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?
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- Lukas is a risk-averse farmer. He grows barley on his 1000 acre farm. In a typical year his farm yields 100 bushels of barley per acre. However, in a wet season, the farm only yields 40 bushels per acre. The probability of a typical season is 0.8 and of a wet season is 0.2. Regardless of the productivity of his farm, he expects to earn $3 per bushel (net of all costs of farming). Assume that Lukas has no other income. Write an expression for Lukas's expected utility.Catalina just inherited a vineyard from a distant relative. In good years (when there is no rain or frost during harvest season), she earns $115,000 from the sale of grapes from the vineyard. If the weather is poor, she loses $35,000. Catalina's estimate of the probability of good weather is 55%. The expected value of Catalina's income from the vineyard is $. (round your answer to the nearest dollar)Wanda works as a waitress and consequently has the opportunity to earn cash tips that are not reported by her employer to the Internal Revenue Service. Her tip income is rather variable. In a good year (G), she earns a high income, so her tax liability to the IRS is $5000. In a bad year (B), she earns a low income, and her tax liability to the IRS is $0. The IRS knows that the probability of her having a good year is 0.6, and the probability of her having a bad year is 0.4, but it doesn’t know for sure which outcome has resulted for her this tax year. In this game, first Wanda decides how much income to report to the IRS. If she reports high income (H), she pays the IRS $5000. If she reports low income (L), she pays the IRS $0. Then the IRS has to decide whether to audit Wanda. If she reports high income, they do not audit, because they automatically know they’re already receiving the tax payment Wanda owes. If she reports low income, then the IRS can either audit (A) or not audit…
- Suppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from outof town, and they are to meet at a local restaurant. When Lisa lived in town,they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Ofcourse, Lisa’s information is out of date, but Grace knows which is betterthese days. Assume that the probability that the Bel Loc Diner is better isp > 1/2 and the probability that the Corner Stable is better is 1 - p. Naturedetermines which restaurant Grace thinks is better. Grace then sends amessage to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to theCorner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from theiractions are as shown in the…Y5 Alfred is a risk-averse person with $100 in monetary wealth and owns a house worth $300, for total wealth of $400. The probability that his house is destroyed by fire (equivalent to a loss of $300) is pne = 0.5. If he exerts an effort level e = 0.3 to keep his house safe, the probability falls to pe = 0.2. His utility function is: U = w0.5 – e where e is effort level exerted (zero in the case of no effort and 0.3 in the case of effort).a. In the absence of insurance, does Alfred exert effort to lower the probability of fire?HINT: Calculate and compare the expected utility i) with effort, and ii) without effort. If effort is exerted, then the effort cost is paid regardless of whether or not a fire occurs.b. Alfred is considering buying fire insurance. The insurance agent explains that a home owner’s insurance policy would require paying a premium α and would repay the value of the house in the event of fire, minus a deductible “D”. [A deductible is an amount of money that the…(Fill in the 4 blanks.) A monthly pass for the Stockholm subway costs $100, and fare dodgers who are caught face a fine of about $160. Stockholm transport has increased the number of ticket checks conducted, and the probability of being caught while riding the subway without paying is now 1%. Liam rides the subway 50 times a month, so that each month the probability that he is caught equals 50 x 1% = !3! 50% and he expects to pay 50 (0.01 x $160) = $80 in fines each month he rides the subway without buying the monthly pass. If Liam does not purchase a monthly pass, his expected monthly savings are $ (accepted format is dollars and cents xXx.xx). Liam's utility of saving $S equals VS , so that if he does not purchase a monthly pass, his expected utility equals (round to 2 decimals: xxx.xx). Liam's certainty equivalent is savings equal to $52.42, and thus Liam's (do not capitalize your answer and make sure to spell correctly) is $7.58. Liam can purchase full insurance from Planka.nu,…
- Suppose you own a house worth $500. However, there is a risk the house could burn down. If the house burns down, it will only be worth $25. There is a 5% chance the house burns down. However, you can buy insurance that will pay you if in the event the house burns down. Call the amount of insurance purchased K. The premium you have to pay for K dollars of insurance is 0.05×K. So, if hypothetically you wanted $100 of insurance, the premium would be $5. Assume you have log-utility u(x) = ln(x). What is the optimal amount of insurance, K ∗ ? (Note: the premium must be paid whether the house burns down or not.)Suppose that Mike, with utility function, u(x) = v x+5000, is offered a gamble where a coin is flipped twice, and if the coin comes up heads both times (probability - .25), he gets $40,000. Would he prefer this gamble or $7,500 for sure? What is his Certainty Equivalent?Utility Theory You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000. A. Apply Bayes’ decision rule to determine which alternative (take the insurance or not) maximizes yourexpected assets after one year.
- Suppose that you have two opportunities to invest $1M. The first will increase the amount invested by 50% with a probability of 0.6 or decrease it with a probability of 0.4. The second will increase it by 5% for certain. You wish to split the $1M between the two opportunities. Let x be the amount invested in the first opportunity with (1-x) invested in the second. Find the optimal value of x. Using expected value as the criterion (linear utility) Using the flowing utility function: u(x)=2.3 ln〖(1+4.5x)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. The expected value of Deborah's bet (after subtracting the $1.00 she bet) is $ Given that Deborah makes this bet, she must beDeborah 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?
