Chapter 2 Flashcards
What is the definition of utility in economics?
Satisfaction an individual obtains from a particular course of action.
In the context of this theory, the individual is viewed as a consumer/investor making choices based on probabilistic outcomes.
What is a utility function?
A representation of the level of utility of an individual over differing levels of wealth (outcomes).
It is primarily measured by the willingness to pay different amounts for different forms of goods or services.
What does the Expected Utility Theorem (EUT) state?
An investor will make decisions in a manner to maximize the expected value of utility, E[U(w)], given their beliefs about the probability of different outcomes.
What are the four axioms of utility theory?
- Comparability
- Transitivity
- Independence
- Certainty Equivalence
Explain the axiom of comparability.
An investor can state a preference between all available certain outcomes.
What is the axiom of transitivity?
If U(A) > U(B) and U(B) > U(C), then U(A) > U(C).
What is the axiom of independence?
If indifferent between outcomes A and B, then indifferent between: p x A + (1-p) x C and p x B + (1-p) x C.
What does non-satiation mean in utility theory?
U’(w) > 0; the utility function has a positive gradient.
What are the three types of risk preferences?
- Risk averse
- Risk neutral
- Risk seeking
What is a fair gamble?
A gamble where the expected value of outcomes equals the cost of participation.
What is the expected return of a fair gamble?
E[Outcome] – Cost.
How does risk aversion affect a utility function?
Risk averse: U’‘(w) < 0; Risk neutral: U’‘(w) = 0; Risk seeking: U’‘(w) > 0.
What is the certainty equivalent of wealth (cw)?
The level of wealth that provides the same utility as a given uncertain gamble.
How is the certainty equivalent of a gamble calculated?
c_x = w + c_x, where c_x is the amount of guaranteed money considered equivalent to an uncertain gamble.
What is the difference between absolute and relative risk aversion?
- Absolute risk aversion: measures how risk preference changes with wealth.
- Relative risk aversion: measures risk preference as a proportion of an investor’s wealth.
What is the formula for absolute risk aversion?
U’‘(w) < 0 indicates risk aversion.
What is the formula for relative risk aversion?
It is the absolute formula with the addition of wealth to make it relative.
True or False: All individuals dislike uncertainty in the same measure.
False.
Who contributed to the development of the axioms of utility theory?
John von Neumann and Oskar Morgenstern.
What is the significance of the Arrow-Pratt measures?
They create measures for risk aversion.
What happens to risk preference as wealth changes?
Risk preference changes with changes in wealth.
What is the formula for certainty equivalent when considering wealth?
Certainty Equivalent = Absolute Formula + Wealth (multiply by w).
How do Dr. Strange’s certainty equivalents behave as his wealth increases?
They increase as his wealth increases.
What does the Arrow-Pratt measure indicate?
It provides a theoretical basis for understanding changes in risk aversion with wealth.
