1. Robert has a lifetime wealth of £225,000 and faces the following gamble: -50 per cent chance of winning £775 50 per cent chance of losing £725 Explain how expected utility theory and prospect theory differ in the way they predict Robert will assess this gamble.
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- 2. Ronald has $18,000. But he is forced to bet it on the flip of a fair coin. If he wins he has $36,000. If he loses he has nothing. Ronald's expected utility function is 0.5x0.5 + 0.5y0.5, where x is his wealth if heads comes up and y is his wealth if tails comes up. What safe income would make him exactly as well off as this bet?1. Risk Premium: Assume your wealth is $100 and like in the Veritassium video you're offered a bet of a 50% chance of winning $10 and a 50% chance of losing $10. Assume you have square root utility. a. What is the utility you enjoy by holding the $100 of current wealth? b. What is the expected utility you foresee by entering the bet? Will you take the bet? c. What is your risk premium? Do you think someone would pay this to avoid the bet? d. Draw a diagram and label the relevant values.Johnny is "paid" by his parents $2o if he gets a grade A, $10 if he gets a grade B, whereas he has to pay his parents back $5 if he gets a grade other than A or B. On average 20% of the grades he gets are A, and 30% are grades B. What is the expected value of what he "earns" per grade ? What is the expected value of what he "earns" at school weekly if on average he gets five grades a week ? How long should Jim save until he collects enough money to buy a pair of brand new Hi-Fi headphones that cost $225?
- 2. Alex plays football for a local club in Kumasi. If he does not suffer any injury b y the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coa ch worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = √X Assume he could buy insurance at price P that could pay $9,900 in case of inj ury. What is the highest value of P that makes it worthwhile for Alex to purcha se insurance? What is the certainty equivalence for this lottery?Economics Shawn's consumption is subject to risk. With probability 0.75 he will enjoy 10000 in consumption, but with probability 0.25 he will have only 3600. His utility function for consumption is given by v(c) = Vc. -What is the expected value of Shawn's consumption? -What is his expected utility? -What is his certainty equivalent of having 10000 with probability 0.75 and 3600 with probability 0.25?**Practice** I have been trying to practcie this question but I always seem to get it wrong What is the expected final wealth of each agent? Pay attention to the names in each option!A. Anna’s expected final wealth is 1440 and Bob’s expected final wealth is 980B. Anna’s expected final wealth is 1020 and Bob’s expected final wealth is 1380C. Anna’s expected final wealth is 1460 and Bob’s expected final wealth is 1105D. Anna’s expected final wealth is 1140 and Bob’s expected final wealth is 1200E. None of the options above
- Hello can any one help with this Economics question: A contractor spends Dollar 3,000 to prepare for a bid on a construction project which, after deducting manufacturing expenses and the cost of bidding, will yield a profit of dollar 25,000 if the bid is won. If the chance of winning the bid is ten per cent, compute his expected profit and state the likely decision on whether to bid or not to bid?4. A taproom owner is trying to determine how to structure his manager's compensation. One option he considers is a flat salary of $70,000 per year. The second option is a base salary of $30,000 plus 15% of the taproom's profit. If the manager puts a lot of effort into her job, the taproom's annual profit will be $500,000 with 75% probability and $100,000 with 25% probability. If the manager exerts only modest effort, the taproom's profit will be $500,000 with 25% probability and $100,000 with 75% probability. The manager's opportunity cost of putting a lot of effort into her job is $50,000, while her opportunity cost of exerting only modest effort is $25,000. a. Draw the game tree for the interaction between the taproom owner and the manager. Assume that the taproom owner moves first. b. What is the equilibrium outcome for this game? What kind of contract should the taproom owner offer? What level of effort will the manager choose? Explain.Suppose Caroline is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds.CombinationFraction of Portfolio in Diversified StocksAverage Annual ReturnStandard Deviation of Portfolio Return (Risk)(Percent)(Percent)(Percent)A 0 1.50 0B 25 3.00 5C 50 4.50 10D 75 6.00 15E 100 7.50 20There is a relationship between the risk of Caroline's portfolio and its average annual return.Suppose Caroline currently allocates 75% of her portfolio to a diversified group of stocks and 25% of her portfolio to risk-free bonds; that is, she chooses combination D. She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5. In order to do so, she must do which of the following? Check all that apply. Sell some of her stocks and use the proceeds to purchase…
- Sam, after taking a $200 loan from the bank to finance an investment that pays $1000 50% of the time and $0 50% of the time at a 100% interest, discovers another riskier investment that pays out $5,000 but only 10% of the time, while the other 90% of the time it pays zero. Would the he want to switch to the riskier investment? Question 4 options: Yes because his return has increased No because his liability to the bank has increased No because his return has decreased None of the above5. You have been hired as a portfolio manager for a fancy hedge fund. Your first job is to invest $100,000 in a portfolio of two assets. The first asset is a safe asset with a certain return of 5%. The second asset is shares of a dying video-game store that has become popular with retail investors, it has a 20% expected rate of return, but the standard deviation of this return is 10%. Your manager wants a portfolio with as high a rate of return as possible while keeping the standard deviation at or below 4%. How much of the fund's money do you invest in the safe asset?5) Philippina's utility of wealth function is VW. She has stocks, bonds and cash worth $360,000 and a house worth $280,000. There is a 1% chance of her house being completely destroyed by fire. Unfortunately, if she has insurance, she is less responsible and so the risk of her house being burned down rises to 2%. a. What is the most Philippina is willing to pay for insurance?
