The decision maker has utility function U(x) = 2 ln(x). With 50% probability x=20 and with 50% x=100. The decision maker can buy insurance. For each unit of insurance they buy the get $1 if x=20 realizes. A unit of insurance costs $0.75. How many units of insurance does the decision maker buy?
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- John wants to buy a used car. He knows that there are two types of car in the market, plums and lemons. Lemons are worse quality cars and are more likely to break down than plums. John is willing to pay £10, 000 for a plum and £2, 000 for a lemon. Unfortunately, however, he cannot distinguish between the two types. Sellers can offer a warranty that would cover the full cost of any repair needed by the car for y ∗ years. Considering the type and likelihood of problems their cars can have, owners of plums estimate that y years of guarantee would cost them 1000y, owners of lemons estimate that the cost would be 2000y. John knows these estimates and decides to offer £10, 000 if a car comes with y ∗ years of warranty, £2, 000 if a car comes without warranty. For which values of y ∗ is there a separating equilibrium where only owners of plums are willing to offer the y ∗ -years warranty? Clearly explain your reasoning.Deborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. a) The expected value of Deborah’s bet (after subtracting the $1.00 she bet) is $________________ b) Given that Deborah makes this bet, is she risk adverse, risk neutral, or risk loving?In any year, the weather can inflict storm damage to a home. From year to year, thedamage is random. Let Y denote the dollar value of damage in any given year.Suppose that in 95% of the years Y = 0, but in 5% of the years Y = 20,000.a. What is the mean of the damage in any year?b. What is the standard deviation of the damage in any year?c. Consider an “insurance pool” of 100 people who homes are sufficientlydispersed so that, in any year, the damage to different homes can be viewed asindependently distributed random variables. What is the probability that ?exceeds $2000?
- "Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,460,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $210,000 is 0.27. The probability of a medium box office of $1,530,000 is 0.64, and the probability of a large box office of $3,190,000 is 0.09.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.61 probability the critic will have a favorable opinion.If the movie will have a medium…"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,460,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $210,000 is 0.27. The probability of a medium box office of $1,530,000 is 0.64, and the probability of a large box office of $3,190,000 is 0.09.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.61 probability the critic will have a favorable opinion.If the movie will have a medium…Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!
- Exercise 3: Risky Investment Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000. She is offered the opportunity to purchase a risky project for price P = 160, 000. 1 1 With probability p = 2 the project will be a success and return V > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]A lottery has a grand prize of $1,000,000, 2 runner-up prizes of $100,000 each, 6 third-place prizes of $10,000 each, and 19 consolation prizes of $1,000 each. If a 4 million tickets are sold for $1 each, and the probability of any ticket winning is the same as that of any other winning, find the expected return on a $1 ticket. (Round your answer to 2 decimal places.Consider a city where everyone commutes to the city center and commuting cost per mile per month is $40. Each household occupies a 1,000-square-foot dwelling and has $7,000 worth of possessions in its dwelling. The probability that any particular household will be burglarized (involving the uninsured loss of all possessions) is 0.10 at the city center and decreases by 0.01 per mile (to 0.09 at one mile, 0.08 at two miles, and so on). The housing price is $1.00 per square foot at the city center. a) Draw the housing-price curve for locations up to five miles from the city center.
- An investor considers investing $17,000 in the stock market. He believes that the probability is 0.22 that the economy will improve, 0.42 that it will stay the same, and 0.36 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $23,000, but it can also go down to $11,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $17,000. What is the expected value of his investment?Bob earn 60,000 a year and an accounting firm each year he receives Reyes Bob has determined that the probability that he receives a 10% raise is .7 the probability that he earns a 3% raise is .2 and the probability that he earns a 2% raise is .1 a competing company has offered Bob a similar position for 65,000 a year Bob wonders if he should take the new job or take his chances with his current job. a. Find the mathematical expectation of the dollar amount of his raise at his current job b.PROBLEM (4) A homeowner with expected utility preferences with ?(?) = √? (sqare root x) owns a house worth $490k. There is a probability p that she will experience a house fire, in which case the damages will cost $240k. A risk-neutral insurance company asks for an insurance premium of $10k in return for covering the damages fully in case of a fire. (a) What should p be so that the homeowner is willing to insure her house? (b) What should p be so that the insurance company is willing to offer insurance?
