Riska 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.

Wealth(thousands of dollars)

Total Utility

TU

As wealth increases, so does the total utility of wealth.But the marginal utility of wealth diminishes.

In other words, the slope of the total utility curve is positive but decreasing.

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 ValueSuppose 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.

Wealth(thousands of dollars)

Total Utility

65

80

10

100

0

85

If she doesn’t have an accident, her utility is 100 units.

If she has an accident that totals her car, her utility is 0 units.

(Assume there are no other options.)

Wealth(thousands of dollars)

Total Utility

10

100

90

90 Her expected utility is 100 0.9 + 0 0.1 = 90 units.

Beth would also have 90 units of utility if her wealth was $7000 with certainty.

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.

7

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.