Two Volunteers?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

Like these?

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

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

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?

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

Data from Our Volunteer

• “Law of Diminishing Marginal Utility” – or, diminishing marginal satisfaction

The cartoons even address marginal utility!

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

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

Quantity

Marginal Benefit

Total Utility

1 10 10

2 8 18

3 6 24

4 4 28

5 1 29

6 0 29

Marginal and Total Utility

Utility

35

30

25

20

15

10

5

0

Quantity of Cups

0 1 2 3 4 5 6

Q MB TU

1 10 10

2 8 18

3 6 24

4 4 28

5 1 29

6 0 29

Diminishing marginal utility … total utility rises, but at

diminishing rate

Utility

35

30

25

20

15

10

5

0

Wealth0 1 2 3 4 5 6

Total utility

Suppose we measure wealth on the horizontal axis

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)

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)

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 by Curt Anderson, Director of the Center for Economic Education at the University of Minnesota, Duluth

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

Risk: Possibility of Financial Loss

• Risks you face: displayed on Visual 10 – 1 – Visual shows what could happen to you

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

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

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

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

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

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 …??

• 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

Key Economic Concept Revisited

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

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

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

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”

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 . . .

Bar Chart Activity

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

A (min ins) B (low lev) C (med lev) D (max ins)0

5

10

15

20

25

30

w/ Insurancew/o Insurance

Activity Debrief

• Who is really happy that you bought the insurance you did?

• Who wishes you would have purchased a lot less insurance?

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.

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.

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

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

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

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

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

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)

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)