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 trinc? How would a .
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- you and a friend decide to run a three mile race. If you agree to run together, you keep up with himfor the first mile, but you overexert yourself and run the last two miles at slower paces on your own. Tomake up for lost time, your friend runs the last two miles at a faster pace. Your mile times are 6:30, 7:00,and 7:30. Your friend’s times are 6:30, 6:00, and 6:00. If you both agree to run on your own, you run aconstant pace of 7:05 while your friend runs at a constant pace of 6:05. If you want to run together butyour friend wants to run solo, he runs his constant pace of 6:05. You, on the other hand, want to showhim that you can run faster, but you end up overexerting yourself after the first mile. You run times of6:20, 7:05, and 7:30. If he wants to run together but you do not, you both run at your pace of 7:05. Thissituation can be turned into an economic game, with the payoffs the overall race times. You each wantto run the fastest time you possibly can.(a) Who are the players in…You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…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)
- 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. Mel is thinking of going on a cruise. Mel values a cruise in nice weather at $2,000 and values a cruise in bad weather at $50. The probability of nice weather is 60 percent and the probability of bad weather is 40 percent. Trip insurance is sometimes available. If purchased, it allows travelers to delay the cruise until the weather is nice. Suppose that the price of the cruise is $1,200. If Mel is risk-neutral, then Mel should: not buy trip insurance. only buy trip insurance if it costs less than $780. only buy trip insurance if it costs less than $20. only buy trip insurance if it costs less than $50. 2. Several web sites, like Pricewatch.com, allow consumers to input the name of a product, and the site then returns a list of suppliers with their respective prices for the product. This: increases the benefit of search.. increases the free-rider problem. reduces the benefit of search. reduces the cost of search.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?
- 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. Do you agree with the statement that “the best strategy is to know what you should not do”? Try to justify your own view and possibly illustrate with a real world examplechris was going to purchase one rotisserie chicken for $10 but decided to purchase a second one becasue it was only an additional $5. Chris' decision to buy two rotisserie chicken is an example of.... 1. marginal decision making 2. SWOT analysis 3. a zero sum game 4. framing decisions
- 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. 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) 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)A friend offers you a chance to play a game in which there are only two outcomes, each with equal probability. If you get the "good" outcome, you win $80. But if you get the bad outcome, you only win $20. What price to play would make this a fair game (fair bet)? Carefully follow all mathematical instructions in your answer.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…