Calculate the expected utility of John when he faces the risky prospect X = {1, 2, 3, 4; 0.2, 0.4, 0.4, 0.2} . His utility function is u(x) = 4 ln x, where x is wealth and ln represents the natural log. (Use two decimals)
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Calculate the expected utility of John when he faces the risky prospect X = {1, 2, 3, 4; 0.2, 0.4, 0.4, 0.2} . His utility function is u(x) = 4 ln x, where x is wealth and ln represents the natural log. (Use two decimals)
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- Calculate the risk premium of John when he faces the risky prospect X = {1, 4, 9, 16; 0.2, 0.4, 0.4, 0.0} . His utility function is u ( x ) = x , where x is wealth. (Use two decimals)Leo owns one share of Anteras, a semiconductor chip company which may have to recall millions of chips. The stock currently trades at $100/share. Leo believes the probability that they have to recall the chips is 50%. If the chips have to be recalled, the stock price will be cut in half, but otherwise it will remain $100. The expected value of Leo's share is ______ Assume Leo has the utility function, U(X)=√X. The minimum price Leo would accept to sell his share is _______ Leo's risk premium is ________Please answer true or false for each of the following statements. A risk-averse consumer has increasing marginal utility. A risk-neutral consumer is willing to pay a positive risk-premium to avoid risk. A risk-neutral consumer has a linear utility function. A risk-loving consumer has a convex utility function. A risk-averse consumer can increase her expected utility by buying multiple stocks whose outcomes are not closely related, instead of buying only one stock.
- Loss aversion refers to the idea that people ________. generally tend to avoid risky activities are more prone to making losses than gains in day-to-day transactions psychologically weight a loss more heavily than they psychologically weight a gain are unwilling to undertake expenditures that reduce the probability of future lossesPlease draw a utility function that exhibits risk-loving behavior for small gambles (low values)and risk-averse behavior for larger gambles (high value).Gary likes to gamble. Donna offers to bet him $31 on the outcome of a boat race. If Gary’s boat wins, Donna would give him $31. If Gary’s boat does not win, Gary would give her $31. Gary’s utility function is p1x^21+p2x^22, where p1 and p2 are the probabilities of events 1 and 2 and where x1 and x2 are his wealth if events 1 and 2 occur respectively. Gary’s total wealth is currently only $80 and he believes that the probability that he will win the race is 0.3. Which of the following is correct? (please submit the number corresponding to the correct answer). Taking the bet would reduce his expected utility. Taking the bet would leave his expected utility unchanged. Taking the bet would increase his expected utility. There is not enough information to determine whether taking the bet would increase or decrease his expected utility. The information given in the problem is self-contradictory.
- Calculate the expected utility of John when he faces the risky prospect X = {4, 9, 16, 25; 0.2, 0.3, 0.3, 0.2} . His utility function isu ( x ) = 50 x − x 2 , where x is wealth. (Use two decimals) ________For constants a and b, 0 < b, b 1, and expected profit E(p), the expected utility function of a person who is risk-neutral can be written as E(U) = Which one: a+b^p a + (E(p))^b. a - bE(p). a + bE(p). a + (E(p))^(-b).In the field of financial management, it has been observed that there is a trade-off between the rate of return that one earns on investments and the amount of risk that one must bear to earn that return. a) Draw a set of indifference curves between risk and return for a person that is risk-averse (a person that does not like risk).
- . Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) √x . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.The von-Neumann Morgenstern utility function is of the form u(e) - In(e). There is a lottery over consumption outcomes: with probability 0.3, the consumption will be 1 and with probability 0.7 the consumption will be 3; Compute the risk premium (round to 2 decimals).Consider the following claim: “If a decision maker prefers one given lottery that yields $x with probability 1 over another given lottery whose expected return is $x, then we can fully characterize the agent's risk attitude. That is, this information comparing two given lotteries is enough to determine if the decision maker is risk averse, risk loving or risk neutral.” If this claim is TRUE, then provide a proof. If it is FALSE, then prove your argument by providing an explanation.