Podcast Beta
Questions and Answers
How is Henrique categorized based on his utility function?
What describes Juliano's attitude towards risk based on his marginal utility of income?
What is the correct outcome for Mike when offered the bet from Adam?
If Mike has a constant marginal utility of income, what can be inferred about his risk preference?
Signup and view all the answers
In the context of utility from income, what does risk averse imply about a consumer's behavior towards uncertain outcomes?
Signup and view all the answers
When a consumer is described as risk loving, how does this impact their acceptance of bets?
Signup and view all the answers
If both Henrique and Juliano are risk averse, what can be concluded about their utility functions?
Signup and view all the answers
How is the concept of marginal utility relevant to understanding consumer risk preferences?
Signup and view all the answers
What is the interest rate paid by the USC Credit Union savings account?
Signup and view all the answers
If Jim invests all his money in option A, what is Jim’s utility function?
Signup and view all the answers
What is the probability that the Los Angeles Panthers will lose the championship game?
Signup and view all the answers
What is the income Pedro Carroll would have if the Seahawks win after betting all his money?
Signup and view all the answers
What income does Pedro Carroll keep if he chooses not to bet?
Signup and view all the answers
Which minimum winning prize would make Cam willing to bet all his money on the Seahawks if they win?
Signup and view all the answers
If Pedro bets on the Seahawks and they lose, what amount will he have left?
Signup and view all the answers
What is the form of the production cost function for the firm aiming to maximize expected profit?
Signup and view all the answers
What is the expected utility for Investment A for Niobe?
Signup and view all the answers
Which investment option has the highest expected utility for Dione?
Signup and view all the answers
What is the expected value of Jim's investment option 1 if he buys shares of ACME?
Signup and view all the answers
What is the expected return percentage for Jim's investment option 2 with shares of Tabajara?
Signup and view all the answers
If Jim's investment in the savings account has a 1% return, what is the expected value?
Signup and view all the answers
Among the investment options Jim has, which one represents the lowest expected value?
Signup and view all the answers
Which expected utility calculation uses the formula 0.6 × (3 × 162) + 0.4 × (3 × 12)?
Signup and view all the answers
What is the main reason Niobe prefers investment option B over A?
Signup and view all the answers
Which investment option yields the highest expected utility for Jim?
Signup and view all the answers
What is the expected utility of investment option 2 (Tabajara)?
Signup and view all the answers
What is the probability P such that the expected utility from the risky option equals the risk-free option?
Signup and view all the answers
Which formula represents the expected utility from the risk-free option (holding cash)?
Signup and view all the answers
What is the expected utility of the risk-free option calculated as E[uRF]?
Signup and view all the answers
What does Iwin equal when both the risky option and risk-free option yield the same expected utility?
Signup and view all the answers
Which option is considered too risky for Jim despite having the highest expected value?
Signup and view all the answers
If the expected profit is given by the formula pq − 2q^2, what role does quantity q play in this profit model?
Signup and view all the answers
What is the maximum amount the consumer is willing to pay for insurance based on the expected utility calculations?
Signup and view all the answers
What is the expected loss calculated for the scenario where the consumer faces a potential loss of $158,400?
Signup and view all the answers
How is the risk premium (RP) calculated in the given scenarios?
Signup and view all the answers
In the case where the consumer buys partial insurance, what will be the consumer's payment in the event of a crash?
Signup and view all the answers
What is the expected utility without insurance (E[uN I]) for one of the calculations provided?
Signup and view all the answers
How much does the consumer receive back if he loses his money under the partial insurance?
Signup and view all the answers
What is the fair insurance premium related to the expected loss of a house value from $1,000,000 to $250,000?
Signup and view all the answers
What was the method used to determine the indifference point between purchasing insurance or not?
Signup and view all the answers
Study Notes
Utility Functions and Risk Aversion
- Risk Averse individuals prefer a certain outcome to a gamble with the same expected value. Their utility function is concave down, meaning the marginal utility of income decreases as income increases.
- Risk Neutral individuals are indifferent between a certain outcome and a gamble with the same expected value. Their utility function is linear.
- Risk Loving individuals prefer a gamble with the same expected value to a certain outcome. Their utility function is concave up, meaning the marginal utility of income increases as income increases.
Problem 1: Henrique and Juliano
- Henrique has a concave down utility function, indicating risk aversion.
- Juliano has a linear utility function, indicating risk neutrality.
Problem 2: Mike
- Mike has a constant marginal utility of income, meaning his utility function is linear. This indicates risk neutrality.
Problem 3: Pedro Carroll
- Pedro faces a choice between a risk-free option (keeping his current income) and a risky option (betting on the Seahawks winning).
- Pedro's utility function is linear, indicating risk neutrality.
- To determine the minimum winning probability P for Pedro to bet, set the expected utility of the risky option equal to the expected utility of the risk-free option:
- E[uR] = E[uRF]
- 20P = 13
- P = 0.65 or 65%
Problem 4: Cam
- Cam faces a choice between a risk-free option (keeping his current income) and a risky option (betting on the Panthers winning).
- To determine the minimum winning prize Iwin for Cam to bet, set the expected utility of the risky option equal to the expected utility of the risk-free option:
- E[uR] = E[uRF]
- 0.75 × Iwin = 6
- Iwin = 8
- Iwin = $64
Problem 5: The Firm's Production Decision
- The firm faces uncertainty about the price p of its product.
- The firm's profit is pq - 2q^2.
- To maximize expected profit, the firm chooses the quantity q that maximizes the expected value of its profit function.
- In this case, the optimal quantity is q = 5*, and the expected profit is $50.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your understanding of utility functions and the concepts of risk aversion, risk neutrality, and risk loving individuals. Explore scenarios involving Henrique, Juliano, Mike, and Pedro to apply these concepts in practical situations.
