Economic conditions Investment Good Normal Bad A $10,000 $5000 $0 B 6000 4000 1000 C 4000 2000 1500 ility for each economic condition would make the investor indifferent to the choice tments A, B and C?
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- . 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.Suppose that the consumer is asked to contemplate a gamble with a probability of 60% of winning Birr 10,000 with a utility of 10 utils, and a 40% probability of winning Birr 15,000 with a utility of 12 utils. A. What will be the expected income and expected utility of the consumer? B. If the utility of this consumer from a risk free alternative which gives him an income equal to the expected income of the risky alternative given above is equal to 11 utils, is this consumer risk lover or risk averse? Why? Illustrate your answer with the help of a diagram8) Three decision makers have assessed utilities for the problem whose payoff table appearsbelow.s1 s2 s3d1 500 100 -400d2 200 150 100d3 -100 200 300probability.2 .6 .2Indifference Probability for PersonPayoff A B C300 .95 .68 .45200 .94 .64 .32150 .91 .62 .28100 .89 .60 .22-100 .75 .45 .10a. Plot the utility function for each decision maker.b. Characterize each decision maker's attitude toward risk.c. Which decision will each person prefer?
- 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.Eunice, the industry analyst of H&M, wants to determine the propensity of Major Clothingcompanies toward risk. She was able to determine the utility distribution of H&M, Uniqloand Dickies. For H&M, If the expected payoff of a venture is a loss of 125,000, the utilityvalue is 0.00, if a loss of 75,000, the utility value is .2, if breakeven, the utility value is .5,if gain of 75,000 .8 and if gain of 125,000 utility value is 1. For Uniqlo, if loss of 125,000utility value is 0, if loss of 75,000 utility value is .1, breakeven is .4, if a gain of 75,000,utility value is .7 and if gain of 125,000 utility value is 1. For Dickies, if loss of 125,000,utility value is 0, if loss of 75,000, utility value is .3 breakeven is .6, if gain of 75,000, utilityvalue is .9 and gain of 125,000, utility value is 1. What is the propensity to risk of the threeinternet companies? Explain your graph.Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)
- Farmer Brown faces a 25% chance of there being a year with prolongeddrought, with zero yields and zero profit, and he faces a 75% chance of a normal year, with good yields and$100,000 profit. These probabilities are well-known. Suppose that an insurance company offered a droughtinsurance policy that pays the farmer $100,000 if a prolonged drought occurs. Assume that the farmer’sutility function is u(c) = ln(c). He has initial wealth of $40,000. What is the economic intuition on why X > Y? Confine your answer to at most three sentences.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?A manager is deciding whether to build a small or a large facility. Much depends on the future demand that thefacility must serve, and demand may be small or large. The manager knows with certainty the payoffs that willresult under each alternative, shown in the following payoff table. The payoffs (in $000) are the present values offuture revenues minus costs for each alternative in each event.What is the best choice if future demand will be low?
- Lela must decide to go on a winter trip to norway with the hope of seeing northern light would yield a utility level of 2,000 but she has only a 50% chance that they will show during the days of her trip. making the trip without seeing the lights would yield a utility level of 100 and there is 50 % chance of this happening. what is lela's expected utilty if show goes on the trip? a. 2,100 b.1,050 c.42 d.950Many 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 utility6) For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) = .35. s1 s2 s3 d1 -5000 1000 10,000 d2 -15,000 -2000 40,000 (a) What alternative would be chosen according to expected value? (b) For a lottery having a payoff of 40,000 with probability p and -15,000 with probability (1-p), the decision maker expressed the following indifference probabilities. Payoff Probability 10,000 .85 1000 .60 -2000 .53 -5000 .50 Let U(40,000) = 10 and U(-15,000) = 0 and find the utility value for each payoff. (c) What alternative would be chosen according to expected utility?
