 + P1 = 1

25. Expected Utility as A Function of Probability • An individual’s subjective probability of illness (P1) will depend on her health stock, age, lifestyle, etc. • Then without insurance, the individual’s expected utility for next year is: • E(U) = P0U($40,000) + P1U($20,000) = P0•90 + P1•70

26. Expected Utility & Income As A Point on AB Line • For any given values of P0 and P1, E(U) will be a point on the chord between A and B. Utility A 90 B 70 $20,000 $40,000 Income

27. Expected Utility & Income As A Point on AB Line • Assume the consumer sets P1=.20. • Then if she does not purchase insurance: E(U) = 0.8 • 90 + 0.2 • 70 = 86 E(Y) = 0.8 • 40,000 + 0.2 • 20,000 = $36,000 • Without insurance, the consumer has an expected loss of $4,000.

28. Expected Utility & Income As Point C on AB Line Utility 90 • A • 86 C B • 70 $20,000 $40,000 Income $36,000

29. Certain Point on Income-Utility Curve • The consumer’s expected utility for next year without insurance = 86 “utils.” • Suppose that 86 “utils” also represents utility from a certain income of $35,000. • Then the consumer could pay an insurer $5,000 to insure against the probability of getting sick next year. • Paying $5,000 to insurer leaves consumer with 86 utils, which equals E(U) without insurance.

30. Certain Point D on Income-Utility Curve Utility 90 • A D 86 • • C B • 70 $20,000 $40,000 Income $35,000 $36,000

31. Price of Insurance and Loading Fee • At most, the consumer is willing to pay $5,000 in insurance premiums to cover $4,000 in expected medical benefits. • $1,000  loading fee  price of insurance • Covers • profits • administrative expenses • taxes

32. Thank You !Any Question ?