Transcript Slide 1

Risk
a situation in which there is a probability
that an event will occur.
People tend to prefer greater certainty and
less risk.
Probability
A number between 0 and 1 that measures the
chance that an event will occur.
If probability = 0, the event will definitely not occur.
If probability = 1, the event will definitely occur.
If probability = 0.5, the event is just as likely to
occur as not.
Example: The probability that a fair (balanced
coin) will land heads is 0.5.
As wealth increases, so does the total utility
of wealth.
But the marginal utility of wealth diminishes.
Total
Utility
TU
In other words,
the slope of the
total utility curve
is positive but
decreasing.
Wealth
(thousands of dollars)
When there is uncertainty, people do not know the
actual utility they will get from taking a particular
action.
They do know the utility they expect to get.
Expected utility is the average utility of all
possible outcomes.
Expected Value
Suppose you have a generous but forgetful aunt. There is a
50% probability that she will remember your birthday and
send you a check for $100. There is also a 50% probability
that she will forget you birthday and send you nothing.
What is the expected value of the gift (G) you will receive
from your aunt for your birthday?
E(G) = 0.5 (0) + 0.5 (100) = 50.
E(X) = p1X1 + p2X2 + p3X3 + … + pkXk
So to calculate the expected value,
you take the amount of each possible outcome,
multiply it by the probability of that outcome, and
add the products together.
Apart from concerns about your aunt’s health,
would you rather have your aunt send a $50 check
with certainty over the current situation?
If the answer is yes, you are risk averse.
If you prefer the current situation, you are
risk loving.
If you are indifferent between the two
situations, you are risk neutral.
In general,
A risk-neutral person cares only about expected
wealth and doesn’t care how much uncertainty
there is.
A risk-averse person prefers the expected wealth
with certainty over the risky situation with the
same expected wealth.
A risk-loving person enjoys the thrill of the
gamble, and so prefers the risky situation over a
situation with the same expected wealth with
certainty.
Most people are risk averse, but some people are
more risk averse than others.
Insurance
Insurance works by pooling risks.
It is profitable because people are
risk averse.
Example: Beth’s only wealth is a $10,000 car.
If she doesn’t have an
accident, her utility is
100 units.
Total Utility
100
85
80
If she has an accident
that totals her car, her
utility is 0 units.
65
(Assume there are no
other options.)
0
10
Wealth
(thousands of dollars)
Suppose the probability that Beth will have an accident is 0.10.
Without insurance, Beth’s expected wealth is:
$10,000  0.9 + $0  0.1 = $9000.
Total Utility
100
Her expected utility is
100  0.9 + 0  0.1 = 90 units.
90
Beth would also have 90 units
of utility if her wealth was
$7000 with certainty.
0
7
9 10
Wealth
(thousands of dollars)
If there are many people like Beth,
each with a $10,000 car and each with
a 10 percent chance of having an
accident, an insurance company pays
out $1,000 per person on the average,
which is less than Beth’s willingness to
pay for insurance.