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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 1.2 Prove rigourously, "Constant relative risk aversion (CRRA) implies decreasing absolute risk aversion (DARA), but the converse is not necessarily true."Mf. Mean variance utility defines risk using certainty equivalent wealth. The lower the certainty equivalent wealth, the lower the mean variance utility. uestion Select one: O True O False Under constant relative risk aversion, the lower the certainty equivalent wealth is than the average wealth of a lottery the riskier the lottery. Select one: O True O False Given a normally distributed risky asset and a risk free asset, a person with a lower CRRA risk aversion coefficient will put less in the risk free asset than a person with a higher CRRA risk aversion. Select one: O True O False Greater risk aversion means a plot of utility vs. wealth would look less curved. Select one: O True O False The greater the wealth, the less the utility of the next dollar of wealth. Select one: O True O False People don't like risk because it means they get poorer when they're poorer and richer when they're rich. In fact, a financial security…
- Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!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.If probability of the student attend the first lecture is 0.55, the probability that he attend the second lecture is 0.40, and the probability he attend both is 0.28. Find probability that he not attend first lecture or not attend the second one: O.72 O.36 O.95 O.27
- 6.33 Statistics released by the National HighwayTraffic Safety Administration and the National SafetyCouncil show that on an average weekend night, 1 outof every 10 drivers on the road is drunk. If 400 driversare randomly checked next Saturday night, what is theprobability that the number of drunk drivers will be(a) less than 32?(b) more than 49?(c) at least 35 but less than 47?2. Kier, in The scenario, wants to determine how each of the 3 companies will decide on possible new investments. He was able to determine the new investment pay off for each of the three choices as well as the probability of the two types of market. If a company will launch product 1, it will gain 50,000 if the market is successful and lose 50,000 if the market is a failure. If a company will launch product 2, it will gain 25,000 if the market is successful and lose 25,000 if the market will fail. If a company decides not to launch any of the product, it will not be affected whether the market will succeed or fail. There is a 56% probability that the market will succeed and 44% probability that the market will fail. What will be the companies decision based on EMV? What is the decision of each company based on expected utility value?You have drawn a painting that you want to sell to an anonymous buyer, but you do not know exactly how much they are willing to pay. Based on past experiences, you estimate that the buyer will be willing to pay in monetary units where a random variable is evenly distributed continuously over the interval [200, 500]. Let's assume that your assessment regarding the random variable is correct, i.e., that it is indeed evenly distributed continuously over the interval [200, 500]. What price �p will you choose if you want to maximize your expected profit? What will be your expected profit?
- Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. What is expected gains/loss.9 10 11 12 answer only1 Question 2. Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r ∼ N(µ, σ2). The investor has an expected utility maximizer with the CARA utility u(r) = −e −Ar. Write down the investor’s maximization problem of choosing α fraction of his wealth will be invested in the risky asset Find the optimal fraction of wealth that the investor will invest in the risky asset α∗Hint: Use the fact that if a random variable x is distributed normally with mean µx and variance σ2x , then for any constant α, What happens to the optimal fraction of wealth that the investor will invest in the risky asset as the risk aversion A increases? Explain the intuition behind your result.