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Questions and Answers
How is Henrique categorized based on his utility function?
How is Henrique categorized based on his utility function?
What describes Juliano's attitude towards risk based on his marginal utility of income?
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?
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?
If Mike has a constant marginal utility of income, what can be inferred about his risk preference?
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In the context of utility from income, what does risk averse imply about a consumer's behavior towards uncertain outcomes?
In the context of utility from income, what does risk averse imply about a consumer's behavior towards uncertain outcomes?
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When a consumer is described as risk loving, how does this impact their acceptance of bets?
When a consumer is described as risk loving, how does this impact their acceptance of bets?
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If both Henrique and Juliano are risk averse, what can be concluded about their utility functions?
If both Henrique and Juliano are risk averse, what can be concluded about their utility functions?
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How is the concept of marginal utility relevant to understanding consumer risk preferences?
How is the concept of marginal utility relevant to understanding consumer risk preferences?
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What is the interest rate paid by the USC Credit Union savings account?
What is the interest rate paid by the USC Credit Union savings account?
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If Jim invests all his money in option A, what is Jim’s utility function?
If Jim invests all his money in option A, what is Jim’s utility function?
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What is the probability that the Los Angeles Panthers will lose the championship game?
What is the probability that the Los Angeles Panthers will lose the championship game?
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What is the income Pedro Carroll would have if the Seahawks win after betting all his money?
What is the income Pedro Carroll would have if the Seahawks win after betting all his money?
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What income does Pedro Carroll keep if he chooses not to bet?
What income does Pedro Carroll keep if he chooses not to bet?
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Which minimum winning prize would make Cam willing to bet all his money on the Seahawks if they win?
Which minimum winning prize would make Cam willing to bet all his money on the Seahawks if they win?
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If Pedro bets on the Seahawks and they lose, what amount will he have left?
If Pedro bets on the Seahawks and they lose, what amount will he have left?
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What is the form of the production cost function for the firm aiming to maximize expected profit?
What is the form of the production cost function for the firm aiming to maximize expected profit?
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What is the expected utility for Investment A for Niobe?
What is the expected utility for Investment A for Niobe?
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Which investment option has the highest expected utility for Dione?
Which investment option has the highest expected utility for Dione?
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What is the expected value of Jim's investment option 1 if he buys shares of ACME?
What is the expected value of Jim's investment option 1 if he buys shares of ACME?
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What is the expected return percentage for Jim's investment option 2 with shares of Tabajara?
What is the expected return percentage for Jim's investment option 2 with shares of Tabajara?
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If Jim's investment in the savings account has a 1% return, what is the expected value?
If Jim's investment in the savings account has a 1% return, what is the expected value?
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Among the investment options Jim has, which one represents the lowest expected value?
Among the investment options Jim has, which one represents the lowest expected value?
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Which expected utility calculation uses the formula 0.6 × (3 × 162) + 0.4 × (3 × 12)?
Which expected utility calculation uses the formula 0.6 × (3 × 162) + 0.4 × (3 × 12)?
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What is the main reason Niobe prefers investment option B over A?
What is the main reason Niobe prefers investment option B over A?
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Which investment option yields the highest expected utility for Jim?
Which investment option yields the highest expected utility for Jim?
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What is the expected utility of investment option 2 (Tabajara)?
What is the expected utility of investment option 2 (Tabajara)?
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What is the probability P such that the expected utility from the risky option equals the risk-free option?
What is the probability P such that the expected utility from the risky option equals the risk-free option?
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Which formula represents the expected utility from the risk-free option (holding cash)?
Which formula represents the expected utility from the risk-free option (holding cash)?
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What is the expected utility of the risk-free option calculated as E[uRF]?
What is the expected utility of the risk-free option calculated as E[uRF]?
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What does Iwin equal when both the risky option and risk-free option yield the same expected utility?
What does Iwin equal when both the risky option and risk-free option yield the same expected utility?
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Which option is considered too risky for Jim despite having the highest expected value?
Which option is considered too risky for Jim despite having the highest expected value?
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If the expected profit is given by the formula pq − 2q^2, what role does quantity q play in this profit model?
If the expected profit is given by the formula pq − 2q^2, what role does quantity q play in this profit model?
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What is the maximum amount the consumer is willing to pay for insurance based on the expected utility calculations?
What is the maximum amount the consumer is willing to pay for insurance based on the expected utility calculations?
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What is the expected loss calculated for the scenario where the consumer faces a potential loss of $158,400?
What is the expected loss calculated for the scenario where the consumer faces a potential loss of $158,400?
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How is the risk premium (RP) calculated in the given scenarios?
How is the risk premium (RP) calculated in the given scenarios?
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In the case where the consumer buys partial insurance, what will be the consumer's payment in the event of a crash?
In the case where the consumer buys partial insurance, what will be the consumer's payment in the event of a crash?
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What is the expected utility without insurance (E[uN I]) for one of the calculations provided?
What is the expected utility without insurance (E[uN I]) for one of the calculations provided?
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How much does the consumer receive back if he loses his money under the partial insurance?
How much does the consumer receive back if he loses his money under the partial insurance?
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What is the fair insurance premium related to the expected loss of a house value from $1,000,000 to $250,000?
What is the fair insurance premium related to the expected loss of a house value from $1,000,000 to $250,000?
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What was the method used to determine the indifference point between purchasing insurance or not?
What was the method used to determine the indifference point between purchasing insurance or not?
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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.
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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.
