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Give two examples of insurance that you would or would not consider buying right now. Explain.

major in econ or finance first

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Economics in Action: Should You Buy Insurance?

Alisa Tazhitdinova

Economics 10A, UCSB

Many Types of Insurances

Mandatory/Semi-mandatory: Car insurance

Home insurance

Earthquake insurance

Health insurance

Government-provided:

Unemployment Insurance

Disability Insurance

Optional

Retail products insurance

Insurance Offered Every Step You Go…

Our example: vacuum costs \$70 and 2-year insurance plan \$8.

Economics tells you: compare expected utility with or without insurance

With insurance: U(“Life” + vacuum − \$78) Without insurance pworksU(“Life”+vacuum−\$70)+(1−pworks)U(“Life”−\$70)

Oh-oh: What is my U(·)…? Hmmm What is pworks….? Hmmm And what does your “Life” have to do with any of this?

Let’s work through these questions step by step!

Types of Preferences

Remember, there are 3 types of individuals Risk-loving

Risk-neutral

Risk-averse

What kind of person are you? Ask yourself Do you prefer \$100 for sure or 50/50 chance of \$0 or \$200?

Do you prefer the Econ 10A grade you earn, or a 50/50 gamble of grade you earn+1 letter up or -1 letter down?

Types of Preferences

If you… prefer the sure thing, you are probably risk-averse. (Most people are). prefer the gamble, then you are probably risk-loving! If you were indifferent, then increase the stakes! What if the stakes are \$100,000,000 vs \$0/\$200,000,000? If you still are indifferent then you are probably are risk-neutral.

If you are risk-loving, then you shouldn’t buy the insurance.

What if you are risk-neutral or risk-averse?

Risk-Neutral Decisions Simply assume that your utility U(x) = x .

Then, you want to buy if:

(“Life” + vacuum − \$78)

−[pworks(“Life”+vacuum−\$70)+(1−pworks)(“Life”−\$70)] > 0

Simplifying, we find:

(1− pworks) · vacuum > \$8

Much simpler and All about “fairness” Can simply further by remembering that vacuum costs \$70.

You shouldn’t spend \$70 if the vacuum is worth less to you. As long as you don’t get attached to this particular vacuum (fond memories?), you can always replace it for \$70.

⇒ buy insurance if you think the probability of vacuum breaking in 2 years is 8/70≈12% or more

Result # 1

You cannot make a decision under uncertainty without having some idea of probabilities.

How can you obtain such information?

Own experience is most important if outcomes occur frequently (e.g. cell phones) Own experience is less important if outcomes are infrequent (e.g. house flooding)

Risk-Averse Decisions

Fact 2: Risk-neutral logic is your upper bound: If a “risk-neutral You” would buy insurance, you should definitely buy insurance

What if a “risk-neutral You” doesn’t want the insurance.

Then the key to keep in mind is that you should account for “Life”:

So buy if U(“Life” + vacuum − \$78)

−[pworksU(“Life”+vacuum−\$70)+(1−pworks)U(“Life”−\$70)] > 0

Why Should You Account For “Life”?

Decision (1): Choose between:

(A) sure gain of \$2.40, and (B) 25% chance to win \$10.00, a 75% chance to gain \$0.

Decision (2): Choose between:

(C) A sure loss of \$7.50, and (D) 75% chance to lose \$10.00, a 25% chance to lose \$0.

Why Should You Account For “Life”?

Decision (1): Choose between:

(A) sure gain of \$2.40, and (B) 25% chance to win \$10.00, a 75% chance to gain \$0.

Decision (2): Choose between:

(C) A sure loss of \$7.50, and (D) 75% chance to lose \$10.00, a 25% chance to lose \$0.

Most of you probably chose A+D

However: Choice A+D implies that you have a 75% chance to lose \$7.6 and 25% chance to gain \$2.40

On the other hand: choice B+C would give you a 75% chance to lose \$7.5 and 25% chance to gain \$2.5

Result #2

A lot of empirical evidence shows that people make decisions separately from each other

This is not “rational”

So what does this mean in case of our example with the vacuum?

In the grand scheme of things: the vacuum purchase is negligible. (Relative to other decisions, relative to your wealth, etc!)

⇒ You should behave as a risk-neutral decision maker!

Remember from Class

Utility Function for a Risk Averse Individual

consumption

utility

7

\$0 \$1,000,000

U(\$0)

U(\$1,000,000)

\$500,000

0.5*U(\$1,000,000)+0.5*U(\$0)

Is U(\$500,000) here?

Or here?

Remember from Class

Utility Function for a Risk Neutral Individual

consumption

utility

9

\$0 \$1,000,000

U(\$0)

U(\$1,000,000)

\$500,000

0.5*U(\$1,000,000)+0.5*U(\$0)

So When Should You Decide as a Risk-Averse Individual?

Home insurance

Earthquake insurance

Car insurance (liability in an accident can easily exceed millions of \$!)

Upper tail of health insurance risk (cancer treatments are costly!)

Same applies to other risky choices, e.g. where to go to school, who to marry, etc.

But for small stakes…

Such as electronics purchases

insurance deductibles

deductibles limits the out-of-pocket expenses⇒ your loss is limited to the size of deductible⇒ typically small stakes

etc only buy insurance if it is a good deal for you!

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