Micro-Econ Essay

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

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…

Should You Buy the Insurance?

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?

Brochures? Google? Consumer reports?

Your own past experience

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

Your decisions are not made in isolation!

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?

When transactions can have profound effects on your life,
your livelihood:

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!