Podcast
Questions and Answers
What is the expected behavior of a risk-neutral individual concerning the choice between option A and option B as they progress through the price list?
What is the expected behavior of a risk-neutral individual concerning the choice between option A and option B as they progress through the price list?
- They will prefer option B throughout.
- They will switch preference to option A at the bottom.
- They will switch preference halfway down after row 4. (correct)
- They will have no preference between the two options.
If a participant exhibits increasing relative risk aversion, how does their choice behavior change as stakes increase?
If a participant exhibits increasing relative risk aversion, how does their choice behavior change as stakes increase?
- They switch preferences sooner in the list.
- They switch preferences later in the list. (correct)
- They prefer lower stakes regardless of options.
- Their preferences do not change with stakes.
In the Holt and Laury experiment, what was the average switch point for participants regarding their risk preferences?
In the Holt and Laury experiment, what was the average switch point for participants regarding their risk preferences?
- Row 7
- Row 10
- Row 3
- Row 5 (correct)
What characterizes the Allais Paradox choices when individuals prefer a certain outcome over a gamble with a higher expected value?
What characterizes the Allais Paradox choices when individuals prefer a certain outcome over a gamble with a higher expected value?
What common choice pattern is observed among participants facing the Allais Paradox?
What common choice pattern is observed among participants facing the Allais Paradox?
How does a risk-averse individual behave on the Holt and Laury price list?
How does a risk-averse individual behave on the Holt and Laury price list?
What does it indicate if an individual's preferences switch farther down the list in the Holt and Laury experiment?
What does it indicate if an individual's preferences switch farther down the list in the Holt and Laury experiment?
What is the implication of constant relative risk aversion in decision-making when stakes increase?
What is the implication of constant relative risk aversion in decision-making when stakes increase?
Which response accurately describes the relationship between risk and the stake levels according to the findings in the Holt and Laury experiment?
Which response accurately describes the relationship between risk and the stake levels according to the findings in the Holt and Laury experiment?
What is the expected value of a gamble that has a 50% chance of winning $32,000 and a 50% chance of winning $1,000,000?
What is the expected value of a gamble that has a 50% chance of winning $32,000 and a 50% chance of winning $1,000,000?
In the context of expected utility theory, what does the variable 'u(x)' represent?
In the context of expected utility theory, what does the variable 'u(x)' represent?
If a gamble is defined as (p1, x1; p2, x2), what does 'pi' represent for each outcome?
If a gamble is defined as (p1, x1; p2, x2), what does 'pi' represent for each outcome?
How would you summarize the expected utility of a gamble A with multiple outcomes?
How would you summarize the expected utility of a gamble A with multiple outcomes?
What is the expected outcome of rolling a fair six-sided die in terms of dollars?
What is the expected outcome of rolling a fair six-sided die in terms of dollars?
If an individual chooses to walk away from a gamble and secures $500,000, which aspect of decision-making is being demonstrated?
If an individual chooses to walk away from a gamble and secures $500,000, which aspect of decision-making is being demonstrated?
In expected utility theory, which of the following correctly defines the expected value of a gamble A?
In expected utility theory, which of the following correctly defines the expected value of a gamble A?
When assigned a probability of outcome i, what key principle does this reflect in a gamble?
When assigned a probability of outcome i, what key principle does this reflect in a gamble?
In the Millionaire example, which choice represents the highest expected utility if you were to make a decision?
In the Millionaire example, which choice represents the highest expected utility if you were to make a decision?
Considering a gamble with outcomes indexed by i, which of the following would be incorrect in defining the structure of that gamble?
Considering a gamble with outcomes indexed by i, which of the following would be incorrect in defining the structure of that gamble?
What does the independence axiom state in the context of expected utility theory?
What does the independence axiom state in the context of expected utility theory?
In the context of the St. Petersburg Paradox, what does the expected value of the game reveal?
In the context of the St. Petersburg Paradox, what does the expected value of the game reveal?
Why does utility function u(x) exhibit concavity in the context of risk aversion?
Why does utility function u(x) exhibit concavity in the context of risk aversion?
What conclusion can be drawn from the average and median amounts a class is willing to pay to play the St. Petersburg game?
What conclusion can be drawn from the average and median amounts a class is willing to pay to play the St. Petersburg game?
What does a utility function of the form u(x) = x^α with α < 1 indicate about a decision-maker's preferences?
What does a utility function of the form u(x) = x^α with α < 1 indicate about a decision-maker's preferences?
How is the expected utility calculated for a gamble involving a coin flip for $25?
How is the expected utility calculated for a gamble involving a coin flip for $25?
What preference does a convex utility function u(x) indicate?
What preference does a convex utility function u(x) indicate?
Which of the following outcomes would likely be preferred by a risk-averse individual?
Which of the following outcomes would likely be preferred by a risk-averse individual?
Which statement aligns with the concept of diminishing marginal utility in economic theory?
Which statement aligns with the concept of diminishing marginal utility in economic theory?
What does the typical choice pattern between A and B indicate?
What does the typical choice pattern between A and B indicate?
Why is the choice between A' and B' significant in the context of expected utility theory?
Why is the choice between A' and B' significant in the context of expected utility theory?
In the context of the Allais Paradox, what does the Common Consequence Problem illustrate?
In the context of the Allais Paradox, what does the Common Consequence Problem illustrate?
What is the expected utility of option A as described?
What is the expected utility of option A as described?
How does the expected utility of option D compare to C?
How does the expected utility of option D compare to C?
What does the utility function u(100,000,000) represent in this context?
What does the utility function u(100,000,000) represent in this context?
In the Allais Paradox, what does the option B' demonstrate?
In the Allais Paradox, what does the option B' demonstrate?
What percentage of participants chose option A in the Moblab results?
What percentage of participants chose option A in the Moblab results?
What does the expected utility calculation of EU(A') imply?
What does the expected utility calculation of EU(A') imply?
In the context of the Allais Paradox, what does option C represent?
In the context of the Allais Paradox, what does option C represent?
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Study Notes
Research Group Assignments
- Assignments are available on Canvas.
- Review guidance for working in research groups located in Module 3.
- Group Management Plan due by September 13; one submission required per group.
Expected Utility: The Classic Theory
- Expected utility helps make choices between uncertain options or gambles.
- Example scenario from "Who Wants to Be a Millionaire":
- Joseph can either guess for a million or walk away with $500,000 guaranteed.
Gambles
- A gamble is defined by potential outcomes, indexed by i, with respective probabilities pi and values xi.
- Representation of a gamble: (p1, x1; p2, x2; ...; pn, xn).
- Examples include outcomes from a die roll or choices in a quiz game.
Expected Value Calculation
- Expected value (EV) formula: EV(A) = Σ(pi * xi), where pi is the probability and xi the outcome value.
- EV example from Millionaire scenario: $516,000.
- For a die roll, EV = 3.5.
Expected Utility Concept
- Expected utility is calculated as: EU(A) = Σ(pi * u(xi)).
- Consumers choose gambles maximizing their expected utility.
Independence Axiom
- A fundamental principle stating preferences between gambles remain consistent when a common gamble is added.
- If a preference exists for one option over another, that preference should remain when both are modified by adding the same additional gamble.
Utility Function Characteristics
- Utility functions can be concave (risk-averse), convex (risk-seeking), or linear (risk-neutral).
- The St. Petersburg Paradox exemplifies diminishing marginal utility; average willingness to pay contrasts with calculated expected value.
Risk Aversion
- Utility function: u(x) = x^α; α < 1 indicates risk aversion.
- Example calculations show preferences for certain outcomes over risky gambles, reflecting risk-averse behavior.
Experimental Evidence
- The Holt and Laury experiment involved 175 students making risky choices.
- Results indicate typical risk aversion, showing participants prefer a secure option at lower stakes and switch to riskier choices at higher stakes.
Violations of Expected Utility Theory
- Allais Paradox: Demonstrates inconsistencies in choice patterns. For example:
- Choices between certain and probabilistic options show a preference for certainty in A over B, yet preferences flip in A' and B' choices.
Common Consequence Problem
- Choices between gambles that add a constant (common consequence) challenge expected utility theory predictions, revealing a common pattern of preference inconsistencies.
Allais Paradox Example 2
- Further illustrates preference inconsistencies between two sets of gambles involving certain and variable outcomes, reaffirming the unexpected decision behaviors contradicting traditional utility theory predictions.
MobLab Activities
- Highlights experimental tasks evaluating risk preferences among participants, facilitating understanding of real-world choices versus theoretical predictions.
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