The marginal utility of income for a risk-averse individual will be: Select one: a. diminishing. b. constant. c. increasing. d. unknown; the answer depends on the value of income.
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- Leora has a monthly income of $20,736. Unfortunately, there is a chance that she will have an accident that will result in costs of $10,736. Thus leaving her an income of only $10,000. The probability of an accident is 0.5. Finally assume that her preferences over income can be represented by the utility function u(x) = 2ln(x).a) What is the expected income? What is Leora’s expected utility (you may leave in log form)? b) What is the certainty equivalent to her situation? What is the risk premium associated with her situation?c) What is the maximum that Leora would be willing to pay for a full insurance policy?d) Illustrate her expected utility, expected wealth, certainty equivalent, the risk premium and her willingness to pay for a full insurance policy in a diagram.Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U’ > 0) and convex (U’’ > 0). a) Draw a utility function in U - I space that fits this description. b) Explain the connection between U’’ and risk aversion.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).
- 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).Risk aversion is best explained by a. Timidity b. Increasing marginal utility of income c. Constant marginal utility of income Decreasing marginal utility of income A Risk Lover prefers the expected utility of wealth to the utility of the expected value of wealth. a. TRUE. It is because a risk lover has a convex utility function b. FALSE. It is because a risk lover has a concave utility function. 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.
- The greater the rate of decrease of marginal utility for an individual, A) The more risk averse the individual is and the more willing the individual is to pay premiums above the actuarially fair premium. B) The less risk averse the individual is and the more willing the individual is to pay premiums above the actuarially fair premium. C) The more risk averse the individual is and the less willing the individual is to pay premiums above the actuarially fair premium. D) The less risk averse the individual is and the amount the individual willing is to pay premiums above the actuarially fair premium is constant.Dr. Gambles has a utility function given as U(w)=In(w). Due to the pandemic affecting his consulting business, Dr Gambles faces the prospect of having his wealth reduced to £2 or £75,000 or £100,000 with probabilities of 0.15, 0.25, and 0.60, respectively. Suppose insurance is available that will protect his wealth from this risk. How much would he be willing to pay for such insurance?A risk-neutral plaintiff in a lawsuit must decide whether to settle a claim or go to trial. The defendants offer $50,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 50% if the plaintiff wins, the amount awarded to the plaintiff is X Will the plaintif settle if x is $62,500? What if X-$250,000? What is the critical value of X that would make the plaintiff indifferent between setting and going to trial? it the plaintiff were risk averse instead of risk neutral, would this critical value of X be higher or lower? If the amount to be awarded at trial with a win (X) were $62,500, then the plaintiff would settle If the amount to be awarded at trial with a win (X) were $250,000, then the plaintiff would not settle The critical value of X that would make the plaintiff indifferent between settling and going to trial is $ (Enter your response using rounded to wo decimal places)
- Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematicallyU(W) in an appropriate utility function, where W is the level of wealth. Which of the following is TRUE for a risk-loving investor? Select one: A. U[E(W)] < E[U(W)] B. U[E(W)] > E[U(W)] C. U[E(W)] = E[U(W)] = 0 D. U[E(W)] = E[U(W)]Consider a risk averse individual who has utility function u(a) which is increasing with u(0) = 0. There are two risky assets: A,B. For A, every dollar invested gives return $0 with probability 1/3 and $3 with probability 2/3. For B, every dollar invested gives return is $0 with probability 1/4 and $3 with probability 3/4. The individual has $120 to invest. Consider two investment choices: (1) invest entire $120 in A and (2) invest $60 in A, $60 in B. (a) Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 1. (b)Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is bad. (c) Drawing diagram of the utility function and showing your work, determine the expected utility of the individual from choice 2 when return from A is good. (d) Drawing diagram of the utility function and showing your work, determine the…