2. Christiaan can go hiking, or he can stay at home. Hiking would be fun if nothing bad happens, but there is a risk if he goes hiking that he will meet a bear (not fun) or get bitten by a snake (very not fun). Christiaan decides that if there is a 5% chance of meeting a bear and a 1% chance of getting bitten by a snake, he would prefer to go hiking rather than stay at home. However, if the chance of meeting a bear is 10% and the chance of a snake bite is 5%, then he definitely would rather stay at home. (a) Consider the utility function: U (stay home) = 25, U (hike no event) = 100, U (hike & snake -1000, U (hike & bear) = -200. Does this utility function represent Christiaan's pref- erences? Explain. (b) Suppose that the utility function in (a) does represent Christiaan's preferences. Would
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- 1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, 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 is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…For the following questions consider this setting. The deciding shot in a soccer game comes down to a penalty shot. If the goal-keeper jumps in one corner and the striker shots the ball in the other, then it is a goal. If the goalie jumps left and the striker shoots left, then it is a goal with probability 1/3. If the goalie jumps right and the striker shots right, it is goal with probability 2/3. QUESTION Say the goalie's strategy is to jump left with probability 1 and the striker shoots left with probability 0.5, then the probability of a goal is (round to two digits) QUESTION If the striker shoots in either corner with probability 0.5 and the goalie likewise shoots in either corner with probability 0.5, then the probability of a goal is (round to 2 digits)(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,…
- When playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 30 or to bet $10 that the outcome is any one of the three possibilities 00, 0, or 1. 3 The gambler knows that the expected value of the $10 bet for a single number is - 53¢. For the $10 bet that the outcome is 00, 0, or 1, there is a probability of 38 of making a net profit of $30 and a probability of losing $10. 35 38 a. Find the expected value for the $10 bet that the outcome is 00, 0, or 1. b. Which bet is better: a $10 bet on the number 30 or a $10 bet that the outcome is any one of the numbers 00, 0, or 1? Why? a. The expected value is $. (Round to the nearest cent as needed.) b. Since the expected value of the bet on the number 30 is C than the expected value for the bet that the outcome is 00, 0, or 1, the bet on is better.2) Veronica is going to sell two vases to a dealer. She can sell each vase for $10. In order to bring her vases to the dealer, Veronica needs to take a bus. There is a 50% chance that all the vases carried on one bus trip will be broken during the trip and a 50% chance that none of the vases carried on one bus trip will be broken during the trip. A roundtrip bus ticket costs $1. Veronica's net income is given by the revenues from the sale of her vases minus the cost of her bus trip(s). 2a) How many trips would Veronica make if she were risk-neutral? 2b) Suppose that Veronica's utility from income is u(w)=100ln(x+w), and that she has no wealth other than the vases (also allow her to have negative wealth as in when she takes two vases on the same trip and both break while she paid the fare). What is the expected utility of net income when Veronica takes both vases on one bus trip? And when she makes two trips? What strategy is preferred? 2c) Would Veronica's preferred strategy change if…7. Suppose the only game in town involves flipping a fair coin (so Heads and Tails are equally likely), with a $x bet. If Heads comes up, the payoff is $0.9x; if Tails comes up, you lose the $x. You have $10,000, and must win at least $5,000 by tomorrow morning to pay off a debt to a mean dude. a. Compute the likelihood of winning at least $5000 by making a single bet of $10,000. b. Compute the likelihood of winning at least $1000 by playing the game 10,0000 times and betting a dollar each time. What is the likelihood of not losing money? Message learned?
- Suppose that a car - rental agency offers insurance for a week that costs $125. A minor fender bender will cost 34000 whereas a major accident might cost $16 comma 000 in repairs. Without the insurance, you would be personally liable for any damages. There are two decision alternatives: take the insurance, or do not take the insurance. You researched insurance industry statistics and found out that the probability of a major accident is 0.04% and that the probability of a fender bender is 0.18%. The expected payoff if you buy the insurance is $125.00. The expected payoff if you do not buy the insurance is $12.52. Develop a utility function for the payoffs associated with this decision for a risk-averse person. Determine the decision that would result using the utilities instead of the payoffs. Based on the expected payoffs, the best decision is to not purchase the insurance. Are these two decisions consistent?In the final round of a TV game show, contestantshave a chance to increase their current winnings of$1 million to $2 million. If they are wrong, theirprize is decreased to $500,000. A contestant thinkshis guess will be right 50% of the time. Should heplay? What is the lowest probability of a correctguess that would make playing profitable?1. Mr. Smith can cause an accident, which entails a monetary loss of $1000 to Ms. Adams. The likelihood of the accident depends on the precaution decisions by both individuals. Specifically, each individual can choose either "low" or "high" precaution, with the low precaution requiring no cost and the high precaution requiring the effort cost of $200 to the individual who chooses the high precaution. The following table describes the probability of an accident for each combination of the precaution choices by the two individuals. Adams chooses low precaution Adams chooses high precaution Smith chooses low precaution Smith chooses high precaution 0.8 0.5 0.7 0.1 1) What is the socially efficient outcome? For each of the following tort rules, (i) construct a table describing the individuals' payoffs under different precaution pairs and (ii) find the equilibrium precaution choices by the individuals. 2) a) No liability b) Strict liability (with full compensation) c) Negligence rule (with…
- 4.6. A person purchases a dozen eggs and must take them home. Although making trips home is costless, there is a 50 percent chance that all of the eggs carried on one trip will be broken during the trip. This person con- siders two strategies: Strategy 1: Take the dozen eggs in one trip. Strategy 2: Make two trips, taking six eggs in each trip. a. List the possible outcomes of each strategy and the probabilities of these outcomes. Show that, on aver- age, six eggs make it home under either strategy. b. Develop a graph to show the utility obtainable under each strategy. c. Could utility be improved further by taking more than two trips? How would the desirability of this possibility be affected if additional trips were costly?You and your roomate are deciding whether to go to a party or not on Friday. Going to the party is fun and gives a benefit of 4. If you go to the party, there is a 50% chance you will get covid. If you do not attend the party but your roommate does and gets covid, there is 80% chance that you will get covid. The impact of getting covid is -10. If both of you stay home, you will not be exposed to covid and will not have fun, leading to a payoff of 0 for both of you. 3. Construct a game matrix based on the description above and find any (c) Nash equilibria. How would your answer change if one roomate was less social and enjoyed (d) partying less than the other? Change the payoff matrix in a way that is both consistent with one roommate being less social than the other and changes the prediction you found in (a). (Note: if you found multiple possible equilibria in (a), changing the outcome could mean either making one of your prior Nash equilbria the only Nash equilibrium or making an…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.)