Please draw a utility function that exhibits risk-loving behavior for small gambles (low values) and risk-averse behavior for larger gambles (high value).
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Please draw a utility function that exhibits risk-loving behavior for small gambles (low values)
and risk-averse behavior for larger gambles (high value).
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- Let b(p,s,t) be the bet that pays out s with probability p and t with probability 1−p. We make the three following statements: S1: The CME for b is the value m such that u(m)=E[u(b(p,s,t))]. S2: A risk averse attitude corresponds to the case CME smaller than E[b(p,s,t))]. S3: A risk seeking attitude corresponds to a convex utility function. Are these statements true or false?An agent makes decisions using U(ct) = (ct−χct−1)1−γ 1−γ . Answer the following: (a) Suppose χ = 0. Derive an expression for the coefficient of relative risk aversion RR(ct)? (b) Suppose 0 < χ ≤ 1. Derive an expression for the coefficient of relative risk aversion RR(ct)?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).
- 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.. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . 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.Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematically
- Let U(x)= x^(beta/2) denote an agent's utility function, where Beta > 0 is a parameter that defines the agent's attitude towards risk. Consider a gamble that pays a prize X = 10 with probability 0.2, a price X = 50 with probability 0.4 and a price X = 100 with probability 0.4. Compute the agentís expected utility for such gamble and find the value of Beta such that the agentis risk neutral? Suppose B= 1, what is the certainty equivalent of the gamble described above? What is the Arrow-Pratt measure of absolute risk aversion?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 ________
- 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 lossesFor 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).A risk-averse manager is considering two projects. The first project involves expanding the market for bologna; the second involves expanding the market for caviar. There is a 10 percent chance of a recession and a 90 percent chance of an economic boom. During a boom, the bologna project will lose $10,000, whereas the caviar project will earn $20,000. During a recession, the bologna project will earn $12,000 and the caviar project will lose $8,000. If the alternative is earning $3,000 on a safe asset (say, a Treasury bill), what should the manager do? Why?
