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- 14 of 17 Attractive conditions in America such as better wages, new technology, and bigger living quarters that would cause one to immigrate to the United States are known as Opull factors. Oliabilities. Ⓒassets. Ⓒpush factors Previous Q Search - 0 2. If you examine the decision tree in Figure 9.12 (orany other decision trees from PrecisionTree), you willsee two numbers (in blue font) to the right of each endnode. The bottom number is the combined monetaryvalue from following the corresponding path throughthe tree. The top number is the probability that thispath will be followed, given that the best strategy isused. With this in mind, explain (1) how the positiveprobabilities following the end nodes are calculated,(2) why some of the probabilities following the endnodes are 0, and (3) why the sum of the probabilitiesfollowing the end nodes is necessarily 1.Marcus is an expected utility maximizer with the Bernoulli utility function u(w) = √w. He faces a gamble in his wealth. In a good state he gets 81 and in a bad state he gets 9. He can take out an insurance plan which will leave him with a wealth of 49 in each state. (a) (b) (c) state? Is Marcus risk averse? Will he purchase the insurance if the probability of the states is ½ for each Let p denote the probability of the good state. For what value(s) of p will Markus be just indifferent between taking out the insurance and not taking it out? Show your working.
- The owner of a ski resort is considering installing a new ski lift that will cost $900,000. Expenses for operating andmaintaining the lift are estimated to be $1,500 per day when operating. The U.S. Weather Service estimates thatthere is a 60% probability of 80 days of skiing weather per year, a 30% probability of 100 days per year, and a 10% probability of 120 days per year. The operators of the resort estimate that during the first 80 days of adequate snow in a season, an average of 500 people will use the lift each day, at a fee of $10 each. If 20 additional days are available, the lift will be used by only 400 people per day during the extra period; and if 20 more days of skiing are available, only 300 people per day will use the lift during those days. The owners wish to recover any invested capital within five years and want at least a 25% per year rate of return before taxes. Based on a before-tax analysis, should the lift be installed?With reference to Fig. 5-3, if the individual's income is either OA = $30,000 with probability of 0.95 or OB = $5000, (a) what is the expected income of this individual? (b) What is the maximum amount of insurance that this individual would be willing to pay? %3Duestion Completion Status: Player 2 L R U 1,0 0,1 Player 1 D 0,1 1,0 Suppose Player 2 is using the following strategy: she plays L with probability 0.70 and she plays R with probability 0.30. In this case: a) If Player 1 plays U, then Player 1 attains an expected payoff of 0.70 b) If Player 1 plays D, then Player 1 attains an expected payoff of 0.30 c) Therefore, the best response of Player 1 is to play U with probability 1.00 and D with probability 0
- A health economist is conducting the analysis and making a choice between the following two choices: Choice A: there is a certain outcome that the patient will stay in chronic health state X for the rest of his life T Choice B: the treatment has two possible outcomes, either the patient is returned to full Health (1) of the rest of his life T with probability p; the patient dies (0) immediately with the remainig probability What is the utilty value of the health state X? X=P X=PT X=(1-P)/P X=PT/(1-P)Players would draw a card from a standard 52 card deck. Whatever card they drew determined what they won. If they draw a face card (Jack, King, Queen) then they win $5. If they draw an Ace, they win $15. For all other cards, they win nothing. A. Fill out the probability distribution table with the probabilities of each possible outcome for this game. Round decimals to four places. x $15 $5 $0 P(x) B. What is the expected value of the distribution above? (Round to the nearest cent, two decimal places.) C. If players were charged $2 per game, would they make and average profit on the games over time, or would they take an average loss over time? D. If players were charged $3 per game, would they make and average profit on the games over time, or would they take an average loss over time?Please no written by hand and no emage Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: Decision s1 s2 s3 d1 150 200 200 d2 50 200 500 The probabilities of s1, s2, and s3 are unknown. Using the optimistic approach, what is the optimal decision and what is the value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to arrive at this decision in the second.
- An investor must decide among three alternative investments A, B and C. The return for each investment, given three future economic conditions, is shown in the following payoff table: Economic conditions Investment Good Normal Bad A $10,000 $5000 $0 B 6000 4000 1000 с 4000 2000 1500 What probability for each economic condition would make the investor indifferent to the choice among investments A, B and C?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 utilityThe Minister of Transport released its Festive season road accident statistics which shows that the probability of drivers committing an accident is 8% with utility U(H) = √H, where H stands for year income. The Minister further claims these Festive season road accidents cost the state (in terms of claims lodged) an average of R84 000 per annum. The Road Accident Fund is an insurance scheme providing compulsory indemnity cover to victims of vehicle accidents and taxi drivers. (a) Suppose that an average commuter earns R84 000 per annum. What is the expected utility of each commuter if the driver decides not to take insurance. (b) What is the cost of insurance policy to the Road Accident Fund? (c) Due to high accident rates during Festive season, the road accident fund has issued a warning to the government that the fund will be insolvent soon. Advise the Minister on the cost of insurance that can collapse the scheme