son is trying to sell cars. The number of cars that she will sell depends on her eno "e" and her luck. Given her effort e, with probability 4e she is able to sell four cars, and with probability (1-4e she is able to sell only one car. Her personal cost of effort is 100e². The dealership pays her a bonus b for each car sold. The salesperson is risk-neutral, and wants to maximize her expected utility, which is her expected income minus her effort cost. a) Given the bonus b, the salesperson's best response function is b) Suppose the dealership pays b = 2. Then the expected number of cars sold will be E(Q)=
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- Joseph Biggs owns his own ice cream truck and lives 30 miles from a Florida beach resort. The sale of his products is highly dependent on his location and on the weather. At the resort, his profit will be $120 per day in fair weather, $10 per day in bad weather. At home, his profit will be $80 in fair weather and $50 in bad weather. Assume that on any particular day, the weather service suggests a 30% chance of foul weather. a) The correct decision tree for Joseph is shown in Figure 3 b) To maximize the return, for selling ice cream, Joseph's decision should be to use the Expected monetary value for Joseph = (enter your answer as a whole number). FIGURE 3 87 resort home 87 71 Fair(0.70) Foul(0.30) Fair(0.70) Foul(0.30) 120 10 80 50At races, your horse, White Rum, has a probability of 1/20 of coming 1st, 1/10 of coming 2nd and a probability of 1⁄4 in coming 3rd. First place pays $5,000 to the winner, second place $4,000 and third place $1,350.Hence, is it worth entering the race if it costs $1050? Your company plans to invest in a particular project. There is a 40% chance you will lose $3,000, a 45% chance you will break even, and a 15% chance you will make $5,500. Based solely on this information, what should you do? On 1st Jan 2006, a business had inventory of $19,000. During the month, sales totalled $32,500 and purchases $24,000. On 31st Jan 2006 a fire destroyed some of the inventory. The undamaged goods in inventory were valued at $11,000. The business operates with a standard gross profit margin of 30%. Based on this information, what is the cost of the inventory destroyed in the fire?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.
- The injured football player Bad news everyone! There is 1 second left in the game, and Tom Brady has injured himself. The matrices below depict the relative probabilities of winning givenan offensive and a defensive play call. (The row player is the New England Patriots and the column player is the opponent.) How much has the all star's home team probability of winning decreased due to the injury? Pass uny Patriots D Pass .4, .6 D Run .9,.1 .8,.2 .5,.5 Pass Run Opponent D Pass D Run .06, .94 .32, .68 .8,.2 .5,.5Deborah 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?17. A salesperson at Joe's Exotic Pets is trying to sell iguanas. The number of iguanas that she sells depends on her effort "e" as well as her luck. Given her effort e, she will sell four iguanas with probability 4e, and only one iguana with probability (1-4e). Her personal cost of effort is 200e. The pet shop pays her a bonus b for each iguana sold. The salesperson is risk-neutral, and wants to maximize her expected utility, which is expected income minus her effort cost. If the pet shop pays b-5, how many iguanas do they expect to sell? a. 1 b. 2.5 c. 2.8 d. 3.55 e. 4 om v sec w you page back
- The owner of a firm must hire a manager to launch a new product. The new product can be successful and generate a revenue of 5000 or fail and generate a revenue of 1000. The probability of succ success is 0.7 (and hence the probability of failure is 0.3). If the manager exerts low effort (e=e,) then the probability of success is 0.2 (and hence the probability of failure is 0.8). The manager's utility effort chosen by the manager, with D(e) = 10 and D(e)-o. The manager's reservation utility is -40 The wage paid by the owner to the manager is the owner's only cost. The owner is risk neutral. If the owner could observe the manager's effort and would want the manager to exert high effort, what contract would he offer to the manager? What is the own Assume from now on that the manager's effort is unobservable. Suppose that the owner still wants to ensure that the manager accepts the proposed contract an this to happen. c) a)? a) b) It can be shown that the constraints in point b) must be…You work at a mechanic shop. 40% of cars that come in have a flat tire. If there are 5 cars in the shop, what is the probability that 3 have a flat tire? Round to three decimal points.It is Lady Bridgerton's first ball of the season and she must select 4 dance partners for the upcoming dances. She cannot dance with the same partner twice. Of the 15 potential dance partners at the ball, there are 3 Dukes, 4 Earls, 7 Barons, and one Prince. Find the probability that: a) she does not dance with a Duke. b) she dances with exactly 2 Barons. c) she dances with at least one Earl. d) each dance partner has a different rank.
- In a tight real estate market, the probability that a buyer's offer will be accepted is 0.50 if she bids more than 15 thousand above the asking price. The probability of acceptance drops to 0.20 if she bids below this amount. Overall, sixty percent of offers are more than 15 thousand above the asking price. The probability that a randomly selected offer will be accepted by the seller is closest or equal to: 0.15 0.38 0.20 0.32 O 0.18Bill owes Bob $36. Just before Bill pays him the money, he gives Bob the opportunity to play a dice game to potentially win more money. The rules of this game are as follows: If Bob rolls doubles (probability 1/6), Bill will Bob double ($72). If he misses doubles on pay the first try, he can try again or settle for half the money ($18). If he makes doubles on the second try Bill will again pay-up double ($72), but if Bob misses doubles on the second try Bill will only pay him one-third ($12). Should Bob decide to play the dice game with Bill, or insist that he pay the $36 now? Use a decision tree to support your answer.An investor with initial wealth W is given the opportunity to invest in a start-up (1) company. If the company does well, the investor will make a 200% profit in her investment, but if the company fails, the investor will lose all her investment. That is, if the investor invests X, she will get back 3x if the company succeeds and nothing if the company fails. The company will fail with probability 1/2 and will succeed with probability 1/2. The investor is risk-averse and has utility function u(x) wealth W should she invest in this company? Vx. What fraction of her initial