[5] Uncertainty

Question 1

We incorporate ___and __ into our models because they can cause ___ and ___ to modify decisions about __ and ___ choices.
• Risk is the when the ________ of each possible
outcome is known or can be estimated, and no single
possible outcome is ___ to occur.
• Estimates of how ___ each outcome is allows us to
estimate the __ ___ __.

Answer 1

risk, uncertainty
consumers, firms
Consumption, investment

Probability, certain

risky
most likely outcome

Question 2

How do you calculate expected (mean) value?

Answer 2

Expected value is the value of each possible outcome (V) times the probability of that outcome P(x), summed over all n possible outcomes: EV = Σ (P(x) * V)

Question 3

• A ___ is a number between 0 and 1 that
indicates the ___ that a particular outcome will occur.

• We can estimate probability with __________, the number of times that one particular outcome occurred (n) out of __ number of times an event occurred (N).
• If we don’t have a ___of the event that allows us to calculate frequency, we can use our best __ or ___ probability.

A probability distribution relates …

Answer 3

probability, likelihood
frequency

total

history
estimate
subjective

…the probability of occurrence to each possible outcome

Question 4

How is expected value used to measure risk?

x2

Answer 4

• Variance measures the spread of the probability
distribution or how much variation there is between the actual value and the expected value.

• Standard deviation ( ) is the square root of the variance and is a more commonly reported measure of risk.

Question 5

How do you calculate Variance? with Expected Value

And Standard Deviation σ ?

Answer 5

Variance = Σ P(x) * [ V - EV ] ²

S.D = √Variance

Question 6

Most of economics assumes that what you
maximize is not expected ___, but expected
___

Compare the expected utility of the ________ to
the expected utility of the _____ _____

___ individuals are more ___ averse

Answer 6

value, utility

Gamble , certain outcome

Older, risk

Question 7

When would an individual prefer the sure
thing to the gamble, even though the
gamble has a higher expected value?

Draw this on a Graph ? Name axis

Answer 7

when their utility function is concave, which means

U’ >0 and U’’ <0

Slide 28

Question 8

The additional utility from getting $475,000
relative to $0 is huge

• The additional utility from getting
$1,000,000 relative to $475,000 is much smaller

What is this descirbing?

Answer 8

Law of diminishing marginal utility of wealth

Question 9

Law of diminishing marginal utility of wealth is..

• Diminishing marginal utility is exactly the
same as ..

• Slope of the utility function is __________

Answer 9

The utility from an additional dollar is lower
when you are rich than when you are poor
• Diminishing marginal utility is exactly the
same as saying the utility function is concave
• Slope of the utility function is negative

Question 10

we say someone is risk ___ if, for any
lottery, they prefer to receive the __ ___ of
that lottery for sure than to ___ the lottery

An expected utility maximizer is risk averse if and
only if they have a __ __ __
• i.e. __ __ __ of money

Answer 10

averse
expected value
play

concave utility function
decreasing marginal utility

Question 11

What is a fair bet?

What is someone who is unwilling to take a fair bet?

Answer 11

A fair bet is a stake with an expected value of zero

risk averse

Question 12

What is EU and how is it calculated?

Answer 12

Expected utility, EU, is the probability-weighted average of the utility, U(•) from each possible outcome:
EU = Σ P(X) x U (V)

• The weights are the probabilities that each state of nature will occur, just as in expected value

Question 13

Risk-neutral utility function is a ___ ___.
• Risk-preferring utility is ___ to the ___ axis

Draw both?

Answer 13

straight line
convex, horizontal

Slide 40

Question 14

The risk premium is …

• For example,

Answer 14

The risk premium is the amount that a risk-averse person would pay to avoid taking a risk.

an individual may buy insurance to avoid risk. Equivalently, the risk premium is the minimum extra
compensation ( premium) that a decisionmaker would require to willingly incur a risk.

Question 15

The degree of risk aversion is judged by the shape of
…

• One common measure is the __ - ____measure of
risk aversion:

• This measure is ___ for risk-averse individuals,
zero for risk-neutral individuals, and ____for those
who prefer risk.

• The larger the Arrow-Pratt measure, the ___
gambles that an individual will take.

Answer 15

The degree of risk aversion is judged by the shape of the utility function over wealth, U(W).

Arrow-Pratt measure of risk aversion

positive
negative for those who prefer risk.

Fewer/smaller

Question 16

Equation to calculate the Arrow-Pratt Measure of risk?

Answer 16

p (w) = - [ d²U(w) / dW² ] / dU(w) / dW

Question 17

There are four primary ways for individuals to avoid risk:

Answer 17

1. Just say no
   • Abstaining from risky activities is the simplest way to avoid
   risk.
2. Obtain information
   • Armed with information, people may avoid making a risky choice or take actions to reduce probability of a disaster.
3. Diversify
   • “Don’t put all your eggs in one basket.”
4. Insure
   • Insurance is like paying a risk premium to avoid risk.

Question 18

A risk-averse individual will ___ insure by buying
enough insurance to ___ ___ if the insurance
company offers a __ insurance.

• In this scenario, the expected value of the insurance is ___ ; the policyholder’s expected value with and
without the insurance is the same

Answer 18

fully
eliminate risk
fair

zero

Insurance companies never offer fair insurance,
because they would not stay in business, so most
people do not fully insure.

Question 19

What determines is a Risk-neutral person invests?

What determines is a Risk-averse person invests?

Answer 19

Risk-neutral
Owner invests if and only if the expected value of the investment is greater than the expected value of not investing.

Risk-averse
Owner invests if and only if the expected utility of the investment exceeds the expected utility of not investing.