Choice under uncertainty

Question 1

Define expected value.

Answer 1

The probability-weighted average payout

Question 2

Are risk and uncertainty the same?

Answer 2

No

Question 3

What is the difference between risk and uncertainty?

Answer 3

Risk is where possible outcomes and their probabilities are known where as uncertainty is when we cannot assign probabilities to outcomes

Question 4

How do we find the expected value of the income?

Answer 4

Times each probability by the income and sum it all.

Question 5

What can the utility function sometimes be used to describe?

Answer 5

Preferences

Question 6

What is the equation for the utility function that relates payoffs and their payoffs?

Answer 6

U(X) = p1u(x1) + p2y(x2) + …. + pnu(xn)

Question 7

What is U(X)? And what does it tell us?

Answer 7

It is the standard utility function and it tells is many many utils consumption of x provides

Question 8

What is the utility of the expected pay off?

Answer 8

The utility obtained by the expected income

Question 9

What is the expected utility of the payoff?

Answer 9

The expected value of the utility of the possible income

Question 10

What is meant by being risk neutral?

Answer 10

It is when agents only care about the expected value of an investment

Question 11

Who is a risk seeker?

Answer 11

Someone willing to take risk

Question 12

Is the utility of the expected income and the expected utility the same?

Answer 12

No

Question 13

How do you find the utility of the expected income?

Answer 13

U[E(x)]

Question 14

How do you find the expected utility?

Answer 14

E[U(X)]

Question 15

Give an example of a utility function for a risk seeker?

Answer 15

u(x) = x^2

Question 16

Give an example of a utility function for a risk averse?

Answer 16

u(x) = x^0.5

Question 17

What is meant by a person being risk neutral?

Answer 17

They value the certain amount of expected value of a risky outcome equal to the outcome itself:
U[E(x)] = E[U(x)]

Question 18

What is meant by a person being risk averse?

Answer 18

They value the certain amount of the expected vale of a risky outcome more than the outcome itself:
U[E(x)] > E[U(x)]

Question 19

What is meant by a person being risk loving?

Answer 19

They value the certain amount of the expected value of a risky outcome less than the outcome itself:
U[E(x)] < E[U(x)]

Question 20

Define a certainty equivalent.

Answer 20

The guaranteed income level at which an individual would receive the same exptected utility level as from an uncertain income.

Question 21

Define risk premium.

Answer 21

The compensation an individual would require to bear risk without suffering a loss in expected utility

Question 22

Give an example of the utility function for a risk neutral person.

Answer 22

U(x) = x

Question 23

What is one application of expected utility and risk?

Answer 23

Insurance markets