Question 3 A decision maker has a utility function U = VĪ. This decision maker is: O risk-loving. O risk-gaining. O risk-neutral. O risk-averse, Question 4 Given the possible outcomes to a lottery being only the values 2, 6 with equal probabilities, calculate the expected value, variance and standard deviation? O EV = 4, variance = 4, standard deviation = 2 O EV = 3.5, variance = 4, standard deviation = 2 O EV = 4, variance = 16, standard deviation = 4 O EV = 4, variance = 4, standard deviation = 4
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- 6) 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 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 withprobability (1-p), the decision maker expressed the following indifferenceprobabilities. Payoff Probability10,000 .851000 .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?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)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…
- 1 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.Clancy has $4800. He plans to bet on a boxing match betweenSullivan and Flanagan. He finds that he can buy coupons for $6 thatwill pay off $10 each if Sullivan wins. He also finds in another storesome coupons that will pay off $10 if Flanagan wins. The Flanagantickets cost $4 each. Clancy believes that the two fighters each have aprobability of ½ of winning. Clancy is a risk averter who tries tomaximize the expected value of the natural log of his wealth. Whichof the following strategies would maximize his expected utility? (a) Don’t Gamble (b) Buy 400 S tickets and 600 F tickets(c) Buy exactly as many F tickets and S tickets (d) Buy 200 S and 300 F(e) Buy 200 S and 600 FThe investor is considering how to optimally invest 1000 euros in stocks and bonds. Let's assume that the optimal decision is made based on expected utility. Suppose the investor has a utility function u(x)=ln(1+x), where x is their wealth. Let y be the proportion invested in stocks and 1−y be the proportion invested in bonds. By investing in stocks, the investor earns 1% with a probability of 39.5% and 4% with a probability of 60.5%. By investing in bonds, the investor earns a certain 2.8%. What proportion of the investment will the investor allocate to stocks and what proportion to bonds?
- 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.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 diagramDeborah 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?
- 8) Three decision makers have assessed utilities for the problem whose payoff table appearsbelow. probabilities and payoffs. S1 S2 S3 D1 500 100 -400 D2 200 150 100 D3 -100 200 300 Probability .2 .6 .2 Indifference Probability for Person Payoff A B C 300 .95 .68 .45200 .94 .64 .32150 .91 .62 .28100 .89…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.Y5 Alfred is a risk-averse person with $100 in monetary wealth and owns a house worth $300, for total wealth of $400. The probability that his house is destroyed by fire (equivalent to a loss of $300) is pne = 0.5. If he exerts an effort level e = 0.3 to keep his house safe, the probability falls to pe = 0.2. His utility function is: U = w0.5 – e where e is effort level exerted (zero in the case of no effort and 0.3 in the case of effort).a. In the absence of insurance, does Alfred exert effort to lower the probability of fire?HINT: Calculate and compare the expected utility i) with effort, and ii) without effort. If effort is exerted, then the effort cost is paid regardless of whether or not a fire occurs.b. Alfred is considering buying fire insurance. The insurance agent explains that a home owner’s insurance policy would require paying a premium α and would repay the value of the house in the event of fire, minus a deductible “D”. [A deductible is an amount of money that the…