Two Volunteers?

1. Two Volunteers? Like these? Eat one at a time. After eating each one, note on piece of paper how good each successive one tastes – use of ranking of: 10 = absolutely delicious - the best 9 = really good, but not as good as a 10 8 = quite good, but not as high as a 9 . . . and so on … 3 = only fair 2 = mediocre 1 = less than a 2 0 = my lowest taste ranking – no more satisfaction eating

2. Session Outline - Objectives • Topic: Principles of Insurance • A couple aspects and activities • Some of which could involve cooperation with other departments/disciplines • Go slower with students! • Direct applicability to PFL in Math Standards: • 3. Data Analysis, Statistics, Probability Expectation: 5. “Probability models…” • High School, Elementary 4th and 2nd

3. Life is Full of Gambles:The Economics of Risk • Go skiing • Risk breaking your leg • Drive to work • Risk an auto accident • Live in a house • Risk a fire • Savings in stock market • Risk a fall in stock prices • Savings in bonds • Risk a rise in interest rates • Invest U.S. T-bills • Risk rapid inflation & loss of purchasing power

4. A Bet Anyone? • A third party will flip a coin: • heads, I pay you $1,000 • tails, you pay me $1,000 • Anyone want to play?

5. Risk Aversion • Most people would reject this bet • Why? • Most people are risk averse • dislike bad things happening to them • But more specifically, • dislike bad things more than they like comparable good things • That is, • the pain of losing $1,000 > pleasure from winning $1,000

6. Data from Our Volunteer “Law of Diminishing Marginal Utility” or, diminishing marginal satisfaction

7. The cartoons even address marginal utility!

8. Definition Marginal benefit (utility, satisfaction): MB(X): the marginal benefit of one more Reese’s cup change in total benefit when you choose one more unit the added benefit gained from one more unit let’s assume your ranking (1 to 10) is also your marginal utility or satisfaction received from each cup

9. Another Example from Previous Semester For Reese’s Butter Cups How much you like (0 – 10) each added cup Last class volunteer ate 5 cups … data next slide

10. Marginal and Total Utility

11. Utility Diminishing marginal utility … total utility rises, but at diminishing rate 35 30 25 20 15 10 5 0 0 1 2 3 4 5 6 Quantity of Cups

12. Utility 35 30 25 20 15 10 5 0 Total utility Suppose we measure wealth on the horizontal axis 0 1 2 3 4 5 6 Wealth

13. Risk Aversion is Common • Most people have diminishing marginal utility  basis for risk aversion in most people • Logic: • Dollar gained when income is low adds more to utility than a dollar gained when income is high • Having an additional dollar matters more when facing hard times than when things are good • Insurance: transfers a dollar from • high-income states (where it is valued less) to • low-income states (where it is valued more)

14. Dealing with Risk Aversion • 1. Buy Insurance: • Person facing risk pays a fee to insurance company • Which agrees to accept all or part of financial risk • Types of insurance: • Health, Automobile, Homeowner (Renter), Disability, Life • Living too long (fee paid today, annuity until die)

15. Insurance ActivityThe Insurance Game: Is Insurance Worth Buying?* • Divide into 8 Groups of ≈ 5 each • Distribute: • One complete deck of cards to each Group *Activity developed byCurt Anderson, Director of the Center for Economic Education at the University of Minnesota, Duluth

16. The Situation • You are a young single person • earning an annual income of $24,000 • living in a rented apartment • You will have to decide: • What types of insurance, if any, you want to buy • and what level of coverage for each type

17. Risk: Possibility of Financial Loss • Risks you face: displayed on Visual 10 – 1 • Visual shows what could happen to you

18. Activity Procedure • Each person select insurance & level of coverage • Applies throughout the activity • Each year: • A card is randomly drawn in each group  what happens that year to each person in group • e.g., “8” drawn  each person needed: • 10 office visits ($200 x 10) + $6,000 hospital = $8,000, if no health insurance • Note: replace the card into deck for the next year’s draw

19. Activity Procedure(continued) • “Double” card events (e.g, “K-K”): • only occur if that card is drawn in consecutive years • possible in year 2 and beyond, for example: • Year 1: K drawn  major fire causes $4K damages • Year 2: K drawn  K - K has occurred  one-year major disability costing $24,000 in income

20. Activity 10 – 1: Insurance • Different types (5) of insurance from which to choose: • Health • Automobile • Renter’s • Disability • Life • Within each, several options for amounts of coverage • As coverage rises  premium rises due to higher insurance company payout • NOTE: premiums shown are annual, covering you one year

21. Types of Insurance & Terms • Health • Co-pay: amount you pay for each office visit • Hospitalization: insurance company pays % shown • Automobile • Deductible: amount you must pay due to accident • Insurance company pays anything above deductible • combine comprehensive and collision for simplicity • Liability: protects from damages you cause others up to amount shown • you are responsible for additional

22. Types of Insurance • Renter’s Insurance • Deductible: amount you have to pay on loss • Insurance company covers above deductible • Covers: loss of personal property • Disability Insurance • Each unit coverage pays $500 /mo for lost income • Maximum of 4 units = $2,000/month  $24,000/year • Life Insurance • Each unit pays beneficiaries $10,000

23. Weigh Benefit vs. Cost in Making Insurance Decision B(X) C(X) • Lower losses when “bad things” happen • - see Activity 10 – 1 • Insurance Premiums paid • - see Activity 10 – 1 • Forgetting anything …??

24. Key Economic Concept Revisited • Choice involves cost • choosing is refusing • choose to buy insurance • refuse to invest $ spent on premiums • suppose could earn 10% • $1,000 on premium • $100 return foregone

25. Weigh Benefit vs. Cost in Making Insurance Decision B(X) C(X) • Lower losses when “bad things” happen • - see Activity 10 – 1 • Insurance Premiums paid • + • Lost Return on Premium • In our example: $1,000(1 + 0.10) = $1,100

26. Now Ready to Complete Activity 10 – 1 • Decide what types & levels of coverage you desire • RESTRICTION: ALL states require basic liability coverage with car insurance, so you must choose at least Option 3 • Goal: buy enough coverage to protect yourself from losses, but not so much that they end up spending far more on insurance than it is worth. • Since no way of knowing what will happen to you, there is no exact right amount of insurance • Compare B(X) v. C(X) & make choice with which you are comfortable

27. Activity 10 – 2 • Enter the Total Annual Insurance Premiums, bottom of Activity 10 – 1, for every year in Column 1 of Activity 10 – 2. • i.e., premium is constant throughout • Then, complete Column 2 for every year • opportunity cost constant throughout

28. Your Life is About to Begin • Each year – shuffle the deck, then one person in each group draw one card at random • Each person in group experiences same event depicted in Visual 10 – 1. • Then: • Fill in Column 3 –actual loss if you had no insurance • Fill in Column 4 – actual loss if you had insurance • Same event for all in group, but since not same coverage, Column 4 may differ for each member • Each group is experiencing a different “life”

29. Conduct 8 Years • Completing Columns 3 – 5 after each year’s draw • After completing 8 years: • Sum the values in Column 5 • Fill in the blanks at the bottom of Activity 10 – 2 • Questions? • Begin . . .

30. Bar Chart Activity

31. Comparing Losses With & Without Insurance(four students – min insurance to max insurance)

32. Activity Debrief • Who is really happy that you bought the insurance you did? • Who wishes you would have purchased a lot less insurance?

33. The Nature of Insurance • Within groups experiencing particularly costly events, those who bought more coverage are likely happy with their choice. • Losses without insurance would have been much bigger • Within groups experiencing fairly inexpensive events, those who bought a lot of coverage may be wishing they hadn’t wasted their money. • Losses without insurance would have been much less.

34. Premiums Based on Expected Payouts of Insurance Company (plus operating cost and profit) • Thus, • There must be some people who pay more in premiums than they get back in claims • And perhaps feeling they shouldn’t have purchased so much coverage • The insurance company uses this extra premium to pay the claims of those who pay less in premiums than claims.

35. Insurance • Every insurance contract is a gamble: • Possible that you will not have accident • Most years you pay premium • get nothing in return, except peace of mind • Insurance company counting on fact that most people will not make claims • or they couldn’t survive

36. Insurance & the Economy • Insurance: • Does not eliminate risk • but spreads it around • For example: • Owning fire insurance does not reduce the risk of losing your home in fire • But if the unlucky event occurs, • the insurance compensates you • Risk shared among thousands of insured people • Because of risk aversion, easier for 10,000 people to bear 0.0001 of the risk than 1 person bear entire risk

37. Simple Insurance Example • 100 young people all face the same risk of loss • statistically, only 1 accident occurs per year • if an accident occurs, the injured party has an accident loss of $2,000 • such a loss is catastrophic for one person to bear • Idea: let’s spread the risk (insurance) • Since one accident occurs per year • Our “society” incurs a loss of $2,000 per year • So, • each of the 100 people pay an “insurance premium” of: • $20 per year

38. A Little More Reality • The “society” decides that the burden of administering their internal insurance plan is too great • getting collections of premiums, etc. • So, one person (an entrepreneur) says, • “I’ll handle all the details if you pay me $500 per year.” • Now, what happens to the premiums? • $2,500/100 = $25 • Greater than the expected loss of each person: • (Prob of accident) x ($ loss if accident) = 0.01($2,000) = $20

39. What Should We Insure? • Since cost of insurance > expected loss • NOT a fair game! • Insurance is NOT a fair bet! • So, most economists recommend insurance for: • large potential losses where you will be severely impacted if accident occurs – catastrophic loss • e.g., Cancer or Liability • But don’t necessarily insure small risk events • that you could self-insure

40. Calculating Expected Loss • Expected loss = Probability x Loss • For example, • Expected loss if “8” drawn = (1/13) x $8,000 = 0.0769 x $8,000 = $615.38 • Complete Expected Value Problem Set • Questions # 1 – 3 (just get the idea with #3)

41. What About the Premium Insurance Company Must Charge? • Expected Value PS Question #4 • Insurance company must charge premium to cover: • Expected payout = Loss – portion paid by insured (deductible, co-pay) • Cost plus profit • Handout with answers to #3 and two Insurance policies (Health and Auto)