Yuki has a utility function given by u(x) = ln(x). She faces a gamble that pays 10 with probability 0.5 and 15 with probability 0.5. Comment on how Yuki's certainty equivalent relative to the expected value varies as her utility function goes from concave from convex.
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- Respond to the question with a concise and accurate answer, along with a clear explanation and step-by-step solution, or risk receiving a downvote.A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $900. There are two bidders. The dealer believes that there are only three possible values, $7,200, $3,600, and $900, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue from selling the car is approximately Group of answer choices $3,600. $2,500. $3,900. $5,400. $7,200.please only do: if you can teach explain each part
- Cheryl Druehl Retailers, Inc., must decide whether to build a small or a large facility at a new location in Fairfax. Demand at the location will either be low or high, with probabilities 0.6 and 0.4, respectively. If Cheryl builds a small facility and demand proves to be high, she then has the option of expanding the facility. If a small facility is built and demand proves to be high, and then the retailer expands the facility, the payoff is $230,000. If a small facility is built and demand proves to be high, but Cheryl then decides not to expand the facility, the payoff is $183,000. If a small facility is built and demand proves to be low, then there is no option to expand and the payoff is $250,000. If a large facility is built and demand proves to be low, Cheryl then has the option of stimulating demand through local advertising. If she does not exercise this option, then the payoff is $45,000. If she does exercise the advertising option, then the response to advertising will…Thelma is indifferent between $100 and a bet with a 0.6 chance of no return and a 0.4 chance of $200. If U(0) = 20 and U(200) = 220, then U(100) = :Problem 3. Carol's risk preference is represented by the following expected utility formula: U(T, C₁; 1 T, C₂) = π √√ √₁+ (17) √√C₂. i) Suppose Carol is indifferent between the following two options: the first option A returns $100 with probability and $X with probability, and the second option B returns $49 for sure. Determine X. ii) Consider the following three lotteries: L₁ = (0.9, $100; 0.1, $49), L2 = (0.7, $225; 0.3, $49), and L3= (0.5, $400; 0.5, $0). What is the ranking of these lotteries for Carol? Calculate the risk premiums of these lotteries for Carol. 1
- Consider the following interaction between a student and a company. The student is either serious or lazy with probabilities 1/3 and 2/3 respectively. The student knows if they are serious or not, but the company does not. Initially, the student decides whether to revise for exams or not. Revising has a cost of 1 for a serious student and 3 for a lazy one. The company observes the student's exam result (that is, whether they have made the effort to revise), and based on this, offers a salary of 3 (for a serious student) or 1 (for a lazy student). The student learns of the proposed salary and can then either accept (and earn the salary) or refuse (and earn O). They also lose the revision effort if they worked. The company's gain is equal to the student's productivity (4 if they are serious, 2 if not) minus the salary if the student accepts the offer, and O otherwise. 1. Represent the game in extensive form. 2. Show that the game has a unique perfect Bayesian Equilibrium, and provide the…Consider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by Ū = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: e=0 e=10 Probability (q=0) Probability (q=400) 0.6 0.4 0.9 0.1 What would the contract look like if the principal tried to push the wages when q=0 to zero? Would the principal want to do this? Explain.Suppose that • The employee has an outside offer to work for $27 per hour, for 1500 hours per year The employee currently works for $20 per hour, for 2000 hours per year The switching cost can be either high ($1'000) or low ($50) • The high switching cost has probability 40%; the low switching cost 60% Suppose that the cost of losing the employee is $800. What is the employer expected payoff from choosing not to match the outside offer?
- 9. Problems and Applications Q9 Dmitri has a utility function U = W, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Dmitri a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $9 million with probability 0.6. Use the blue curve (circle points) to graph Dmitri's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million. Utility (Thousands) 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0 0 2 4 8 6 10 12 14 Wealth (Millions of dollars) 16 18 20 V Utility Function ?Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?Lucy, the manager of the medical test firm Dubrow Labs, worries about the firm being sued for botched results from blood tests. If it isn't sued, the firm expects to earn profit of $120, but if it is successfully sued, its profit will be only $20. Lucy believes that the probability of a successful suit is 20%. If fair insurance is available and Lucy is risk averse, how much insurance will she buy? Lucy will buy insurance that costs her $ when not successfully sued. (Enter your response as a whole number.)