Choice under uncertainty Flashcards
Define expected value.
The probability-weighted average payout
Are risk and uncertainty the same?
No
What is the difference between risk and uncertainty?
Risk is where possible outcomes and their probabilities are known where as uncertainty is when we cannot assign probabilities to outcomes
How do we find the expected value of the income?
Times each probability by the income and sum it all.
What can the utility function sometimes be used to describe?
Preferences
What is the equation for the utility function that relates payoffs and their payoffs?
U(X) = p1u(x1) + p2y(x2) + …. + pnu(xn)
What is U(X)? And what does it tell us?
It is the standard utility function and it tells is many many utils consumption of x provides
What is the utility of the expected pay off?
The utility obtained by the expected income
What is the expected utility of the payoff?
The expected value of the utility of the possible income
What is meant by being risk neutral?
It is when agents only care about the expected value of an investment
Who is a risk seeker?
Someone willing to take risk
Is the utility of the expected income and the expected utility the same?
No
How do you find the utility of the expected income?
U[E(x)]
How do you find the expected utility?
E[U(X)]
Give an example of a utility function for a risk seeker?
u(x) = x^2
Give an example of a utility function for a risk averse?
u(x) = x^0.5
What is meant by a person being risk neutral?
They value the certain amount of expected value of a risky outcome equal to the outcome itself:
U[E(x)] = E[U(x)]
What is meant by a person being risk averse?
They value the certain amount of the expected vale of a risky outcome more than the outcome itself:
U[E(x)] > E[U(x)]
What is meant by a person being risk loving?
They value the certain amount of the expected value of a risky outcome less than the outcome itself:
U[E(x)] < E[U(x)]
Define a certainty equivalent.
The guaranteed income level at which an individual would receive the same exptected utility level as from an uncertain income.
Define risk premium.
The compensation an individual would require to bear risk without suffering a loss in expected utility
Give an example of the utility function for a risk neutral person.
U(x) = x
What is one application of expected utility and risk?
Insurance markets
