Paul hires Amy to manage his bakery shop. The following table gives the shop's profits (without subtracting payments to Amy) under 2 different levels of Amy's effort and two different states of the world (good and bad weather). There is a 50% probability that the weather will be good. Bad weather (50%) Good weather (50%) Low Effort High Effort 300 The cost of low effort is 10 and the cost of high effort is 41. Paul offers a fixed salary of 100 and bonus B if revenue is strictly higher than 300. What is the value of the lower bound of B, above which Amy would be incentivized to put in high effort? 100 300 500
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- The project manager of Good Public Relations gatheredthe data shown in Table 7.15 for a new advertisingcampaign.a. How long is the project likely to take? b. What is the probability that the project will take more than38 weeks?c. Consider the path A–E–G–H–J. What is the probability thatthis path will exceed 38 weeks?Many decision problems have the following simplestructure. A decision maker has two possible decisions, 1 and 2. If decision 1 is made, a sure cost of c isincurred. If decision 2 is made, there are two possibleoutcomes, with costs c1 and c2 and probabilities p and1 2 p. We assume that c1 , c , c2. The idea is thatdecision 1, the riskless decision, has a moderate cost,whereas decision 2, the risky decision, has a low costc1 or a high cost c2.a. Calculate the expected cost from the riskydecision.b. List as many scenarios as you can think of thathave this structure. (Here’s an example to get youstarted. Think of insurance, where you pay a surepremium to avoid a large possible loss.) For eachof these scenarios, indicate whether you wouldbase your decision on EMV or on expected utilityEconomics A person likes to gamble and has $100 on him. He is going to play the following game: if he bets $b, then with probability p, 0 < p< 1, he will win $b; with probability 1 – p, he will lose his $b. He is given the opportunity to play at most 20 times. He is a very disciplined gambler and is going to use the following strategy: • Every time he plays, he will make a bet equal to half of the amount of money he has at that moment. • If the amount of money he has gets to $300 or higher, then he will stop playing. Find the probability that, starting with $100 and given 20 chances to play the game, this person will get to $300 or more. Formulate this problem recursively by writing down the “Bellman equation." What is (are) the state variable(s)? Be specific about any constraints or initial/boundary conditions for this problem.
- 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)Decisions Involving Uncertainty - End of Chapter Problem You're a project manager overseeing five teams that are developing a new app. Each team must complete their work by July 1 in order to release the app by the end of the year. Based on your work managing the project, you know that each team has about a 75% chance of meeting the deadline. a. The probability that your firm will complete the project by the end of the year is b. Suppose that before you calculate the probability of completing the project, you walk into a weekly status meeting with the CEO. When she asks you for your "gut feeling" about the probability of finishing the project by the end of the year, you respond with an answer that exhibits the anchoring bias. Your response will likely be, "About 70%." "About 90%." "About 25%."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…
- 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?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.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…
- 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%, he definitely would rather stay at home. then (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 Christiaan prefer to hike or stay home if the probability of meeting a bear is 6% and the probability of being bitten by a snake is 4%? Show your work.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.Answer correctly with in 50minutes