6 (A) Sudesh invests in the business which will give him a return of 64 if it turns out to be successful, and Rs. 36 if it is a failure. The probability of failure is 2/3 and that of success is 1/3. The utility function derived from the wealth from this business is given by u(w) = w². Suppose the insurance company offers to insure Sudesh against low earnings. The price of the insurance is 75 paisa for each rupee of benefit. How much of the insurance will she buy to maximize his utility?
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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.Cost-Benefit Analysis Suppose you can take one of two summer jobs. In the first job as a flight attendant, with a salary of $5,000, you estimate the probability you will die is 1 in 40,000. Alternatively, you could drive a truck transporting hazardous materials, which pays $12,000 and for which the probability of death is 1 in 10,000. Suppose that you're indifferent between the two jobs except for the pay and the chance of death. If you choose the job as a flight attendant, what does this say about the value you place on your life?Suppose that Bill's utility function of wealth is given by u(w) = √w, where w represents his total wealth in dollars. Bill's total wealth is $360,000. If an earthquake happens, his wealth will be reduced to $250,000 with the loss of his house. Suppose the probability of an earthquake happening is 10%. (a) Is Bill risk-averse, risk-loving, or risk-neutral? Explain. (b) If Bill could buy insurance to completely avoid the loss, how much would he be willing to pay for this insurance at most? Explain.
- Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.19. An individual has initial wealth Wo = 3 and has the opportunity to invest some quantity of money x in an extremely risky corporate bond. With probability p= 1/4, the bond will be worth 10x at maturity. With probability 1 – p, it will be worth zero. The individual's utility function over final wealth is u(W) = W0.5. What is the level of investment x that maximizes expected utility? (а) 0 (b) 1 (c) 4/3 (d) V3 (e) 2Consider a gamble/lottery in which a coin is tossed rapidly until a tail comes up. 2m rupee is given if the tail comes up at the mth toss. Let the individual be risk neutral, having u(x) = x where x is the amount of winning. Find the expected utility from the lottery.
- If the utility function is U (W) = ((W0.75) / (0.75)), what is the absolute risk aversion coefficient?Suppose you manage a factory with ten workers. Each worker’s output is determined by the equation q = e. Output sells in the market for a price of 40. The firm has fixed cost equal to 800, and variable costs aside from labor are 8 per unit of output. Worker utility is U = w – e2. Suppose you are paying workers a wage equal to bq. What is the profit- maximizing value of b? Suppose that the probability of worker error increases as the worker increases effort, and that worker error results in unusable output. Suppose that the probability of worker error is Pr[Error] = e/10. Then for worker effort level e, expected (usable) output is now determined by the equation E[q] = (1-Pr[Error]) x e. However, the problem is that you cannot detect errors until after the product is shipped to customers, meaning you pay workers for output before you know whether it is usable or not, and you have to refund your customers for unusable output. Demonstrate why you should not pay your workers the same…A client (the principal) is trying to determine the best possible contract to enter into with her favoring the client is x and the probability of winning is 8. lawyer (the agent). The principal makes the following assumptions: the dollar amount of a judgment The lawyer has offered to () work for a fixed fee of F. (i) pay the client a fixed fee of F and keep the remainder of the judgment, and (ii) work for a contingent fee or a share of the contract with t lawyer's share being a If the principal is highly risk-averse and is interested in production efficiency she will choose option i option i option i
- 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?Seung’s utility function is given by U = ln(C), where C is consumption. She makes $30,000 per year and enjoy jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $15,000, and lose an additional $5,000 from missing work. (a) What is Seung’s expected utility without insurance? (b) Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is her expected utility if she buys it? (c) Suppose Seung can buy insurance that will cover her medical expenses and forgone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it?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).