WEEK 6 - Uncertainty

Question 1

Why do we incorporate risk and uncertainty in models of choice?

Answer 1

can cause consumers and
firms to modify decisions about consumption and
investment choices

Question 2

What is risk?

Answer 2

When the likelihood of each possible outcome is known or can be estimated and no single outcome is certain to occur
Estimates of how risky each outcome allows us to
estimate the most likely outcome.

Question 3

How do you figure out what consumer’s would maximise given their choice?

Answer 3

The expected or mean value of the game

Same thing

Question 4

How do we calculate the mean value of the game?

Answer 4

Use the Probability Concept

SEE EXAMPLE OF CALCULATING IN NOTES

Question 5

What is Probability

Answer 5

A number between 0 and 1 that indicates the likelihood that a particular outcome will occur

Question 6

How do we estimate probability?

Answer 6

With the frequency, the number of times that one particular outcome occurred (n) out of the
total number of times an event occurred (N).

θ = n/N

Question 7

If we don’t have a history of the event how do we best calculate the probability/

Answer 7

Use our best estimate or Subjective Probability

Question 8

What is a Probability Distribution?

Answer 8

Relates the probability of occurrence to each possible outcome

Question 9

How do you calculate the expected value (EV)?

Answer 9

Value of each possible outcome (Vi) times the probability of that outcome (θi) summed over all n possible outcomes

SEE EXAMPLE IN NOTES

Question 10

How do we use expected value to measure risk?

Answer 10

Use it in calculations for:

• Variance
• Standard Deviation

Question 11

What is Variance?

Answer 11

Measure how much variation there is between the actual value and the expected value

(SEE FORMULA IN NOTES)

Question 12

What is Standard Deviation?

Answer 12

The square root of the variance and is a more commonly reported measure of risk

Question 13

EXAMPLE OF ASSESSING RISK

Answer 13

SEE IN NOTES

Question 14

How do you analyse the expected utility?

Answer 14

Comparing the utility a person gets from all options

SEE IN NOTES FOR EXAMPLE

Question 15

When does a person prefer a sure thing to a gamble even if the gamble has a higher EV?

Answer 15

When their utility function is concave, which means:

U’ > 0 and U’’ < 0

Question 16

What is the intution behind being risk averse (using the pauper example)

Answer 16

Additional utility from the sure thing compared to 0 is huge (I.e getting 475,000 compared to 0)

• Additional utility from the risky reward relative to sure thing is much smaller
• So additional utility from winning the lottery (winning the risky reward) relatively small and not worth the additional risk

Question 17

What is the diminishing marginal utility of wealth?

Answer 17

The utility from an additional dollar is lower
when you are rich than when you are poor

Same as saying the utility function is concave

Question 18

How can people’s attitude toward risk be classified?

Answer 18

Via an example of a fair bet

Receive £1 if you win, lose £1 if you lose

Question 19

What are Risk Avere, Risk Neutral and Risk Preferring people’s response to a fair game

Answer 19

Someone who is unwilling to make a fair bet is risk
averse.
• Someone who is indifferent about a fair bet is risk neutral.
• Someone who is risk preferring will make a fair bet

Question 20

How do we calculate expected utility?

Answer 20

Sum of θi U (Vi)

Where:
θi is Probability of that outcome
Vi is value of each possible outcome

Question 21

EXAMPLE OF CALCULATING UTILITY AND ATTITUDES TOWARD RISK

Answer 21

SEE NOTES FOR EXAMPLE

TRUST ME IS GUD SHIZ

Question 22

What do the utility functions for Risk-neutral and Risk-preferring people look like?

Answer 22

Risk-neutral utility function - Straight line

Risk-preferring utility function - Convex

SEE GRAPH IN NOTES

Question 23

What is a risk premium?

Answer 23

Amount a risk averse person would pay to avoid taking a risk

Question 24

How do you measure the degree of Risk Aversion?

Answer 24

Using the Arrow-Pratt measure of risk aversion

p(W) = - d2U(W)/dW2 / dU(W)/dW

Where:
W is wealth
U(W) is the utility function over wealth

Measure is:
Positive for risk averse
Negative for risk preferring (the larger it is, the more they like to take risks)

SEE THE CALCULATION IN NOTES

Question 25

What are the 4 ways for an individual to reduce risk?

Answer 25

1. Say no
2. Obtain Info
3. Diversify
4. Insure

Question 26

How would you avoid risk via insurance?

Answer 26

Risk averse person fully insure to eliminate risk (Under the assumption that company offers fair bet)

• In real world, no such thing so people never fully insure

Question 27

What are the responses from a risk-averse and a risk-neutral individual from investing under uncertainty?

Answer 27

• 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